TTfW m mm LtelEE H'A'A BmHS? mm ' wA Ih^H imm mm. WJUa'a^^U mmhmhfaw*?4MB Wm& Cfte Library of tfre «anftier0itp of J13ort& Carolina (Entiotoeu bp Uf)e ^Dialectic ant) philanthropic feortetfe* V78I.3 S857 P .vX* R«> ifffSH %%fc.,' /^ *-■: M K C IBS 3MH&&ttfi£2i3 w^ This book must not be taken from the Library building. mw mmm '1^/M^mmm ~\r\.<-*/?sm. CO: *,..'j%m mMm 4. :-.^wJ /&/+/*■/&/*>. ^^M4v?/ "n^wm> '/bSsK^M m$0- 4$00* NCIPLE 7T* T H /AND IT CAME TO PASS, WHEN THE EVIL SPIRIT FROM GOD WAS UPON SAVL, THAT DAVID TOOK A HARP, AND PLAYED WITH ■HIS HAND: SO SAVL WAS REFRESHED, AND WAS WELL,' AND THE EVIL SPIRIT DEPARTED FROM HIM. I. SAMVEL XVI, XXIII. CTW \ LONDON: PRINTED BY J. AND H. H U GH S : AND SOLD BY S. BAKER AND G. LEIGH, YORK-STREET; WHITE, FLEET-STREET; J. ROBSON, NEW BOND-STREET ; AND J. WALTER, CHARING-CROSS. MDCCLXX I. Digitized by the Internet Archive in 2013 http://archive.org/details/principlespoweroOOstil PREFACE. H E high opinion which I had long entertained of the mufic of Sig. Tartini, together with his great reputation over all Europe for many years, made me expect fomething extraordinary from a Treatife publiflied by him, intitled, Trattato di Mufica fecondo la vera Scienza deli' Armenia. I always imagined he had principles unknown to other Artifts in his way. A fupe- rior effect muft imply a fuperior caufe. In this .©pinion I was not difappointed. I found his treatife full of many new and well-founded doctrines, practical as well as fpe- dilative. To give fome idea of thefe, is the defign of the following fhort Piece. As there are many parts of the original very complicated, and difficult to comprehend, and as the language it is writ- ten in is not generally underftood, I thought it would not be unacceptable to fome lovers of Mufic, to fee his prin- ciples explained in a more eafy way : But my defign is not to render his treatife ufelefs to muficians by profefiian, which could not have been done without almoft an entire tranilation, and a great number of plates ; on the contrary I mean to excite fuch perfons to read and ftudy the origi- nal, as the beft means to make fome improvement in one *©f the moft delightful of all arts. A 2 I doubt n & 572340 m?p IV PREFACE. I doubt not but the greatefl part of my Readers will be offended with fome of Tartini's flricl notions, particularly thofe contained in the 5th chapter, as being fo very oppo- fite to every thing they have been taught to admire: but be- fore they condemn, Idefire they will calmly weigh and con- fider them — that they will reflect that fafhion is never the tell of truth, though they may fometimes happen to coin- cide — and that theie ftridt notions do not come from a dull plodding artifl, who for want of genius would willingly circumicribe the flights of thofe, who are blefled with fuperior talents, by the rules of a barren and narrow theo- ry y but from one who, I may almofl fay, led the way in the flowery regions of harmony, and of whom mod artifts axe but diftant followers. When an artifl fpeaks flighting- ]y of that in which he excels, one may fafely, I imagine., rely upon his opinion. But the Reader will perhaps be apt to think, that inflead of making an apology for Tartini, I ought rather to make one for myfelf, as having taken the liberty to diflfent fo fre- quently from him ; and that too without referve. But I hope it will be allowed that one may very fincerely admire an author, and yet freely cenfure him. Thofe who think otherwife, know very little of that mixed character, which is not uncommonly found in men of fuperior talents , When Huygens, Cofmo. lib. 2. p. 131. fays of Kepler. ' But he ' flood in need of thefe (fan tail ical) ideas, in order to con- 4 firm his cofmographical my fiery, &c.' And again, € All this my fiery, if well confidered, appears to have 1 been PREFACE. v 5 been a dream arifing out of the Pythagorean or Platonic *■ philofophy; nor do his proportions anfwer, &c.' When We read thefe paflages, can we fufpedt that Huygens had not a juft regard for the great and excellent Aftronomcr whom he fo freely cenfures ? The fame may be faid of Mr. Maclaurin, whom I have quoted in the following pages, and who, on the fame occafion, ufes the fame language as Huygens. It appears by many paflages in my author, that he alfo had ftrongly imbibed the notions of Pythagoras and" Plato; nor is it extraordinary that this fhould happen to a mufician, when we confider that their philofophy was founded on harmonic principles. This was the very cha- ra&eriftic of it; and fo truly great and fublime it is in ma- ny refpeds, that one would be apt to think it originally flowed from a higher fource than mere human notions ; and that it was the obfcure remains of the patriarchal reli- gion, which undoubtedly was very early eftabliihed in /Egypt, and from thence was brought into Greece by Py- thagoras, but delivered in a myftical and fymbclical me- thod as to particulars. This myftical method, I am apt to think, contributed greatly to miflead Tartini. Platonic numbers and figures had made a ftrong impreffion on. his mind, and ftt him upon the very laborious tafkof dedu- cing every thing in muiic from ab ft radt ideas ; but theie were accompanied with fuch important phyfical experi- ments, fo fine an ear, and fuch a thorough practical know- ledge of his art, that he feldom draws wrong confe- quences* Ktrufi vi P R E F A C E; I truft I mall not be thought to have mifpent my tunc in writing on this fine art, if I have, in any degree, con- tributed towards clearing up the principles of it. To take away all doubt in relation to this point, from thofe who are unacquainted with the hiftory of mufic, I will give a rift of ioinQ writers upon it. Democritus, Archytas, Plato, Antifthen.es, Ariftotle, Ariftoxenus, Theophraftus, Plu- tarch, Euclid, Ptolemy, Varro, St. Auftin, Boe-thius, Caffiodorus, • Albertus magnus, Pope John XXII. Guidon 'Merfennus, * Galileo, Defcartes, Huygens, Wallis, Lord Keeper North, Euler, Smith, all of them men of very con- fiderable character in their times. In fuch a lift of writers who would be a (Lamed to be enrolled, even though it were allowed, that on this occafion they defcended below their ufual dignity ? Ptolemy very juftly fays, ' That it is the bufinefs of ' contemplation and fcience to fhew that the works of na- * ture are conftituted according to fome proportion and * fettled order, and not at random, or as it were, by chance. 4 But particularly this ought to be done in relation to the 6 fineft of her works ; fuch as thefe fenfes that approach c the neareft to reafoh, viz. the fight and hearing/ Har- mon, p. 7. In this I have laboured and endeavoured to reduce to a greater degree of facility, an art which has hitherto been involved in calculations formidable enough to deter every common reader from attempting to underftand it, calculations that feem to me more ingenious than ufeful, and therefore more fitted to obftrucl" than to advance its im- provement. P R E F A C E. vit provenient, for want of that fimplicity which ought to ac- company every art, and every fcience. But fimplicity cannot be obtained without a juft and well- founded fyftem; and to form fuch a fyftem, is to create, ac- cording to the Platonic fenfe of that word. For it is to take the confufed elements of things, and bring them into order. Now to do this is to make them the objedts of knowledge. For knowledge, properly fpeaking, is feeing the properties, connections, and dependancy of one thing on another; it is feeing effefts in their caufes, and therefore it is forefeeing natural events, and confequently it is knowing the ufe of things, and in what manner they are to be applied, in or- der to anfwer our purpofes. It is with the utmoft humility, and a confcioufnefs of the great diftance between the great Galileo and myfelf, that I prefume to apply to the doctrines in this treatife, what one of the interlocutors in his dialogues is made to fay of fome of his difcoveries. ' This extreme eafinefs wherewith 6 you manifeft the moft abftrufe conclufions, will be * apt to leffen the value they had whilfl they lay hid ' under contrary appearances : Thus I dare fay it is with * the generality of mankind ; they have a much lefs efteem * for that knowledge that is fo very eafily acquired, than c they have for that, about which more tedious and puz- 4 zling debates are bandyed to and fro.' EX.PLI- EXPLICATION O F Some TERMS ufed in the following Piece. HExachord, in the following piece, fignifies the firfr. 6 notes arifi in the harmonic feries ; vide fig. I, example i. This word gene- rally means the firil 6 notes in the diatonic fcale; viz. C, D, E, F, G, A. First Rase fignifies the key-note, fuppofe C. —The Second Base fignifies the 3d of the key-note, or E. — The Third JBase fignifies the 5th of the key-note, or G. Tetrachord fignifies the interval of a 4th, as from C to F. Monochord fignifies a mufical firing that is flopped by prelnng on a moveable prop. String of Three Sounds fignifies a firing that is founded without flops, and which always gives the 12th and 17th (i.e. 5th and 3d when reduced to the fame ocfave) along w T ith the found of the whole. Trumpet Marine fignifies a firing founded by touching it gently with- out prefling on a prop. In this the Jongefl part of the firing is flruck, and the fnorteft part founds. The Twelfth, in mufic, means the 5th above the oclave, which is frequently called the 5th. The Seventeenth means the 3d above the oclave, and is frequently called the 3d. The Diatonic Scale, which is alfo called the fyftem of the 3d major, or fharp 3d, is that which has neither Flat nor Sharp belonging to it. as being the primary exemplar of the octave. The Chromatic Scale, which is alfo called the fyftem of the 3d minor, or flat 3d, is that which has Flats or Sharps, or both, be- longing to it, as being a deviation from the Diatonic, and therefore neceflanly fubject to Flats and Sharps, i. e. alterations as to gravity and acutenefs. N. B. Chromatic, in the vulgar fenfe of the word, means no fixed fcale at all, but a variable fucceflion of notes pafling from one key to another, as genius or fancy leads. When a feries of notes is marked by great btters, as G, B, D, the firfl .note is always fuppofed to be the lowefl, and fo to afcend regularly; but when fmall letters are mixed with the great ones, the (mail letters reprefentthe high notes, and the contrary j thus, fuppofe the following letters, c E g C 3 here you fall fropa c to E, then rife to £, and laflly fall 4o C, I NTR O- C * 3 N the account I propofe to give of Tartini's Treatife on Mu- I n t n o- fie, I fhall have very little to fay on his Introduction ; which duct ion. confifts of numerical proportions and calculations only •, though he fays it contains the foundation of all the refpeftive de- Numerical monftrations employed by him. But as I mail make ufe of other P ro P QrttoMU principles, in their nature I hope not lefs certain, and much ea- fier to be comprehended, I think it is not neceilary to enter into any detail on this fubje6t Says he, " I allow and confefs that " the method employed by me has fome novelty in it, and con- " fequently fome difficulty 5 but I alfo know that they are ne- " cefiary. 55 As to their novelty and difficulty, they muil indeed be both allowed by every one y as to their necefiity, that point mull be left to the decifion of proper judges, I am forry to be forced to own, that he fets out in a manner that will at firlt fight offend every mathematician, and hinder many from pay- ing that regard to his book, which it deferves. He wanted, on this occafion, a little of that fkill in writing, which he fliews in fo eminent a degree in compofing, I may fay in playing ; for fo it is reported of him 5 viz. the fkill of palling from note to note, and from tone to tone, almoft infenfibly. Infcead of this art, which was fo necefTary in writing to mathematicians •, for to them he muft write or nobody ^ he begins with a ftrong dif- cord, by thrufting into his proportions a geometrical mean, as he calls it, which he owns is no mean at all, as it really is not. B "Of [ 2 ] Intro- " Of this geometrical mean," fays he, " people have no idea, nor duct ion. « can have, as being contrary to the definition and common " meaning of that term." After this confeilion, and after hav- ing granted to mathematicians all they can wifh -, fays he, we m - what they ought to give up in their turn to mufi- cians. This idea is quite new ! mathematicians will be apt to re- ply, with indignation : Give up and compound for error ! why we retire into the regions of demonstration in order to avoid it ! But however harm Tartini's language may found to delicate eai*s, there is at the bottom no great harm in calling things by wrong names, provided notice is given ; and this is the cafe here. For the reft, Tartini ftiUft have employed great thought and la- bour throughout his whole treatife, in order to prefs fuch calcu- lations as he ufes into the fervice of mufic, for which they feem very ill fuited. This is all I have to fay on the Introduction ; as entering into a detail would be both tedious and ufelefs. Thofe who are curious in Mich matters may have recourie to the original, which will be necefiary to my readers on many occafions. I now pafs on to Tartini's firfc chapter, which contains an account of all the phenomena on which mufic is founded ; and amongft them one quite new and very important. Chap. I. Tartini begins his firfc chapter with giving an account of a *- — * -^ well-known phenomenon ; which is, that a mufical firing, which § 2. being flruck, one would imagine mould produce but one found, String of 3 yet in reality produces three ; viz. the found of the totality, and bcfides that its I2th and 17th, commonly called the 5th and 3d, which are in the harmonic proportion 1, f, f. The Trumpet Marine, the Common and French, or rather German Horn, F . have no notes but what are exprefled by 1, *-, f, -J-, &c. Vide . i»j .■ icw2. figs i. c::ample 1 or 2. T&fc Trumpet Marine is played upon, not C J 1 not by pre01ng down the firing on a finger board, as on the violin. Chap. £ violoncello, &tV. j but by touching it laterally and gently with the ^^v 8 *"*^ finger, which ferves as a reft or prop, in fuch a manner, that the vibrations of the pans of the firings when ilruck, may pals on freely to the part not touched, the found of which will be chiefly and almoft iblely heard. Now unlefs the part of the firing which is not [truck be an aliquot part of the whole, no diitinct found will be heard at all, but a jarring difagreeable noife. 1 call f, f, ;, Sec, aliquot parts of unity, beeaufe they are generally called fo, though Tartini rejeds the term ; however his way of exprefTion comes to the fame. For the better underftanding my meaning in relation to the § j, Trumpet Marine, fee plate fig. 2, where the line A B reprefents a Trumpet Ma* mufical firing 1 let A C be one half, A D one third ; A E ™*' Fig " a & I * further ex- one fourth, of the whole, &c. ; flop at C with the linger, plained. as direded above, and ftrike C B % and A C, which is not flruck, will found. Again, flop at D, and ftrike D B, and A D will found. Laftly, flop at E, and ftrike E B, and A E will found \ and fo in any other part, where the fliort part of the firing is an aliquot part of the whole, But if a part of the firing, as fuppofe A F, is not an aliquot part, no diftin6b found will be heard, as Tartini undertakes to prove, and is known to be facl. By an aliquot part of any quantity, as of a line, a iurface, &c. is meant fuch a part as will meafure the whole without a remainder. Thus an inch will meailire a foot, without a remainder, but not a foot and half an inch, I mail confder this fubjecl; more parti- cularly i rds. I have dwelt longer on this phenomenon than perhaps may be thought neceiiary, c ing it is fo well known % beeaufe 1 fhall make great ufe of it in the courfe of this piece ; and therefore defire fuch readers, to whom it is new, to attend particularly to it ; alluring them, that they will be able to underftand the principles of mufic by the help of this phsenome-- B 2 eon. [ 4 ] Chap. I. non, when a little farther explained ; and one or two -others, full L- *""" v ~— *■* as eafy. § 4« Tartini obferves, that the pipes of an organ that found, when Organ, the full harmony is ufed, are many and various in pitch, and yet but one found is heard, which is the lowed. Their difpofitions are different, according to the different flops, but all harmonic ; it being impoffible otherwife to produce this effect. The notes mud be C, C, G, C, E, G, or fome of them. I fhall have occa- fion to mention this, or a fimilar and very important phenome- non, in another place. § 5. Suppofe there is a number of fonorous firings of equal thicknefs, Ofcillation of and of lengths, as the fquares of the harmonic feries, 1, 4, .1, JL, firings. & Ct 1 e> as ^ x x ,j_ ? & c# an d that thofe firings be fufpended, and an equal weight faflened to each ; the founds produced by linking them will be C, C, G, &c. as mentioned in the lafl §, according to the number of firings. The ofcillations alfo of thefe firings will coincide, but with this condition, that while the firing 1 ofcillates once, the firing ~ will ofcillate twice, the firing f three times, the firing ~ T four times, &c. The very fame thing will happen, if we fuppofe a feries of firings equal in length and thicknefs, and a weight as 1 be fafiened to the firfl, a weight as 4 to the fecond, a weight as 9 to the third, a weight as 1 6 to the fourth. We fhall have the fame founds as before, and the fame Fig. 1. ex. 2. coincidences, example 1 or 2, fig. 1. § 6. " Thefe," fays Tartini, " are phenomena commonly known ; Harmonic " their indication and fignification are phyfically manifefl. The unity. 4t firing f the monochord, or of the harpfichord, although one in " itfelf, produces three founds of the harmonic feries. The Trum- tc pet Marine, the Common Trumpet, and the German Horn, nei- " ther have nor can have any founds but what arife from unity as " harmonic. [ 5 I « c harmonic. The pipes of the organ, though different in pitch, Chap. L " yet form but one found, when they are difpofed harmonically. u -"~"v~-' " Sonorous firings fufpended, when they are in harmonic pro- " grefnon in their founds, are reduced to unity in their ofcilla- " tions. Therefore the harmonic fyfeem reduces diverfity to " identity, multiplicity to unity 5 and fimple unity divides itfelf " harmonically, as appears by the three founds that are heard " upon ftrikihg a firing, fee § 2. Therefore unity, confidered " in any refpecl whatever, is infeparable from the harmonic " fyflem. The confequence is perfectly legitimate, becaufe it " arifes from nature, and therefore is abfolutely independent on " the human will." The lafc phenomenon which Tartini mentions is quite new, § 7. and proves, he fays, the foregoing doctrines wonderfully, axid'T&ird founds* goes flill farther. It is as follows : Two founds being given on any mufical inftrument, which will admit of their being held out for any time, and of being flrengthened at pleafure, as on the trumpet, the German horn, the violin, hautboy, &c. a third found will be heard. On the violin, let the notes C E, C n E, BE, B G, B^ G, be founded with a flrong bow, the third founds will be heard as in plate fig. 3. and are marked by clofedFig. 3, notes or crotchets. The fame thing will happen if the fame in- tervals be founded by two players on the violin, diflant from one another about 29 or 30 feet ; always ufing a flrong bow, and holding out the notes. The auditor will hear the third found much better, if placed in the middle between them, than if nearer to one than the other. Two hautboys will produce the fame ef- fect, placed at a much greater dtftance, and even when the hearer is not in the middle, and flill more if he is. From this pheno- menon he deduces all the third founds ariiing from fimple in- tervals, that together compleat the harmonic feries, as far as it is t 6 3 ftice. The 5th gives the third found 1 nifon r ■ the So ^ -: 4th gives the 5r.I1 belor note, £ but I {ball not enumerate all the third founds, though the detail is extremely curious and inftruclive, becaufe they would be ill comprehended without plates, and many plates do not come wit my defign ; I mud therefore refer the mufician to the original, which, if he has any genius, will be of great ufe to him h refpeels befides this. I will juft obferve, that -'ing any in- terval in any key is founded, if a 4111 or a 6th of the fundamental note conies into the chord, we have always the 4th of the funda- mental for third found ; in all other cafes we have either the fun- imental note itfelf, or the 3d of it. I will likewife obf that the fmaller the interval, the farther diftant is the third found 1 infomuch that the third found to the interval of the fernk minor G*, is the 26th below the lowed note. Ought not this to regulate the bafs in common practice ? N. B. There is one exception to the progreffion above-mentioned, which is wlien the chord of the 3d major is reverfed. §, 8. He then gives a fhort fketch of rnufic along with the third Mufualjketch founds for a bafe, in which he lias introduced a new interval into TnJ' lTA1 ^ c > new * n rc ^ tv 5 though not fo in appearance ;, of this an account will be given in the proper place. In his obfervations on that fketch there is a paifage which puzzled me for fome time, and may porTibly puzzle others •, for which reafon I will explain it. Ke reckons, page 17, D°, G*, amongft the di- minished 3ds, which, fays he, will appear to be fuch, by put- ting G* above. He means to fay, that putting G } * in its place, in dead of putting it above, the dirninimed ^d^ will ap- pear •, and fo it will if you place every note in its natural order •, for then they will fland thus, E, G*, B, D^ ; where the two lad notes form the 3d above fpe iiied. He obferVes on thefe third [ 7 J third founds, that if any adjoining two fiinple intervals in the Chap. I. harmonic feries i, 4? 4> i-> & c - ^ e founded, the third found '*—'*~x~ will always be that of half the firing ; from whence he draws foine confequences which I will pafs over at prefent, and per- haps entirely. We have now" gone through the firft chapter, which contains § 9. the moil curious and important discoveries ever made in mufic ; Accounts of difcoveries fully fufficient to account for every thing praclifed, d J^ rtes m or practicable, in that art. Some of my readers may perhaps delire to know fomething about the hiilory of tliefe difcoveries \ which defire I will endeavour to gratify as well as I am able. My account, I forefee, will be very imperfect ; for want of books and previous inquiries ; but even an imperfect one may perhaps be better than none,' efpecially as I believe that it is not to be found in any one book. Unlefs the proportions of intervals in mufic are afcertained, no § 10. mufic can be noted ; unlefs it is noted, none regular can be had. Nning cfmu* Noting in mufic is as important, as an alphabet, or fomething-^* analogous, in the other arts and fciences. But how this afcer- taining and noting were to be brought about was the difficulty. That the Greeks looked upon the firft as a difficulty, and a great one, appears by their attributing its difcovery to mere chance \ and that the fecond, viz. noting, was not more ancient, in their opinion, appears by their attributing 'it likewiie to Pythagoras. Vide Meiborn. in Aiiftbx. p. 105. The Bfft difccvery then, in order of time as well as importance, § 1 j tt was that mentioned § g % z'z. that if there be a fenes of firings, Difcovery of equal in length arid micknefs, &c. and a weight as 1 be M- wtercvals ^ tened to the firft - 9 a weight as 4 to the fecond -, a weight as 9 to 2 the [ 8 J I. the third, &c, we fhall have the fame founds produced, uvm linking them, as arife upon the monochord when the whole is founded, or the parts at the points -J, i-, ~, &c. refpectively. This difcovery, or what is fimilar, is by the Greeks attributed to Pythagoras, and many circumftances ' attending it are related. The ftory is io well known, that I mould not trouble the reader with it, if I had not particular reafons for fo doing. The (lory then is as follows : § 12. Pythagoras one day meditating on the want of fome rule to Hammers of guide the ear, analogous to what had been invented to help the Pythagoras, Ql ^ tv fe n fe^ chanced to pafs by a blackfmith's fhop, and ob- forving that the hammers, which were four in number, founded very harmonioufly, he had them weighed, and found them to be in the proportion of 6, 8, 9, 12. Upon this he fufpended four firings of equal length and thicknefs, &c. and fattened weights in the above-mentioned proportion, to each of them refpeclively •, and found that they gave the fame founds as the hammers had done - 5 viz. the 4th, 5th, and octave to the gravett tone -, which laft interval did not make part of the mufical fyftem before j for the Greeks had gone no farther than the heptachord, or {even firings, till that time. This is the abridged fubftance of the account given by Nicomachu:, in Harmon. Manual, p. 10^ Gaudentius, in Harm. Introd. p. 13; Iamblichus, de Vit. Pythag. p. 97 ; Macrobius, in Somn, Scip. lib. 2. c. 1. § 13. Some difficulties occur to me in this ftory : ift, If the weights Qbjeaiom, were what all thefe writers mention, the founds produced would not have been what they tell us. It is well known, that the weights mutt have been as the fquares of thofe numbers. Yet all thofe who give this account agree as to the numbers ; which error fhews on what a precarious tradition this ftory was originally founded. [ 9 ] founded. 2dly, It feems very wonderful, and indeed incredible, Chap. I. that four hammers mould be in the proportion requifite, by mere ac- *— ■**V— »* cident. 3. This ilory is not told by fome of the beft Greek writers, though they fo frequently mention thefe celebrated numbers, and fo frequently quote his doctrines in relation to mufic. 4thly, Thefe very numbers were known to the Chaldaeans, who, as Plutarch fays, Vol. II. p. 1028, divided the feafons of the year by the fourth, fifth, and octave -, making fpring as 6 ; autumn as 8 ^ winter as 9 •, and fummer as 12. 5thly, But farther, Py- thagoras could not find the numbers 6, 8, 9, 12, by the method above mentioned, without the help of a fingle firing, which would have fuificed, without any weight at all : For though it is poffible that he might obierve that the numbers 36, 64, 81, 144, repre- fenting the weights neceffary to produce the mufical intervals, 4th, 5th, and 8th, fuppofed to be heard at the blackfmith's fhop, were the fquares of 6, 8, 9, 12 - 9 yet he certainly could not from thence conclude, that a fingle firing, fhortened in thefe proportions re- fpectively, would give the fame founds ; and therefore he muft proceed thus. Having prepared a firing A B, fixed upon reds at each end, § 14. with a moveable bridge •, fuch an one as Ptolemy ufed, and called Difcovery of a monochord ; and having fufpended weights, in the proportion inte,cvaiu of 36, 64, 8 1, 144, to four firings, he raifes or lowers the tone Fig. 2. of the firing A B, till he finds it unifon with firing 36 ; next he flops fomewhere in the firing A B, till he finds an unifon to the firing 64 -, we will fuppofe the point found is E -, he meafures EB, and finds it to be -J. of the whole firing. Afterwards he flops fomewhere in the firing A B, till he finds an unifon to firing 8 1 ; we will fuppofe the point found is D ; he meafures D B, and finds it to be 4. of the whole firing. Laftly, he does the fame in regard to firing 144, and finds the point C 4 of the whole firing. Now call- C ing [ io ] Chap. I. tog A B 12, 1 of 12 is 9, 4. of A B is 8, and 4. ABis 6. Here then v^^i-yo^J we naye tne numbers that give the 4th, 5th, and 8th; but the fame might have been done without the weights -, for had he tuned feveral firings by the means of pegs ; as is ufed on many inftruments ; or by the means of weights which he didnot know adjuiled, till the intervals became agreeable to the ear, he might, by making unifons with the feveral firings at feveral points on the fingle firing, have found the proportions above-mentioned. If we fuppofe therefore the very reverfe of this flrange tale to have been the cafe, every thing will be natural : For it is highly probable, that fo curious a man as Pythagoras might try what weights would produce the 4th, 5th, and octave ; and he perhaps might be the firft who ever made fuch an experiment. This was a fufTicient ground for his ignorant admirers to build the whole flory upon, without know- ing the true numbers, or the impoffibility of making out the in- tervals, without certain circumflances which they take no notice of. That Pythagoras did actually ufe this method, is probable., becaufe he is faid to have recommended the monochord to his difciples, Vide Arirtid. p. 116. § 15. The next confiderable improvement made in. mufic was filling Ptolemy. up the octave, by Ptolemy the aflronomer, in a way perfectly conformable to nature. He could not, I believe, prove it to be fo ; that tafk was left for Tartini, which he has done to a demon- flration. Before the time of Ptolemy, there was no fixed rule for filling up the tetrachords : Some pretended to ufe two tones and a femitone, which intervals were fettled by the ear only -, for there is no fuch thing as a half tone, nor can be, in mufic : Others, as Pythagoras, and thofe who followed his doctrines, made ufe of two tones major, and a limma or remainder, reprefented by the proportion 243 : 256. This limma was arbitrary, as well as the two tones major, there being no two equal intervals following one t ii 3 orie another immediately in natural mufic. However the tone Chap. 1* major, confidered feparately, was perfectly right ; for it v/as found ***"****** by Pythagoras, upon meafuring the interval between the 4th and 5th. This gave him an advantage over the oppofite party, who neverthelefs continued to conteft the point, till Ptolemy's fyftem was known. From that time this fyftem was generally followed, till the temperament took place -, and is ftill practifed by all fine players on the violin, violoncello, and fuch inftruments. From Ptolemy we mud make a great ftride, before we meet § i6# with any new difcovery ; for the next was made by that excellent Galileo* philofopher Galileo •, who firft made ufe of the doctrine of pen- dulums to explain the principles of mufic, and, I believe, firft afcertained the law of the vibrations of pendulums in general. Vid. Difcorfi e Demonftrat. Matemat. p. 95, &c. He feems to have been extremely fond of mufic, and very defirous to account for the form of mufical ratios. He fays he had never met with any thing fatisfaclory upon that fubjecl ; and indeed nothing had appeared, as far as I know, that gave a phyfical folution of the pleafure we receive from mufic. Abftracl numbers and propor- tions we meet with in abundance in every writer, both ancient and modern, upon this fubjedt ; but abftract numbers and pro- portions are not phyfical caufes. Galileo was of this opinion, and therefore fought for fomething further -, and having ob- ferved that the times of the vibrations of pendulums are in the fubduplicate ratio of their lengths -, fo that if you would have the time of the vibration of one pendulum to be double the time of the vibration of another pendulum, the length of the firft muft be four times the length of the laft ; and alio having obferved, that all the vibrations of the fame pendulum are performed in the fame time ; he undertook from hence, and fome other pheno- mena, to deduce fuch principles of harmony, as, he fays, in part Q % fatisried [ » 1 G h a p. I. fatisfied him. It is well known that he was miftaken, when he u - - "*v-*- J thought that all vibrations of the fame pendulum are performed in the fame time ; but this error does not in the lead affect his doctrine ; becaufe the vibrations of a pendulum in fmall arcs, and fmall vibrations in a mufical firing, are refpectively ifochro- rious. He then obferves, that, if you flrike a firing on a harp- flchord, it will put into motion, and caufe to found, not only another ftring, which is unifon to it, but even the 8th and 5th ; for the firing that is flruck begins and continues to vibrate all the time that its' refonance is heard. Thefe vibrations caufe the air near the ftring to vibrate, and, gradually extending farther and farther, affect not only all the firings of the fame inilruments,, but alfo of other inflruments that are near. The unifon firings being difpofed to make its vibrations in the fame time as the firing flruck, begins on the firfl impulfe to move a little ; and a 2d, 3d, 20th, Sec. impulfe fucceeding, and all in periodical times, it receives at latl the fame tremor as the firing flruck ; jufl as a pendulum, by repeatedly blowing upon it in a proper manner* may be put in motion. § 17. That fuch vibrations are produced in the air, appears highly Phenomenon probable, from the regular undulations which he obferved in wa- §n a glafs. ter contained in a glafs, upon rubbing it on the edge and making it found. This is a phenomenon at prefent commonly known j but what he adds, I do not remember ever to have feen ; viz. that if the tone happens to rife to an octave, every undulation will be divided into half ; an accident, fays he, that clearly proves the form of the octave to be 1 : 2. § 18. He obferves farther, that thefe undulations in the air, produced :.''. 1 xomenon by the firing, caufe not only the unifon firing to vibrate, but lib any other body difpofed to tremble \ fo that if you fix on the en a harpji- chord, [ '3 3 the Me of the inftrument different bits of hair, or other flexible Ck a p. h matter, you will fee, upon founding the firings of a harpfichord, K ^'^ r ' i fometimes one of thefe pieces, fometimes another, tremble, ac- cording as the firing flruck' performs its vibrations in the fame time ; whereas the other pieces will not move at the found of this firing, nor will that piece give any found on finking another firing. He mentions another curious phenomenon produced upon § 19. fcraping copper, which tends to confirm his doctrine ; but I fnall Phenomenon pafs it over at prefent, and proceed to the conclufion he draws !* ^' r from the phenomena above-mentioned \ which is, that the im-* mediate and proximate caufe of the form of mufical intervals is not the length of firings, nor the tenfion, nor the thicknefs ; but the proportion of the numbers of vibrations and undulations of the air, which ftrikes upon the drum of the ear, and caufes it to tremble in the fame time. From hence he accounts for the effect of confonances and difTonances, in an eafy and natural way \ but, to avoid prolixity, I fliall not mention it ; and mail finifh all I have to fay, about the mufical fyflem of this excellent and inventive philofopher, with obferving > that Dr. Smith does not exprefs himfelf accurately, in faying that he (Galileo) called in queflion the truth of mufical ratios - 5 for he only fays, that no phyfical explication had been given of them, which is a very dif- ferent affair ; nor has his difficulty any thing in common with that of Huygens, as is there fuppofed. Smith's Harmonic, p. 247. I come now to one of the moft important difcoveries ever § 20* made in mufic ; for which we are indebted partly to Dr. Wallis, Dr. Wallis* and partly to two other Gentlemen of Oxford. I fliall give an account of it in the very words cf Dr. "Wallis, taken out of the Philofophical [ H 1 Chap. I. Philofophical Transactions, abridged by Lowthorp, Vol. L ^-— "v— — ' p. 6c6. § 21. u It hath been long fince obf rved, that if a viol -firing Points ofreji. « or lute-firing be touched with the bow or hand, another firing, " on the fame or another inflrument, not Far from it, if an uni- " fon, or an octave, or the like, will at the fame time tremble of " its own accord. But I can now add, that not the whole of that " other firing doth thus tremble, but the feveral parts feverally, " according as they are unifons to the whole or the parts of that Fig. 4. " firing fo ftrack. For inftance, fuppofing A B to be an upper " eclave to a r, and therefore an unifon to each half of it flop- " ped at b ; if, while a c is open, A B be flruck, the two halves " of this other, i. e. a b and b c will both tremble, but not the " middle point, at b ♦, which will eafily be obferved, if a little " bit of paper be lightly wrapt about the firing a c, and re- " moved fucccfiively from one end of the firing to the other. § 22. " In like manner, if A B be an upper 12th to a d, and confe- Tbe fame. " quently an unifon to its three parts equally divided in b, c, if, "ad, being open, A B be flruck, its three parts, a b, be, c d, " v/ill fevefally tremble, but not the points b, c. In like man- " ner, if A B be a double oflave to a e, the four quarters of " this will tremble when that is ftruck, but not the points b, r, d< " So if C D be a 5th to a d, and confequently each half of that " flopped in E an unifon of this flopped in b e, while that is " flruck, each part of this will tremble feverally, but not the " points b c \ and while this is flruck, each of that will tremble, * c but not the point E. The like will hold in leffer concords * " but the lefs remarkably as the number of divifions increafes. § 2 3' " This was firfb of all (as I know of) difcovered-by Mr. Wil- The fame. 2 " liam C M ] 4 * Ham Noble, M. A. of Merton college ; and by him mewed to C h a p. " fome of our muficians about three years fmce ; and after him, v -*-'V" " by Mr. Thomas Pigot, A. B. of Wadham college, without " knowing that Mr. Noble had difcovered it before. I add this " further, which I took notice of upon occafion of making trial " of the other, that the fame firing as a c, being {truck in the " midft of (at) £, each part being unifon to the other, will give no " clear found at all, but very confufed -, and not only fo, which " others have obferved, that a firing does not found clear if {truck " in the midft, but alfo, if a d be ftruck at b or c, where one part " is an octave to the other - 9 and in like manner if a e be {truck at " b or d\ the one part being a double octave to the other y and (o " if af be ftruck 111 c or d -, the one part being a 5th to the other ; " and fo in other like cenfonant divifions \ but the lefs remarkable^ " as the number of divifions increafeth. This and the former I " judge to depend upon one and the fame caufe \ viz. the con- " temporary vibrations of the feveral unifon parts, which make " one part tremble at the motion of the other ; but when {truck C4 at the refpeclive points of divifions, the found is incongruous, " by reafon the point is difturbed, which mould be at reft." Philofophical Tranfactions, abridged by Lowthorp, Vol. I. p. 607. In order of time, the difcovery of the three founds heard in § 24. every mufical firing, when {truck, which Monf. Rameau attri- Rameaiu butes to Merfennus, mould have been mentioned before -„ but I referved it for this place ; where I am to obferve, that the above- mentioned fkilful mufician firft applied this important difcovery to the purpofe of practical mufic, and was thereby enabled to reduce its rules into a clearer and (hotter meihod, than had ever been done before. But he fell into errors, a fcw r of which I may perhaps take notice of as I go along, for want of knowing fome thing farther, which Tartini has fupplied. It t >6 ] Chap. T. It may perhaps feem extraordinary, that I have faid nothing *-*~/~~"«~> a ll this while about the difcovery of die lingular properties of the § 25. Trumpet Marine, though I took notice of its importance § 3. My Trumpet Ma- reafon for this omiflion was, that I am totally ignorant when, or by whom, this inftrument was invented. I fliculd imagine, that it was not known to the ancient muficians, as there is not the leafl notice taken of it amongft them, as far as I can find; and it does not feem probable that they fhould pafs over in filence a phenomenon fo very lingular, if they were acquainted with it. On the other hand, the Greeks were certainly acquainted with the Common Trumpet, as early as the time of Homer ; yet they never mention the defect of certain notes on that inftrument, which are juft the fame as are wanting on the Trumpet Marine. But whether it was or was not known to the ancients is not a matter of any importance ; that it mould be known is of the greater!:, as v/ill appear before we proceed much farther. But to return to Tartini. Chap. II. I fuppofe there never was an artifc of real genius, who was not w- "~ v """' fohcitous to clifcover the principles upon which his art was founded. § 26. Tartini is a linking proof of this aflertion, throughout his whole Of the circle treatife, and particularly in this 2d chapter, of which I am now 'J1 ua t0 gj ve a ver y {hort account, and to me an unpleafing one. One cannot, without fome impreffions of companion, fee him wander- ing in the perplexing labyrinths of abftract ideas, almoft without a guide, or at bsfl with one which it is molt likely would miflead him. He muft have taken infinite pains to purfue nature in a wrong path, and trace her footfteps where flie feems to have come by chance. He had fancied that harmony was to be found only in the circle, in conjunction with the fquare, which he looked upon as infeparable companion-, and enentklly united. They really proved in his tends, what they have been often called, magical j [ i7 1 magical ; for I can think it little lefs than magic, that he found Chap* IT the miftrefs he was in purfuit of there, but with fo few tokens of i~»"**v— D - i * legitimacy about her, that a man muft be little lefs than an en- thufiaft, or he would have fufpecled fome deceit, had fhe not furnifhed proofs in her favour, of a nature totally foreign to what are required in fuch a cafe, and thofe confirmed him in his error. Ptolemy was deceived in the fame manner exaftly i He alfo §27. firmly believed, as did all the antients, that no other figure butptolemyV the circle was worthy of the heavenly bodies to move in : and ar " eu though it is certain, that the heavenly bodies do not move in cir- cles, yet by the help of geometry, and an ingenious fyftem, he was able to folve the phenomena of the univerfe almoft in every cafe. But, in fome particulars, Kepler affords an example more Kepier* refembling Tartini. He was, according to Maclaurin's account, all his life in purfuit of fancied analogies ; in which Tartini alfo abounds * and we may apply to the latter, what he (Maclaurin) fays of the former ; that to this difpofition we owe fuch difco- veries as are more than fuffi cient to excufe his conceits. Account of Sir Ifaac Newton, &c» p. 49. What I have already faid, will be a fufficient excufe for my §28* not entering into a detail on this long chapter ; as fuch a detail Tartini'^ would be extremely tedious to fome, unintelligible to others* €rroru and would appear firange to the only men, who are qualified to form any judgment on this matter, I mean the mathematicians. However, in order to vindicate the harmnefs of this cenfure, I will juft mention one or two inftances of his errors, ift, he fays, '" that it is demonflrable by algebra, that unity, and an indeter- " minate quantity x being given, no other harmonic mean can be " found between them but the number 2 -" whereas it is de- D monflrable, £ is 3 C h A ?. II. monftrable, both by algebra and the nature of the hyperbola, that 2 cannot be an harmonic mean between unity and any other num- ber lefs than infinite. This would not fuit his purpofe. 2dly, He fays upon tins occafion, and others, that though there may be demonftration againfi him, yet his demonflration may be true, hecaufe he means quite another thing by his y, which he calls in- definite, than what mathematicians mean by their x, which they fuppofe infinite ; and adds, that it is known amongft mathema- ticians, that this is not the only cafe, where two oppofite propo- rtions may be demonftratively proved. § 29. His other errors are quite of another kind, and, befides being Errors of ano- curious as mere matters of fpeculation, have the merit of leading him right. I call them errors, becaufe they are, as I obferved before, arbitrarily preffed into the fervice of mufic y and not be- caufe the propofitions themfelves are falfe. I lhall therefore lay Fig. 4. them before the reader. In the circle ABM, fig. 4. let the diameter A M. be divided according to the harmonic feries, 4- 5 t> i* & c * '•> dr-aw the chords A B, A C, A D, &c. and the ordinates 4 B, 4- C, £ D, &c. and the complements to the chords M B, M C, M D 5 &c. ; fquare the chords, and they will be 4> t> i? & c - *• e * t ^ e > 7 will reprefent the harmonic notes in fig. 4, example 1 and 2. Square the chords fupplement, and they will give i, -J, |, &c. viz. the notes in example N° 3, which arife from the arithmetical divifion of a firing, feme of the very notes wanting to fill up the octave in common ufe. Lafrly, fquare the ordinates ~ B, i- C, ~ D, &c. and they will be ~, Jj, T V, &c. i. e. they will repre- fent the notes in N° 4. example, which he calls difcords -, two of which certainly do not belong to the diatonic fcale - 9 the other three ; viz. C, D, F, certainly do ; and therefore cannot be called difcords, according to his own principles. 'It [ 19 J It muft appear a very Angular thing, that moft of all the Chap, ft notes commonly praclifed fhould arife in a regular way from u **" v ~-* l ~ f a figure which feems to have nothing in common with harmony, § 3 a and thofe too in their exact proportions, Y/ho would not be^ad to truth* ftruck with fueh a coincidence ? but who would think of looking for mufical notes in fach a place ? Yet why not ? the circle has bey/itched many a fober man, Its. great fimplicity and beauty, joined to the facility of drawing it, naturally tempts every one to deduce from its properties whatever can be deduced, rather than from the properties of any figure j infomuch that this is a ftanding rule amongft mathematicians. I have no doubt but if Tartini had been as well acquainted with the hyperbola as with the circle, and had the hyperbola been as eafy to draw, he would have fought for his fyfrem rather there > 9 becaufe it is actually in its own nature harmonic*! - y and 1 verily believe, that, with his fagacky and unwearied diligence, he would have found the fame fyftem in that figure. But I muft obferve, that coincidences are often merely accidental - r and therefore are no proof that we have found the true explication of any thing, becaufe we, in our re« fearches meet with them : I gave an inftance of the contrary already, in Ptolemy's aftronomy. But, after all, how this co- incidence mould happen will eafily appear $ for fig, 4, -J x -J equals A M or the diameter % i e, as 4 gives the harmonic note, 4 or *n e fupplement will give the correfpondent arith- metic note, But, by the known property of the circle, AC* x G M * = A M : 1 i, e, the fquare of the chords added to the fquare of the fupplement, equals the fquare of the diameter % therefore, if the fquare of the chord reprefents an harmonic, the fquare of the fupplement reprefents its- correfpondent arithmetical note \ for the whole fquare reprefents the fundamental note : fa D % tfeti€ [ 20 ] Chap. II. that Tartini has only fubftituted furfaces in die room of lines. %-> & c - 1. e. harmonically, before he could apply the feveral parts, in order to find the chords. But the diameter is a right line, that might as well be the diameter of any other figure, as well as of the circle •, and he wanted to deduce all from the circle. It may be natural therefore for fome people to afk this queftion ; but not for any man who ever felt the fpirit of fyftem working in him. Muft fome of Tartini's notes be deduced from the circle, and others from a right line ? as well give up the whole, or better j for then all confiflency, the chief merit, is gone. For this reafon, he fet out with endeavouring to prove the infeparability of the circle and fquare. Had- he not done this, the inconfiflency I juft mentioned would, he forefaw, be objected to him, § 32. I do not know whether it be worth while to obferve, that the Vfe of Tar- firft feries, deduced in the manner Tartini has done, furnifhes X ^er S Jbcut"th a met h°d °f making a fquare or circle any aliquot part of another circle. fquare or circle, where the numerator is unity. For let A M, fig. 4, ri £- 4- be the fide of the given fquare, or ABM the circle ; and let it be required to find another fquare or circle, which fhall be to the given fquare as 1 : 3 -, draw the chord. A C, and the fquare of it will be the fide of a fquare equal to 4- of the given fquare. The fame may be done, if a fquare 4, |, &c. of a given fquare is required. But if a fquare, which fhall be 4, 4, &c. of another, is required, then draw M C, M D, &c. and do the fame as be- fore, i. e. take M C, M D, for the fide of the fquare required. The [ 21 ] The method of making a fquare, double, triple, &c. of a given Chap. II, fquare, is well known ; but this problem, as far as I know, is *-^-v— -> quite new. I have hitherto omitted to give an account of another phasno- §33. menon, mentioned by Tartini in this fecond chapter; it is curious, Brum. but whether new, I know not : " Let there be," fays he, " a fo- " norous cylinder \ for example, a drum ; let it be beat -, and " if the two fkins be unifon, you will hear two founds ; one na- ' " tural to the inftrument, call it C 5 the other of confent, and " will be G below, i. e. lower 4th to the natural found. Sepa- " rate from the drum the upper or lower fkin, leaving the little " circle on, which fattened it down, and kept it tight. "When " you beat now, you will hear two founds, as before ; one will " be the fame C, which is the natural found; but the other, " which is the found of confent, will not any longer be G below, " but G above, v/hich is a 5th to the other found. The expe- " riments muft be made with great exactnefs ; the two fkins " of the drum muft be unifon, equal, and as fmooth as poffible, « that the effect may be evident." He draws confequences from this phenomenon, in favour of his fyflem ; but fuch as, I be- lieve, will, hardly be admitted by mathematicians. For this rea- fon, I fhall pafs on. I. obferved above,. § 28, that Tartini's deductions from the § »^ circle and fquare give the true fyftem of mufic j it may therefore Tartini 5 / de- be reafonable to afk me, how I can know this, when I look on d * aion > ^h- right* his theory as imaginary, and all others as imperfect ? To which I anfwer, that I know his deductions to be true by, another theory, not liable, I believe, to any objection. This theory it fhall be my bufinefs to explain, in a fliort compafs, and in a way level to the capacity of almoft every reader. I chufe to explain it in this place 3 1 22 ) C h a p. II. place, and before I enter upon giving an account cf the 3d chap* *— -^r**— ' ter . becaufe there will begin matter of another fort, and which fuppofes, in general, a knowledge of the principles of mufic, § 25* Inftead of referring to § 2 for an account of the phenomena Trumpet Ma- of the monochord, I fhall. for the eafe of the reader, and alfo be- caufe I have fome necefiury obfervations to make upon them, re~ &Z- 5« peat the whole again in this place. Let the line K L, fig. 5, reprefent a mufical firing, firmly fixed at each end, and ftretched properly. This firing, when founded in the way I fhall defcribe, is called the Trumpet Marine : K C is 4- of K L, K G -J- of K L, Kr^ofKL, K E i- of K L, K^^of KL, Prefs the ftring gently and laterally at any of the points 4, -^ t> & c - w * tn y our finger, and ftrike the longer part of K L with a bow, and you will hear a mufical found, which found arifes from K G, K f, K E, &c. and not from G L, c L, EL, &c. the longer part. I have placed under every divifion the name by which every note is called by muficians. § 36. I fhall now make an obfervation or two on the notes of this Trumpet Ma- Trumpet Marine, ifl then, the firfl note that arifes after the octave 4, is G f, or the octave and 5th above it, i. e. the 12th above the found of the whole firing. The fecond note, c % is 2 octaves above the whole firing \ and fo of the reft. This pro- grefllon of founds is reprefented in fig. 1, examples 1 and 2. 2dly, No 4th or 6th can ever arife in this way ; fo that it feems irnpodible to fill up the octave in common ufe, without finding out fome other method s for we are not to take it for granted, that, becaufe mathematicians have contrived numbers for inter- vals, that therefore they ought to be adopted as a part of mufic intended by nature ; if fo, many inconfiflencies and abfurdities would follow, in this and other arts, gdliy, I defire the reader 2 to f 23 I 10 recollect what I mentioned towards the beginning of this trea-CnAP. II. tife, that no diftinct found v/ill be heard, upon fir iking the mo- w-~v**~^ nochord, unlefs the upper part be an aliquot part of the whole, i. e. unlefs it meafures the whole without a remainder. Now this can never happen, unlefs the fraction that expreiTes the part has unity for its denominator. Tliefe things being premifed, let us proceed. Suppofe now § 37. this Trumpet Marine to be changed into a monochord, and to Trumpet Ma- ke flopped en a fingerboard, or bridge, at the fame point of r ^^^l" division, 4, t? i? & c - an ^ ^ et us ^ ee what will be the conte- fared*- quence. In this cafe, if the longer part of the firing is flruck with a bow, that part will found. Thus, if the firing is flop- ped at -5-, then L 4- will found ^ and fince K ~ is 4- of the whole,. KL, L | 5 will be \ ; but ^ reprefents a 5th above K L : There- fore the note is the very fame that we found when the upper part K i- gave the found. Let the firing now be flopped at i. ; then £ L will found ; and fince K -i is ^ of the whole firing, i- L will be 4 of the whole firing ; but A reprefents a fourth. Therefore we have here a new note called F. Next, Let the firing be Hopped at f , then f L will found - 3 and fince K f is f of the whole firing, Y E will be 4- of it •, but 4 reprefents a 3d major ; therefore the note is the fame that was found when K f gave the found. Laflly, Let the firing be flopped at ~, and then f L will give the found -, and iince K f is $ of the whole, f L will be 4 of it y but 4 reprefents a 3d minor, which is another new note. When I fay that L f , and f L, give the fame note as K G and K E, I mean as to denomination -, for octaves make no difference. Upon thefe phenomenal mail make fome obfervations. id § %%'*- then, Thefe notes, contrary to the progreffion of the harmonic Monochord notes, defcend, as may be feen fig. 3, examples 2 and 3 -, &ora^ '^ ( whence [ 2 4 ] Chap. II. 'whence this confequence maybe drawn, that the rule amongfl *°~*~~v~-~*J muficians, that parts in concert fhould move contrary ways, Is founded on nature. That th y do defcend, is evident at firft fight ; for juft in proportion as that part of the ftring is fhorten- ed which produces the harmonic notes, it is lengthened in that part which produces the correfpondent notes in the common fcale, 2dly, This fcale is called the arithmetical -, becaufe the new note F divides the octave arithmetically : For fuppofing C to be added below, it will be expreffed by the number 60, fig, 1, example 3. Now c 30 falls as much fhort of F 45, as F 45 does of 60. On the other hand, G 45, the other mean, divides the fame octave harmonically ; for 30 is to 60 as the difference be- tween 30 and 40 is to the difference between 40 and 60. So again, E ^ 50 divides the 5th, G 40, c 60, arithmetically 1 whereas E 48 divides it harmonically, as will appear upon trial The ufe of this laft obfervation will appear afterwards, § 39. My next ftep will be to mew, that the notes in example 3. are Mcnocbcrd naturally connected with the notes that ftand over them -, and that and String ^ found of the whole firing is the univerfai and fundamental Trumpet, g ° bafe of them all, both in examples 2 and 3, fig. 1. In order to prove this, I muft refer to § 3, where it was afferted as a known fact, that when a firing founds in the fhort part, it founds becaufe it is an aliquot part of the long part, as well as of the whole ; Fig. 2. therefore, when A -*-., (fig. 2.) founds, the whole ftring, as well as the longer part ^ B, is divided into aliquot parts ; i. e. this laft is divided into 3, viz. from ~ to f , from £ to F, and from F to B, each of which is equal to A -J, and vibrates, and confequently founds, however obfcurely, as well as the longer part, and the whole firing. Nov/ the longer part ~ B is a 4th to the whole firing, and is the very note found upon flopping clofe at that point of divifion. I chofe this inflance to prove my affertion, for an t 25 ] an obvious reafon -, but any other inftance would have ferved as Chap. IL well. Here then we have all the fundamental notes in nuific, viz. t-«*-" a v~" , "* J C, F^ G, intimately and effentially connected together, and arifing necefTarily with the harmonic divifion. They are the fame which Tartini deduces, v/ith a moft complicated apparatus, from va- rious proportions, and groundlefs notions about the circle, and had they not been confirmed by the phenomenon of the 3d founds, they mult have remained of doubtful authority. In order to give the reader a clear conception how all thefe notes arife on the trumpet marine, I have exhibited them in fig. 6. N° 1 and 2. Fig. 6. They both reprefent the fame firing. N° 1 has the notes arifing from the fhorter part of the trumpet marine ; N° 2, thoie arifing from the longer -, and the curves reprefent the vibrations of the part : Thus, while K ~ vibrates in N° 1, 4 L vibrates in N° 2, &c. It will be faid, perhaps, that, according to the foregoing doc- § 40. trine, it is not enough that each note mould make an aliquot Objection; part of the whole, 'but that each interval mould be an aliquot part or parts of every other interval ; or, what comes to the fame, that the intermediate, fpaces between the notes mould be .an ali- quot part or parts of every interval, v, g. the fpaces .fig. 6. N° 1. between f and f, f and ^, &c. Let us then examine how this is in fact : If f be deducted from f, there remains %V.of the whole firing -, if f be deducted from ~, there remains T \, or —> or -3V ; if 4. be deducted fro m f. , there remains -f-, or j-g- - ? if f be deducted from f , there remains f , or * °.. Again, if f be de- ducted from ~ , there remains T v, or ^ ; if f be deducted from f, there remains T 2 T , or ^ ; if f be deducted from f , there remains T %, or ~^. Again, if -J be deducted from f y there remains ~, or T 5 o ? if ~ be deducted from f, there remains •J, or -J, or -J4- Laflly, if f be deducted from f , there remains is or 44. Hence it appears, that all the intermediate fpaces between the notes may break into aliquot parts when they vibrate, E and £ ^ 3 Chap. II. SCftd that th(5 fmalle ft vibrating partis T V of the whole firing \ . <— -nr-~° and fop Doling the whole ftring be one foot long, the fmalleft. vibrating pari will be no more tlian f of an inch long. That fo frnall a part fhould vibrate feems to us almoft incredible, but nothing ought to be efteemed really fo, which is deduced by juft reafonino- from certain and notorious facts. Thus far all the notes . are harmonious & let us ftep out of the hexachord, and fee what will be the cafe. Deduct f from £, and there remains T \, which . does not divide 60, and therefore has no common meafure with any of the notes in the hexachord. The fame may be faid of al- rnoft all the refl. I have many obfervations to make on the fore- going doctrine ; but as my whole fyilem is not yet compleatly. explained, I mail defer them for the prefent ; and endeavour to let this affair' in the cleared light I am able, by removing fome apparent difficulties. § 41. Firft, then, the common phenomenon of the Trumpet Marine, Trumpet Ma- §3, proves, that if an aliquot part of a firing is founded, the faljrilf."' lon g er P art > as wei1 ' as the whole, founds likewife ; for if it be touched in any point but that which makes the fhorter part an aliquot of the whole, no difiinct found is heard, but a jarring noife is produced. Now this could not happen, if the longer part did not alfo found, and by this means produce the jarring above-mentioned. 2dly, That it is poflible for the longer part, as well as the whole, to found in their refpective totalities, is evident by the phenomenon mentioned § 2. viz. that, when a mufical fcring is founded, the 3d and 5th, or rather the 17th and 1 2th, are heard along with the found of the whole ftring. 3dly, The experiment mentioned by Dr. Wallis, vide §• 20, proves the fame point. 4thly, The phenomenon of the 3d founds, disco- vered by Tarcini, confirms the whole. Here then is a coincidence of experiments that mutually Support one another, and muft re- move all doubts concerning the proportion laid down in § 39, that •[ V ] that the notes in example 3, fig. 1, arc naturally coiinecled with Cu k p. ft, thofe notes over them in example 2 , and the note of the whole ^^v^**^ iiliinsr is the univerfal and fundamental bale cf them all. o But it will be faicl, that there remains behind, example 4. fig. 1. § 42* of which I have given no account. This contains the difcords \ QbjeQim* -and it will perhaps be thought impoiTible to deduce thefe, with* out uiing his proportions, or fbmetrmig analogous to them. If this is impoifible, then my fyflem is incompleat ; for thefe dif- cords, and many others, are allowed by all profeflors to be ex- tremely agreeable, and are certah ly neceffary, according to the modern tafte. Befides, one of thofe notes is wanted to fill up the diatonic fcale--, viz. D ; which by no means can be found in the way I found the other notes. This difficulty mull be removed, and fhail be, in the next chapter, to which we are now coming.; but I v/ill firft give an account of a curious phenomenon men- tioned in it. Towards the beginning of the third chapter, Tartini gives Chap. III. a proportion which he takes to be new, and I believe is id : w*-y— w It is this ; that if weights, as 1, 2, 3, 4, &c. be fufpended § 43. by firings of the fame diameter, but in length, as A"*M, Strings with A B, A C, A D, &c. i. e. the diameter and chords of tke^f as circle anfwering to the points f, f, -J, &c. fig. 4. thefe firings, when founded, will give the harmonic notes. This I take to be his meaning •, for it is not a little obfeure. As I do not underfland his proof, I will give one of my own. It is a known thing, and mentioned before, that firings equal in length, with "weights as 1, 4, 9, 16, &c. will give founds as 1, f, f, % &c. Now 2 is a mean between 1 and 4, 3 is a mean between 1 and 9, 4 is a mean between 1 and 16, &c. But A B is a mean be- tween A M and A f, A C is a mean between A M and A f , A D E 2 k f 28 ] Chap. III. is a mean between AM and A -J-, &c. Therefore firings of. the *—-Y^— ' lengths AM, A B, A C ? AD, Sec. with weights as 1, 2, 3, 4, &c. will give the fame founds as firings of the length A M, with weights as 1, 4, 9, 16, Sec. ♦, for mean weights with mean lengths mufl have the fame effects as extreme weights with extreme lengths, refpectively. § 44. After many numerical calculations, which I fhall pafs over entirev Tblrd minor, ly, Tartini undertakes to account for the fyflem of the third minor^ that greatefl of all difficulties in harmony, and to mew its necef- fary connection with the fyflem of the third major, to which he has added a difficulty that was not known before ; for he found, that upon founding fome chords in the third minor, p. 6j^ that the 3d founds, which were double, were intolerable ; and fo they appeared to eight profcflors, who were prefent when the experiment was made \ whereas the fame chords in the third major were perfectly agreeable, producing only fmgle third founds. From hence he concludes, that if the third founds could be heard as diflinctly as the natural founds, the execution of mufic would be impoffible, in the fyflem of the third minor. But I fhall not enter upon this fubject, i. e. the fyflem of the third minor, at prefent, as a better opportunity of confidering it will occur afterwards. § 45. He proceeds to the examination of diflbnances and difcordan- Difcords, ces, and their preparation and refolution. The notes in example 4, fig. 1, he calls diffonances ; thofe in example 3, fig. 1, dis- cordances. The reafon he gives for this diflinclion is, that the diffonances require both preparation and refolution ; the dis- cordances only refolution. He then enters into particulars, and mews the manner of preparing and refolving the 4th, the 6th, the 7th, and 9th ; as for the 2d, he rejects it, and proves it to be no [ 29 ] no difcord, explaining clearly how the miftake happened, viz. Chap. Ill, by an inverfion of the harmony, p. 66. He alfo clears up the ^--^r"—-' difpute about the 4th, and fhews that it arofe by confounding that 4th which belongs to the trumpet marine with that which belongs to the monochord -, and laftly adds a new difcord, which he calls- the fuperfluous 13th, and refolves in a new way. Before him, all difcords, he fays, were refolved upon the firft and fecond bafe only \ this difcord is refolved on the third bafe, i. e. G* defcends to G, which is third bafe to C. For farther particulars, I fhall refer the reader, who is curious in thefe matters, to the original, which, I am certain, he will find well v/orthy of his perufal ; and come to what I promifed, § 42, about the difcords. The method I take to find the difcords is as follows : Let us § 46. ■ take any of the notes in example 3, fig. 1. for a bafe, which muft Invention of be allowable, as they have all been proved to be connected with ^ " the harmonic notes that fland over them ; and let us fee what will be the confequence, according to phenomenon § 2. Let the note be G, which founded, will give 3d and 5th as harmonic notes. Here then we have not only got D, but B alfo, which was wanting to fill up the diatonic fcale, &c. and though a difcord does not appear in any of the fcales fig. 1. Next let F be made the bafe, which will produce A and C ; A was wanting in all the fcales. Again, take E for a bafe •, this will produce G* and B. G^ is a new note, and the very fame with that in example 4, fig. 1 5 for the inteival from G to G^ is 24 : 25, as Tartini makes it. Laftly, take E^ for a bafe, and it will produce G and B^ this laft is a new note, and the fame with that in example 4, fig. 1. I pretend not to any merit in ufmg this method of finding the § 47. difcords ; it is the very fame that Tartini himfelf takes to fill up Tartini mif- the diatonic fcale, as will appear aff.rwards. Why he did not^f x/ *^ c ' perfue [ 3° J 11 rfue it, in order to find all the difcords, I cannot guefs, uiilefe M " v *" ' becaufe he was milled by his fcndnefs for the fqu re and circle ; which can be the only reafbn why he has omitted 13 in his icale of difcords, though he calls it a difcord, and (hews the difFereiK ways of refolving it ; for I fuppofe he could not poillbly find it in his favourite figures. Though 1 fpeak thus freely of Tartini, I mean not to {at myfelf in competition with that truly great ar- tift, n:teven as to theory : On the contrary, had he not traced out the whole fyftemas he has done, and pointed out the way in every feep I have taken, and ill ail take, throughout this treatiie, I mould never have been able co prove, in a method much more fimple, and I imagine more convincing, what he undertook to ove with infinite pains •, and, I m-uft add, with fome perplexity. Mere accident indeed kd me at firft, having a curiofity to lee what notes the longer part of a ftring, if flopped as on a violin, at each divihon of the harmonic intervals, would produce -, but without his ainftance I faculd have been totally incapable of making the ufe 1 have done, and fhall do, of this fcale. / § 48. Not only my method of finding the difcords, but my idea of ■Rcfchtion of them, and of their refolution, is different from that of Tartini : It is taken however from his examples, though not from his doc- trine. My idea then of "a diffonance is, that if two conibnant notes be held on, while a third note changes to another harmony, the two notes, which were pleafing before, become dil agreeable., if not refolved, becaufe they do not belong to it. All the in- ftances Tartini gives of diffonances and difcordances, p. So, 8i, are of this fort. From hence it appears, that ail chords com- monly called difTonant, are fuch by pofition only, and confe- quently 'every note may be rendered difTonant •, but to do it pro- perly is the work of fkill and genius only. In fact, there can poiiibly be no conlonance but with the harmonic notes, and , 2 therefore [ 3i 1 therefore all chords mull take their origin from thence, and end Chap. IfL there. Bat befides the method of introducing dlfcords, by con- tinuing two notes while the third changes to another harmony, discords may be introduced, by taking in a note before its time, that belongs to another ; however this comes to the fame, Thefe two cafes, and the inverfion of notes, will, I believe, account for all the figures properly placed over bale notes, for the harpfichord. As to the 7th, I (hall confider it in another place. If the foregoing doctrine about dinonances is juft, then,.. lit, §. 49. what Dr. Smith afferts, in his Harmonics, That nature has put Errors aboitt< no limits between them and confonances, is not true ; but it is a ^ c0 common error to confider intervals per fe, and not in relation to a fyftem, as Tartini obferves, and has given an inftance in two parts, where the 5ths are confonant, and by adding a bafe to them they became diiibnant. 2dly, It is faid in the Harmonics, that there is no harmony without dlfcords. This is not {Irictly true ; for there are none, as long as we confine ourfelves to the notes on the firing trumpet, i. e. in all tunes properly compofed for the trumpet and German horn ; though there are both the 6ths, the 4th, and both the 3ds, on that infcrument. But the proportion is true, as foon as we ufe the diatonic fcale ; for there all mufic ccnfifls in a perpetual refolution of imperfect con-r fcnances and real diifonances. What I have faid upon the fubject of diifonances, and their §50. refolution, will appear very fhort and imperfect, to all fuch read- Apology for ers as are converfant in the practical part of mufic ; but, I think^ orin ^ s ^ ' the mortnefs ought not to be deemed as an. object ion,, if there is no deficiency 5 I mean, as to the principles which I have ufed j- ... as to the practice, I know too well the perplexity and intricacy, of this part of mufic, to pretend to give - any inilructions ^ and., 'were; t S» 3 ! . III. -were I able and inclined to do fo, it would be unneceffary, as v ~'T ' Tartini has dom it already to my hands. I might indeed have translated this part of his work, as I have done fome others, and as I might .have tranflated the whole -, but that did not fuit my purpoie. I fhall therefore put an end to my obfervations on the third chapter* Chap. IV. Chapter the 4th contains many curious and infiructive obfer- *~"*"~ v ~ ^ vations, of which I mail give fome account in my ufual way, ■ § 51. adding, as I go along, reflections of my own. Our author fets 03aw. out with a principle, which he had mentioned in the laft chapter, that harmony muff be ilippoied, before the parts which arife from the harmony, i. e. the long. The difference between them is this ; in the harmony, the founds are fimultaneous \ in the fong, they are fuccefiive. Thefe fuccerlive notes conftitute the octave, and therefore it is of great confequence to fettle this. I believe moft people will be apt to think, that there was not much thought required to fettle the common octave, which almoft every one who lias an ear can run over v/ith the greateit eafe, and, as he thinks, naturally -, yet there were many divifions of it propofed, before that was invented which now takes place. Ptolemy the aftronomer was the inventor ; and it is no wonder it has gene- rally prevailed from his time to this day, as it is the only one which was truly founded on nature. However this foundation does not appear by any thing we find in Ptolemy j nor does it appear in any other- writer, but Tartini, that I know of. § 52. "When we firft begin to learn raufic, we are, or mould be, 03ave. taught to play or fing the octave : Tartini ufeel really to teach it, and fometimes to the great mortification of his conceited lcho- lars \ but he does not call it the foundation of mufic, as other matters do, who do not teach it. However, we are taught to go through f 33 1 through it after a manner, and are ever after apt to look upon Chap. IV". it as natural ; but it is undoubtedly artificial, and the refult of ^— -"V— -*' much and profound thought. However paradoxical therefore it may feern, yet it is certainly true, that harmony is more natural than the notes of the octave ; for a firing cannot be founded, either as a trumpet marine, or as a monochord, i. e. in the common way, without producing harmony •, whereas the notes of an octave never appear but in highly civiiifed countries. Amongft the birds we hear the 5th, the 4th, the 3d major and minor •, but the notes of the octave from no animal that has not been taught, unlefs we believe the extraordinary account of the Sloth. The intervals we do hear, are thofe of every mufical firing, and therefore mull be deemed natural. I have in part anticipated Tartini's method of getting the notes § 53. of the octave ; but I will neverthelefs repeat again what 1 faid Osiave. about it § 46. In order to obtain thefe notes, he takes the four notes which are expreffed by the numbers 6, 8, 9, 12, or rather three of them, C, F, G ; for the octave to C gives no new note j and then confiders what other notes they will produce, according to the phenomenon of the mufical firing. He finds that C gives E and G ; F gives A and C •, and laflly, G gives B and D. But thefe notes fill up the diatonic fcale or octave, and are exactly in the fame proportions that Ptolemy firfl invented, and that have been in ufe ever fince. From hence Tartini juflly concludes, that the fcale arifes from the harmony, and not the harmony from the fcale. This makes a great difference ; and we fliall fee prefently, that the want of this diflinction has brought much con- fufion into mufic. But fome will fay, why pitch upon thefe three notes to fill up § 54. .the octave, one of which does not even belong to the harmonic objeffin. F feries, [ 34 I Chap. IV. feries, viz. F; and particularly when the difcords §46 are pro* duced in the fame way, and yet do not belong to the common fcale ? Is not this arbitrary ? An anfwer to thefe objections mud Solution, be made. lit then, All mufic confifts in clofes ; and thefe clofes muft be by riling a 4th, or, which comes to the fame thing, by falling a 5th. If it be afked, Why this muft be ? I anfwer, Be- caufe the ear requires it. Farther than this, I pretend not to go.. Taking it therefore for granted, as a principle, that in clofing we ' miii! rife a 4th, I mall proceed. There is no clofe in the harmo- nic notes but from G to C ; and the next note that offers itfelf naturally out of that feries is F, being intimately connected with G, as has already appeared, and will appear more ftrongly after- wards. However the ancients hit upon it, I do not pretend to- explain ; but moil certainly they adopted it very early, and laid firch a ftrefs upon the invention, that the numbers which expreffed the two tetrachords became famous above all others. As to the other part of the objection, that Tartini has proceeded in an ar- bitrary manner j I afk, whether that which is founded on a co- incidence of phyfical caufes, human fentiment, and mathematical calculation, can be called arbitrary ? Now this is the cafe of the notes of the diatonic fcale 5 and thus one of the fineft arts is built on the moil folid foundation -, an art that was undoubtedly firfl begun in vEgypt, and from thence propagated over the reft of the world, wherever any true mufic has been known ! § 55- But why all this trouble, feme muficians will fay, to fettle Temperament, the notes of the fcale, when it is notorious that they muft all be changed, upon lh 5 but foch compofitions are fcarcely to be found, To f 40 ] Chap. IV. To confirm what I laid above, § 59, that the Harp was for- merly a favourite infirumcnt in this nation, I will cite fome paf- § 62. fages out of our old and bell writers. Harp. u Mufic which his [Arion's] Harp did make." Spenfer, Sonnet 38, " Orpheus with his Harp." Ibid. Sonnet 44. " By the judgment of Aicibiades, the Harp is to be preferred," &c. Praife of Mufic, printed 1586, p. 13. " The Harp lived after Orpheus was dead." Ibid,; p. i§\ And in many other places Harp for Lyre. " The office of a phyfician is to put the curious Harp of " man's body in tune." Bacon, de Augm. Scien. " His word is more than the miraculous. Harp" Shakefpear's Tempeft, Act 2, fcene 1. " The battle of the Centaurs, to be fung by an Athenian eu- " nuch to the Harp." Midfummer Night's Dream, Act 5, fcene 1. " Harping loud in folemn choir." Milton, on the Nativity, Stan. 11. " And fet my Harp to notes of iaddeft woe." Id. on th^ Pafiion, Stan. 2. ." Touch their immortal Harps of golden wire." Id. at a fo- lemn mufic. " Then crown'd again, their golden Harps they took, " Harps ever tun'd." Parad. Loft, B. 3. v. 36$. " And touchd their golden Harps" B. 7. v. 258. " And the found " Symphonious of ten thoufand Harps, that tun'd cc Angelic harmony." lb. v. 559. " The Harp had work, " And relied not." lb. v. 594. " A golden [ 41 I u A golden Harp with filver firings flie bore." Chap. IV. Cowley's Complaint. *"""" v mmJ I have quoted no paffage from Scripture on this occafion, be- § 63. caufe David's Harp is To well known, and the places, which are Lyre. many, where that inftrument is mentioned, are fo familiar to every one •, inilead therefore of ufelefs quotations from thence, I will juit obferve, that the word in the Scptuagint, anfwefing to Harp in our translation, is moltiy KAccgcc, but fometimes SP^Atjuw, Ki»u?a 5 or N^Ag:. All thefe inftruments are eflentially of the fame nature, confiding of one row of firings without a ringer- board ; fome were ftruck with the finger, others with a plectrum, and others perhaps with a flick, as our dulcimer. Prints of ail thefe inftruments are given by Monfignore Bianchini, in a book intitled, De Tribus Generibus Inftrument. &c. from ancient monuments. Two of them 5 tab. 3, fig. 13 and 15, refemble- in fome degree the common Harp in fhape : The firft is taken from an Egyp- tian vafe in the villa Medici ; the other from an ancient vafe, belonging alfo to the Medici family, and has 1 2 firings, and there- fore agrees with the Nablium of Jofephus, as Bianchini obferves* He alfo obferves, that the Harp of the barbarians, mentioned by Venantius Fortunatus, in this line, Romanufque lyra piaudat tibi, barbarus harpa* is properly compared with the Lyre. No doubt, thefe inftru- ments are properly compared \ for there feems to be no difference between them but a little in fhape, and the number of firings* fome of which were added after mufic had fallen from its ancient fimplicity. I will add, that Bianchini finds, what he takes to be a Cithara, or Lyre, on a tripod placed before the bull Apis, in the Ifiac table -, which conjecture feems not improbable ; this figure refembles the Harp. Diodor. Sic. p. 313, fays exprefsly, that the inftrument ufed by the bards was like the Lyre, From G all [ 42 ] Chap. IV. all thefe circumftances, there is great reafon to think, that David's ^-^v—— ' Nablium did not differ from the Old Britifh Harp with a fmgle row of firings. § 64. When I faid above, that the KAaox, ^PasAT^/or, &c. were ef- Cithara* fentially of the fame nature, I went on the fuppofition, that the Cithara and Lyre did not differ, as Bianchini feems to fuppofe. It is true, thofe two words are frequently confounded, even by an* cient writers •, but Plato, p. 618, plainly makes a diflinclion be- tween them : What the difference was, does not appear, as far as I know. There is a muncal inflrument in Bianchini, found on an antique vafe, tab. 4, fig. 7, which is totally different from what is generally called the Lyre, fuch as is frequently found in the hands of Apollo, the Mufes, &c. h has a finger-board, and therefore mod undoubtedly was flopped in playing, as the lute. This, Bianchini calls a Lyre, or Cithara •, but the fame word can- not properly and critically be applied to two inflruments fo to- tally unlike. I mould be inclined to call this the Cithara ; and the more fo, as the words Guitar and Cithern feem to be derived from it. What Arifiotle fays of the Cithara feems to confirm all I have advanced •, for he dilapproves of it as an inflrument to be ufed in education, as being too artificial. This agrees very well to the Cithara, in contradiftinclion from the Lyre, which was vaflly more fimple. I will farther obferve, that there feems to be a difference between the Lyras, properly fo called, in one re- fpect •, for fome have a belly, or founding- board, others not. J*. § 65. I faid, § 56, that to ufe a temperament is to disfigure the Terfta mu- fair form of harmony •, and will now add, that they only know what true harmony means, who have heard a well - compofed piece performed by a fet cf muficians, who keep perfectly in tune with one another. I never heard fuch mufic but once, and the [ 43 ] the effect was wonderful : It was performed in the Pope's chapel, Chap. IV. during Paflion-week : It feemed to come from one fingle voice, ^--'^V*"— * and that the chords were only the refonances naturally belonging to it ; or rather, the mufic did not feem to be produced by any human voice or inftrument •, but that fpirits were diverting themfelves, and trying, like Ariel in the Tempefl, the powers of harmony over the human frame. It may be looked upon as whimfical, but I will venture to fay, that he who Jias not, heard fuch mufic as I have defcribed, may get a better idea of it, by lifteniiig to JEolus's Harp, than by any other way I can think of. Could we but add air and time to it, it would be the mofl perfect of all mufical inftruments. But of this more in another place- The refonances which I mentioned above, and by which 1 mean § 6& the harmonic notes, that conftantly accompany the found 0$ Harmonic every mufical firing, are the life of mufic. Without thefe re- n fonances, every found is flat and obfcure ; and in a certain degree of this deficiency becomes mere noife • a flriiig, that is not per-^ fectly even throughout, gives an idea of what I have been faying. When we fay, by way of encomium, that a voice rings like a bell, we mean to exprefs that effect, which arifes from the har- monic notes ; and probably the want of thefe notes is owing to fomething analogous to what I mentioned of a firing, i. e. the or- gans that ferve for finging or fpeaking are not perfectly even or homogeneous throughout. Drawing a good tone out of a violin, I believe, depends not fo much upon any particular Height, as fome people are apt to imagine, as on the following circumflances : 1 ft, Having perfectly good and even firings ^ 2dly, Stopping per- fectly well in tune ; jdly- and confequently, Not ufing open firings on certain occafions, where they mufl be out of tune ; 4thly, Strik- ing at a proper difcance from the bridge, fo as not to interrupt G a the [ 44 ] Chap. IV. the vibrations; vide § 23 : All thefe circnmflances are necefiary, *•" * "^ in order to produce the references of which I have been fpeak- ing ; but are too frequently neglected by inuficians. I do not however exclude a certain Height in managing the bow, which fc ne can never acquire, and which perhaps cannot be taught by the bed mailer. Thefe refonances give to mufic that identity and diverfity mentioned by Tartini ; whereby every part is intimately fympathetic with every other part, and alio with the whole. From hence it appears, that the word harmony has been with propriety employed to exprefs perfection, in many other fubjedts, where identity and diverfity are in a remarkable degree connected toge- ther -, but this word has been hitherto thus applied, not fo much from theory, as from mere mechanical fenfation. Any tempera- ment whatever deflroys thefe bands of identity and diverfity, and therefore ought not to be admitted into mufic, unlefs in the way pradtifed by P. Valloti, and recommended by Tartini.. § 6j. In order to illuflrate farther the phenomenon reprefented in trumpet Ma- fig. 6, N° i,. 2, on which all true mufic feems to me to be founded, I will exhibit to the eye what is fuppofed to happen when any homogeneous fixing is founded. It is, as I obferved §2, a fade agreed on univerfally, that every fuch firing has an accompani- ment of 1 2th and 17th •, i. e. f and 7 part of the firing vibrates, Ffg. 8. as well as the whole. Let A B, fig. 8, reprefent a mufical firing - y AD = DE = EB=fAB; AK = KM = MO = OQ fc srQBsfAB-j DM = OE=.tKM = ^.AB. The firing A B being founded, will give the note belonging to its totality, and therefore will vibrate in the manner reprefented by the curve A C B ; but it will likewife give the 12th, which belongs to each 3d part of the firing ; therefore each third part will vibrate in the manner reprefented by the curves A F D, D G E, E H B : But ;t v/ill likewife give the 17th, which belongs to each 5th part of the I 45 1 the firing -j therefore each 5th of the firing will alfo vibrate iri Chap. I\ r . the manner represented by the curves A I K, K L M, M N 0, x -~~~>r~~~* OPQ, QJl B ; therefore the points K 7 D, M, G, E, Q, are comparatively at reft, and not only thofe, but every 15th part of the firing ■ for D M is i~t of tne whole firing, being f of f •, and being an aliquot of the other parts, and of the whole, muft pro- duce analogous vibrations. Were we to add the vibrations of * and f , and combine them with thefe, the phenomenon would be flill more complicated ; and yet all thefe frnall vibrations certainly exift, and are fo far from caufing any confuficn, that they give the greateft perfection to mufic, I own the laft-mentioned phenomenon is incomprchenfible, and § 68. fo is every hypothefis that has been invented to explain how the Difficulty of air can poftibly convey diftinct founds to the ear in a full concert/ n ing cau J M£t Thus all our fpeculations lead us at laft out of our depth : We are obliged frequently to deal with quantities, and other matters of an indefinite nature ; in thefe cafes it is our aim, as it is our interefl, to circumfcribe and bring every object that concerns our perfuits within limits. This aim has produced every fyftem, and every hypothefis, that has difgraced human fcience. It is not wonderful, however, that fo many ingenious men have been tempt- ed into this ocean > where few, very few, efcape fliipwreck 5 when we reflecl, that knowledge, without a fyfrem, confifts of nothing but detached fcraps, with which the memory is overbur- thened, and the mi^d very little enlightened. Lucky is he who hap- pens to circumfcribe any portion, however inconfiderable, from the chaos of materials fet before us by the Deity, for the employment of our faculties, and, by reducing it to order, renders it fit for our purpofes ! > How far I have fucceeded in fuch an attempt, the world muft judge % and, if the general voice is againft me, I will fay with Huygens, Cofm. p, io, " If any one fnall think that. I " have t 46 ] Chap. IV. « have fpent my time to little or no purpofe, in propofing con- '~* r ' i - J cc jeclures about things, which we muft allow cannot with cer- " tainty be comprehended : I will anfwer, that the whole ftudy " of phyfics, fo far as it is concerned in rinding the caufes of " things, muft for the fame reafon be condemned ; where the " higheil merit is to find out what is probable •, and where the " inveftigation either of very important or very obfcure truths " gives delight." § 69. But to return to my main bufinefs. Tartini next comes to the Counterpoint. Counterpoint, the efTential part of mufic. He obferves, that the 3d, 5th, and 8th, are never marked upon the bafe where they belong, becaufe in a figured bafe they are all fuppofed without marking, where there are no figures at all, as being infeparable from the fundamental bafe, in confequence of the phenomenon mentioned more than once in this treatife. H~ then diftinguifhes the three cadences -, viz. that from G above to C below, which he calls the harmonic, becaufe it goes from the harmonic mean to its extreme ; from F to C, which he calls the arithmetical,, becaufe it goes from the arithmetical mean to its extreme ; and the next, from F to G, which he calls the mixt, becaufe it goes from the arithmetical to the harmonic mean. From hence he forms the bafe notes belonging to the octave, in a way that admits of no difpute. From this bafe arifes modulation, or tranfition from one harmony to another. Why he has confined the tone of C to this modulation, will be fnewn afterwards. § 70. He then proceeds to fhew, that the common way of figuring Figuring the the notes of the octave is erroneous •, v. g. when a 6th alone is put to D and A, of which Rameau is guilty as to D, calling it a 4th fundamental. This muft be an abufe both of words and harmony •, for a fundamental bafe, in its very idea, ftippofes no accompa- niment [ 47 ] niment but 3d, 5th, and 8th, either direct or reverfed : So much Cka?. f V", for the words. As to harmony, D never can have the 6th be- v — ' ****y~"— u longing to it, unlefs as 5th of G \ in which cafe G is firft funda- mental, and not B, or the 6th ; and therefore the 4th alfo mould have been added. This is explained, in the cleared way, by our author, though it has puzzled the profefTors, who have hitherto had no certain rule to guide them. Tartini very properly calls C, E, G, which notes are heard in §71. every founding firing, ift, 2d, and 3d bafe, becaufe they are and j/?, zd y and may be ufed as fuch, only putting the proper figures over, or, as 3 t,ajss ' it is called, reverfing the chord, i. e. putting that above which ought to be below : And this idea gives an opportunity of mew- ing how all the notes in the octave, if ufed as bafes, ought to be figured y which is very different from the common method, p. 106*, but I mail not enter into the detail, as I could not well explain myfelf without more plates, which fo flight a work does not deferve. However, I thought it right not to pafs over in filence a point of fuch confequence 5 vide p. 106, 107. He now enters upon a very curious fubject, on which he throws ^72° great light ; and has put an end to the many difputes that have Ancient moda, arifen. The fubject is, the modes of the excellent compofers of the 1 5th century, who ufed a fcale for prime bafes, which he ex- amines : " This fcale, as being formed of a mixture of the har- " monical and arithmetical progreifion, has,'* he fays, " many " and particular beauties belonging to it -, but infeparable from " a certain crudity of modulation, which many of thofe compofers " either could not or would not guard themfelves againft." He then fhtews, that the crudity or harfhnefs of this fcale proceeds from the tritones necefTarily refulting from it ; and propofes a method to avoid this crudity, by making D and A, in the fcale of the oc- 2 tave. [ 48 ] Chap; IV. tave, fundamental bafes, with a third minor ; il> that every note V ~-~"V~***«' has 3d, 5th, and 8th for its accompaniment. I fhall not par- ticularly mention how he proves the connection between thefe 3ds minor with the common diatonic ♦, became I think what he lays is rather too fubtile-, but as this connection gives the two fun- damental clofes in the octave, in a regular manner, there is no reafon to doubt but that he is in the rigiit. § 73. tc The effect of the harmony of this fcale," fays he, " cannot Mixt fcale. " fail of being highly agreeable in its modulations •, becaufe it " includes in itfelf the two harmonies of 3d major and minor, " different in that refpect from the fcale deduced from the harmony " of the three cadences, (he means thefe of C, F 3 and G) which " confifts, by its very nature, of the harmony of the 3d major cc only •, and therefore this laft, as being wholly of the harmonic " genus, will have indeed more force ; but the other, which has Ci a mixture of the harmonic and arithmetical kinds, will have " more variety and fweetnefs. Whoever knows how to avail " himfelf of one and the other, or of their conjunction, in a ci proper manner, according to the nature of the fubject, will " be able to produce ail the effect he aims at." § 74. What follows, about refolving difcords, I have already confi- Difcords. dered, in another place ; and I find nothing in this chapter that inclines me to alter my opinion, § J 5. His deduction of the meafure from the cadences is curious Meafure. and new. Common time, as we call it, or meafure, arifes from the octave, which is as 1:25 triple time arifes from the 5th, which is as 2 : 3. " Thefe," adds he, " are the utmoft limits " where we can hope to find any thing worth notice. This is " fo true, that many having attempted to introduce ether kinds " of [ 49 ] « of meafure, inftead of a good efifecl:, have found the greater!: Chap, IV, " confufion -, and fo it will always happen." I have feen mufic ^- aa " , v-— -> with 5 equal notes ; hut I never faw any body who could per- form it. Our author proceeds to obferve, that the cadences belonging § y6. to the octave do not arife from the arbitrary rules of arts, but are Cadences. required by nature. u I do not, however," fays he, " draw this " confequence, that thefe primary examples ought to be an uni- w verfal unalterable law ; if fo, mufic would want the beauty " arifing from variety : But I will fay, that variety itfelf ought " to have a pattern to go by, that it may not become extrava- cc gant ; and that to determine the cadence where it ought to be, u and to reduce the {enfe of the mufic, or, in other words, its u meaning, to a proper period, contributes greatly towards V unfolding the fubject. propofed, and making it clear and in- " telligible to the hearers." When words are fet to mufic, the length and fhortnefs of § 77. fyllables ought to be regarded ; in fuch a manner, that a long Metre. fyllable ought to have a longer note belonging to it than a fhorter ; but not only that ; for this diftinction may be exactly obferved, and yet the effect may be very bad, and abfurd :, for it is necef- fary that the accented part, which is the long fyllable, mould alfo be accompanied by the accented part of the mufic. Now, the accented part of the bar is where the harmony of the key is, which, in common time, is, or ought to be, in the beginning or middle of the bar. This Tartini demonftrates in the clearer!, manner. " It is one thing," adds he, " not to chufe to have a cadence " upon the harmony propofed, for two or three bars, dwelling £C on the fame fundamental bafe % and another thing, whether '" there is not, in fact, a cadence virtually in the greatefi part H « of C 50 3 Chap. IV. " of practical cafes \ and, in general, whether it is not required " by nature, in conformity to the primary exemplar in the places " above mentioned, i. e. the beginning and middle of the bar,. " I am fcnfible, that prejudice may have fome effect, in making " a whole orcheftra accent flronger at thefe places, efpecially in " certain kinds of mufic, from being ufed to fee it done by their 44 director •, but this does not hinder me from holding the fame " opinion. The fact is, that, independently of mufical habit, " I have often obferved popular and country dances directed by 44 a cymbal, an inftrument void of any mufical found. Three 44 things I have obferved upon this occafion ; greater and lefs 44 ftrokes equivalent to long and fhort ; the mod exact confor- 44 mity with the two kind of meafures, common and triple ; and 44 always flronger ftrokes in the beginning of each refpective 44 meafure or bar. Being thus convinced by a fact refulting from 44 nature, and perfuaded, that, in fimilar circumftances, the 44 fame thing muft happen in every other nation, I am con- 44 {trained to rely on my theoiy, fupported and proved in fuch 44 a manner as to take away all fufpicion of prejudice." The fame thing does actually happen in Perfia, by Kcemfer's account. I mall tranfcribe what he fays about this point, when he is de- ferring the way of life amongft the inhabitants of Ormuz, during the hot months, which they pafs in the palm-groves, upon the neighbouring mountains : " The Perfian muficians," fays he, Amaen. Exotic, p. 743, 44 know no rules ; they have no fkill in 44 finging or playing \ but they keep well in time, ufing only 44 unifons, or octaves ; and vary their rhythm, or time, in fo maf- 44 terly a manner, that their mufic not only pleafes the ignorant, 44 but even the learned -, who cannot but wonder, that the com- 44 mon people mould excel fo perfectly in a thing, which we are 44 taught with much pains. bit I 5* ] Sir Ifaac Newton fays, Chronol. p. 14, that the Idaei DacTyli Chap. I" cc keeping time by jftriking upon one another's armour with their v -*^^ r * " fwords, brought in," i. e. into Greece, " mufic and poetry." § 7°« This account feems to me to be highly probable - 9 for rhythmical, Rhythm* or meafured motion, always has* in fome degree, and always ought to govern, poetry, as well as mulic. Suppofe thofe country people mentioned by Tartini, who danced to the Cembalo, had prevailed on a poet and a mufician to. give them words and air to their meafures ; is it not evident, that one in his clofes, and the other in his metre, would have been tied down to the rhythmic motion ? Tartini therefore juilly lays a great ftrefs upon the rhythm, as the ancients did ; for unlefs this is well marked, mu- ll c is lifelefs, infipid, and, one may fay, without a foul, as it is bereaved of that which firft produced it. On the contrary, the effect of a well-compofed minuet, a jig, or a horn-pipe, on the generality of mankind, is a fufficient proof of the efficacy of rhythm, I may fay, of its magic. It is this which gives air to a tune, and which fo few muficians have excelled in. Learned and ingenious compofitions we have in abundance, fuch as make a very handfome appearance upon paper ; but they are forgotten as foon as the performance is over. I will obferve, upon this occanon, that if the blackfmiths hammers ever were of ufe to mufic, it muff have been by mewing the power and beauty of rhythm -, for it behoves all thofe who work in company at the an- vil, to be very careful in keeping time, as great mifchief would happen from the want of it. Nothing is more certain than what was faid, in the beginning § yg„ of § j j, ought to be an inviolable rule in vocal, mufic \ viz. that Accents mu* accented fyllables ought to be accompanied with accented notes. \£ tr ™ a i I will not particularly examine, how far this rule of nature is ob- H 2 ferved 5 [ 52 ] Chap. IV. ferved; becaufe, as things go on at prefent, any notes will ferve v -*—V—*- ; for any words : Thefe are fo frittered away, that they feem rather the ghofts of mangled words, lingering and flicking to the tongue, like the ghofts of wicked men, which, as Plato fays, are frequently feen hovering about their tombs. But I will leave them to linger and hover on, according to the mercy of their arbitrary mailers ; and return to the dictates of nature, which determine, that mufical and poetical accents ought to go toge- ther. This is fo certain, that no mufician in his fenfes would, in common time, begin his fubje6t, if the verfe is iambic, without putting the fecond fyllable at the beginning or middle of the bar, as long as he has any regard to the words at all -, whereas, if the verfe is trochaic, he will as certainly put the firft fyllable in the aforementioned places. § 80. Ifaac Voflius published a treatife concerning vocal mufie and If. Voffius rhythm, in which there are many ingenious and folid obferva- tions, mewing how much the antient Greeks furpaffed the mo- derns, by their attention to the rhythm and metre of their mufic and poetry -, that mufic cannot be perfect without this attention ; and that the Greek and Roman are more adapted to mufic than any of the modern languages. All thefe propofitions mufl be allowed to be true ; but when he fays, that, for want of long and mort fyllables, no good mufic can be compofed at prefent, I think he goes too far. That our profody is not exact. ; i. e. that we have not the fame regard to the quantity of fyllables, arifing either from what grammarians call nature, or from pofition, is certain. The Greeks, we know, had fixed rules, by which the quantity of almoft every fyllable in their language was determined ; and no poet could offend againft thofe rules without incurring con- tempt. The Romans imitated them in this, as in every other art, as far as their genius would allow. But it does by no means follow, [ 53 ] follow, that, becaufe we fall infinitely ftiort of the precifion of Chap. IV, the antients in this particular, the modern languages will not ad- ^ 00 ^Y mmmmJ mit of good vocal mufic. Could Voflius read any modern poetry, and not obferve that it was regulated by accent ; now accent im- plies quantity. It is true, that our fhort fyllables are often loaded with confonants, which makes them very uncouth and difficult to pronounce •, and this great defect throws an additional burthen on the finger, which would be avoided in a fmoother language ; but fcarcely, if at all, affects the compofer, if the poetical num- bers are juft, and the words expreflive. Monfieur RoujGTeau has taken up this opinion of Voffius, and applied it to the French language •, but, as I do not remember that he has enforced it by any new reafons, I fhall not particularly meddle with this lively writer, and only obferve, that the French language is perhaps lefs capable of being well fet to mufic, than other polite Ian* guages in Europe, for many, reafons which might be given. But, whatever the cafe may be with the French language, in § 81. relation to mufic, it mull be allowed, that the Italian is not want- Profody Ita~ ing in variety of long and fhort fyllables. They have many words ' of two fyllables, that are iambic, as cosi, trove, virtu, pero, &c. •, very many that are trochaic, as canto, parla, fono, ufo, &c. which may alio ferve as fpondees \ many words of three fyllables that are dactylic, as trovano, parlano, proffimo, ottimo, &c. ; feme anapsefts, as vanita, unka ; many that are amphibrachys, or Bacchian, as catena, fidele, alcuno, &c. There is alfo great va- riety in the words of four fyllables, as curiofo, infimto; intrin- feco, malevolo, verifsimo \ difficolta, perpleffita, ebrieta, &c. This variety of accents, joined to the wonderful fmoothnefs of the Italian tongue, gives it a fuperiority, for the purpofe of fing- ing, over all the modern languages, that cannot be difputed. Were it not for this want of. fmoothnefs, . we might perhaps be Enghfi* rivals [ 54 ] Chap. IV. rivals to the Italians -, for fome of our words of two fyllables arc u **^ / ^^ iambic, as deteft, employ, belong, &c. ; others trochaic, as le- vel, hinder, bleffed, kindred, &c. -, many cf our words of three fyllables have the accent on the firft, as u fury, lenity, villany, &c. ; fome on the fecond, as confidcr, beloved, deliver, dec. The at- tempt of Sir Philip Sidney, to introduce what is called heroic verfe into our language, fucceeded fo ill in his hands, and has been fo much ridiculed ever fince, that I was carried away with the ftream, and once thought we could not ufe dactylic feet -, but I am convinced of the contrary, and fhall now make it evident, to any competent judge, that we not only may, but do ufe them. Every fcholar will own, that the following verfe, rioAAflS cf 1 ' CCVCCVM KXiOlV.CC 7TCLP OLVlOLTS ^OC\/JX'.CLT TftWOVy confifts of dactylic feet, as being a verfe in Homer. Now, add the word yctp at the beginning of it, and cut it off at ttolodlv^ and I defire to know what difference there is between that, and this well-known Englifh verfe, My | time, 6 ye | Mufes, was | happily | fpent : That the metre is fundamentally and effentially the fame, is evi- dent from hence, that if any compefer was to let thefe lines to mufic, he muft neceflarily accent both on the fecond fyllable ; and, which is more to the purpofe, the fecond fyllable, and the two following ones, muft make a whole bar, or half a one, which is the fame thing ; and the two laft notes of the bar together mould in ftriclnefs be equal only to the firft by itfelf. N. B. The redundant fyllable, fpent^ at the end of this verfe, joined to the firft fyllable of the next, and fo on, keeps up the rhythm throughout the whole fong. § 82. I wifli it were confident with my defign, to give a full account hifcordant of Tartini's doctrine on this head, which is very clear, and very motes. inftructivc to muficians -, but, befides that many plates would be required, [ 55 J required, I always meant to refer the inquifitive reader to the Chap. IV, original. After having given an example of the right manner of *— -"V—^ ufing difcordant notes, with reference to cadences, he fays, " In- 6 finite deductions arife from this example, as a firft principle, * which may be equivalent to an entire practical treatife. But 5 my intention is to eftablifh firft -principles, exemplified fo far c as is neceffary, and no more." He then adds the following mufical canon : " Tou may confine the difcordant notes within li- mits, as much lefs as you pleafe than half the bar ; but never ought to let them exceed it. There may," fays he, " be fome excep- tions, in regard to fuch modes of mufical expreffion as are fa- miliar to the reigning tafte, in which no fcruple is made to fubftitute the fhadow for the fubftance ; i. e. inflead of the fundamental notes of the fong, to give us thofe which are de- duced from them. According to this tafte, the difcordant notes may very well be placed in the beginning and middle of the bar ; but this, being a more than ordinary poetical licence of the prefent age, does not affect the truth of the above-men- tioned canon." Tartini enters next upon a moil perplexed and intricate fubject, § 83;. viz. the chromatic and enharmonic fyftems of the Greeks ; which Antient cbro*- though he does not pretend to have cleared up, yet he has cvi* matiC * dently fhewn, that either thefe genera have been totally mifun- derftood by the moderns -, or that the antients ufed them in direct oppofition to the firft principles of harmony. He has given an example of his own, in the chromatic, which is practicable, and which proceeds by two hemitones following one another, and an. uncompounded interval confifting of three hemitones. Now this is perfectly conformable to what all the Greek writers on mufic call the chromatic ; but this in reality feems to be nothing more than a common paflage from a 3d.. major to a 3d minor. It may 5 be [ 56 ] Chap. IV. be afked then, How this chromatic happens to be practicable, and ^-^'~"— ' the antient not ? The anfv/er is, That the antients began theirs, as is generally thought, from a note that was diftant from the next above it by a hemitone •, v. g. from B to C, and from thence to C *, and E, which completed the tetrachord, but which led into a tone which had no relation to the firfl : Whereas Tartini fets out from G, then goes to G*, A, and C. This method carries him from C 3d major to A 3d minor -, which two keys are mofl intimately connected. I mall have an opportunity of giving an idea of ano- ther chromatic, by the .afliftance. of Tartini, but not according to the antient fyitem ; which is, I believe, as well as many other things relating to the Greek mufic, a perfect enigma -, though we have fo many confiderable old writers on that fubj^ct, and fo many commentators upon them ; fome proofs of this I (hail offer in the courfe of the prefent work. A plain proof that the antient and modern chromatic are intirely different, is, that, ac- cording to Ariitoxenus, two tones cannot follow one another in that genus -, p. 65. § "84. Tartini, after having examined the fuppofed chromatic of the Antient en- antients, proceeds to the enharmonic, which he likewife finds to be contrary to the principles of harmony : But he undertakes. to give one of his own, by means of a note, as he fays, out of the limits of the hexachord, expreffed by f, which he calls a confo- nance ; giving us to understand that is a note arifing from na- ture, and is founded with the greater! facility on the trumpet ma- rine and German horn. But when he comes to give an example of the ufe of this note along with the bafe, it appears not to be the note he imagined. B , it is true, which is expreffed by ~, when C is principal note, (lands againft C in the bafe, and very properly ; but C here is 5th of the tone -, for the tone is F ; and therefore B^, as he marks it, is not 7th, as it ought to be, but 4th, of F. The whole is cleared up, when he tranfpofes his ex- ample harmonic. [ 57 J ample out of F into C ; for then G with the 7th minor is nothing Chap. 1\ but the common chord, in paffing from the 5th of the tone to the v « o *^V^*- clofe, and therefore requires no particular refol" as appears both by common practice and by theory ; for F 7th of G is a confonant note, that joins- the harmonic and arithmetic fyftem to- gether. It is true, he lov/ers F natural \ but owns afterwards, that it is fo near the truth, that it does not in the leaft defiroy the fine effect of the harmony. From what has been faid, it appears that our author has not § S$. difcovered the enharmonic, any more than others, who have at- Enharmonic tempted it before *, but he has however kept within the bounds °1 Mon f teur of harmony, with that fobriety and excellent tafte, which never fuf- fer him .to go wrong in practice, however he may fometimes be mifled by his theory. But Monfieur Rameau, Generat. Harmon. p. 1 $%) not altogether fo well qualified in thofe refpects, undertook to give us an enharmonic iyftem, not only in theory but in pradlife ; for he fays he had introduced it into one of his operas. He owns honeflly indeed, that it had not all the effect he expected from it 5 but this he attributes, as is ufuai in fuch cafes, to the bad execu- tion of the performers. He had more reafon, in my opinion, to take all the blame to himfelf ; for his enharmonic confifts in one of the groffeft paraioglfms that ever entered into the head of a muMcian. It is a thing well known, that on the harpfkhord the lame key is made ufe of for two different notes, belonging to harmonies, that have no relation to one another. What then is the art of Monfieur Rameau ? Why truly, nothing more nor lefs than, by help of this ambiguous way of marking two notes, to join two harmonics together that ought never to meet. This me- thod he dignifies with the name of enharmonic \> ana fays, that it makes you feem to pafs in an inftant from one hemifphere to ano- ther \ an excellent conceit this, no doubt, to recommend mufic, I which [ 53 ] Chap. IV. which, from the earlieft times down to our own, has furnimed all t^— v-— ■> the civihfed part of the world with ideas of beauty arifing from identity and diverlity combined together. But if he had a fancy to hurry his audience to the antipodes in fo precipitate a manner, why not begin with A natural, 3d major 5 and, after having well fettled the tone, ftep at once boldly into E b, 3d major ; which would have anfwered his purpofe full as well. But to return to Tartini. § 86. He obferves, that in going through the octave with the full Tritone*: accompaniment, the inconcinnous interval of a Tritone between F and B arifes ; which he fays has a very good effect in afcending, as the progrefs is from worfe to better, i. e. from the arithmetic to the harmonic fyftem \ but that in defcending it is by no means to be allowed, and is an error when practhed. I fhould rather think, that the reafon of this difference is, that in afcending F, which makes a tritone with B in the next chord, becomes after- wards the 7th of G, and fo is refolved, as beloaging properly to it, before the clofe in C : whereas in defcending to the next chord, which is C E G, F cannot be held on, and confequently there can be no refolution. It appears to me evident, that there is no poffibility of going through the octave in counterpoint with- out a difcord, and therefore the octave, confidered as proceeding by tones and hemitones, is merely artificial. Tartini's laft obfer- vation is a proof of this ; for if every note were natural through- out the fcale, i. e. if the fucceffion were natural, it would be quite indifferent whether we afcend or defcend, as in the diatonic hexa- chord and heptachord. §87. I am now coming to the conclusion of the 4th chapter, and Perfection of mall give fome of his obfervations on the doctrines contained in it, in his own words, as follows. " In relation to the univerfal " diffonant I 5* 3 ■« diffonant fyflem, the fundamental harrnotiy by which the dif-CHAp. IV. " fonances are regulated is always diatonic ; as there is not, " nor can be, any cafe, in which a difTonance is founded on any " other notes but the 3d, 5th, and 8th. Here then is explained " by practife what I undertook to prove demonftratively in the " fecond chapter, in relation to the hexachord, as to the period where the parts were Chap. V. worked with great judgment and labor, and where they produced Vw -"" ,v "-' a great effect, as none of the common paffions were to be excited, § 109* and only a pomp of folemn and grave harmony was or ought to Old church* be expected ; for I look upon the mifererfs and ft ah at mater's o{ mu ^ iC * later matters to be deviations from the genuine old church ftile. I can for myfelf fay, that I never was fo little pleafed with mufic, as with what I heard in the churches in Italy ; it being fo ill fuited to the folemnity of the place* and the occafion *, and fome of my friends exprefFed the fame fentiments : So that, as church-mufic at firft carried a bad tafte into opera-mufic, the reverfe afterwards took place, and church-mufic now fufFers, in its turn, from the influence of its fafhionable rivah The latt- mentioned perverfion of mufic is of more corifequence § no* than the former, and much more blameable. If we are fuffered Corruption of to enjoy perfect tranquillity at the theatre, while the finger, 0X church ' mK I ic * at leaft the compofen> means to plunge us into all the tumult of varying paffions, the hurt is not great. But in the church, to fubftitute gay airs, or paflionate exprefilon, in the room of folemn mufic, is a perverfion that defeats the great end for which mufic was firft inftituted) as appears by the unanimous teftimony of hiftory. We know that this was the cafe amongft the Jews \ and it is no lefs certain, that it was the cafe amongft the pagans. I ihall content myfelf with producing one fmgle proof of this af- fertion out of Plutarch; who fays thus, Vol. II. p. 11401 ** Amongft the Greeks, in antient times, theatrical mufic was 4 not fo much as known. Mufic then was wholly employed * for divine worlhip, the inftruction of youth, and the praife x of illuftrious heroes ; and again, p. 1131, it is a part of * piety, and even a principal duty of man, to fing hymns to ** the gods, who have given to man alone an articulate voice.' L 2 I -now [ 76 3 C h a p. V. I now return to my author, who having mewed, in a v "" - " v ~ way peculiar to himfelf, that the Greek mufic turned entirely § in. upon the tetrachords, which he properly calls the props of Old Italian harmony, proceeds thus : " We have many examples in the " old church -mufk, which is all of the diatonic kind, of " cadences formed by the hernitone major defcending. I " mould be apt to think, that, amongft the antient longs, there " are fome genuine ones according to the example of the Greeks,. " if it was not for the entire contrail between the mufic and the " profody. It mull be owned, that there are fome fo full of gra- u vity, majefty, and fweetnefs, joined to the moll perfect mu- M fical fimplicity, that we moderns fhould find it a very hard " tafk to rival them. An inquiry into their date is of little imr " portance ; their mufical nature is all we want. It is certain " then, that they were made 'for a fingle voice ; if this voice was M multiplied by the ■ unifons of a whole people, that does not de*-> " rogate from the defign of the kiftijtution •, becaufe unifon is in M its ratio only one voice ; that they are fimple in the higheil u degree \ that they partake of the nature cf recitative, but largo ;•' " that many of them are like canzoni, or fongs, many of a mixt " nature; that none are confined to regular bars, but difcretionary; " and that in each of them- the key is determined, and is limited " by a convenient extent, as to grave and acute." This idea is ia general conformable to nature -, and, with regard to the univer- sality of circumflances, it is impoffible to contrive with more fim- plicity ; nor could the Greeks thcmfelves have contrived or in- tended otherwife* § H2. " The Greeks being, with refpecl to us, the firft inftitutors Idea of the " of mufic, it follows, that they fet out with this idea of fim- e mu J* c% " plicily ; becaufe, however capable men may be of ufing art " and refinement, yet, in the firil invention and institution " of [ 77 3 " of things, it is certain, that nature does all, art nothing j Chap. V. " which itfelf has no exiflence, but upon the data of nature. i** 00 ******* " In this univerfaiity of mufical ideas, I hold for certain, that " the antient modes of the Greeks agreed with our old Italian " modes, which I muft here diftinguifh from our prefent modes* " Of thefe lafb, I ihall foon give an account. The fpecific " difference of the antient Greek modes confifts in the precifion ■" of movement, which we may call the breaking of mufical " notes, according to the different value of fyllables ; in the prc- cc cifion of c hoofing a certain voice in relation to grave and cc acute, which we will fuppofe to have been bafe rather than " tenor, tenor rather than contralto,, &c. ; in the precifion of " certain intervals, as props or re lis of the fong, and of thofe " leffer intervals (we may call them fcales) which ought to fill t£ up the greater, and to be limited to a certain extent \ in " the precifion of the manner of expreffion, which is different " in every different mode, (we call it tafle) according to the " nature of the paffion intended io be raifed ; in the precifion " of a certain inftrument to accompany the voice, fuch as " fuited the mode and the paffion. Thefe are all the dictates « of nature •> but I do not undertake to enumerate them all. " Add to this, that amongft the Greeks the mufician was joined tc to the poet, the poet to the philofopher ; and th at the fame " perfon, being mufician, poet, and philofopher, treated natural " fubjects in conformity to nature, amongft a people lively, " cultivated and interefted in the fubjects themfelves." Tartini, in the preceding paffage, has given a moil formidable § nj, lift of requisites to qualify a man to produce any thing extraor- Unknown or dinary in mu-iic. If we are not to look upon our author as ^ de fP'J ed h*^ mere enthufiafl, a modern compoier, cne would think, muft be very full of hiaifelf, who would not blulh when he examines his own r 78 i \P. V. own works by die rules here laid down. However, human ria~ ^— -"v— — J tunj i 3 wonderfully ready at finding out reafons for felf-compla* cency •, and here the expedient is at hand -, for almoft every mart compares himfelf with the rival of his own time ; his ambition looks no farther ; and 'tis a thoufand to one, if he mould deign to look backward, that he pities the ignorance or bad tafte of for- mer ages, inftead of trying to gain inftruction from them. But to return to my maften § 114. " I am fat from thinking that mufic pafted from the Greeks koman mufic " to the Romans with the idea I have given •, much lefs from n °ttfo Greek. " t ^ ie R° mans to us. From thence fprung its declenfion and " total destruction. What remained, amongft our old Italians, is 6C only the material fubftance, flript of the greateft and moil " important parts of the above-mentioned precifions. That in " the modes of the old ecclefiaftical hymns is preferved faithfully, " and with precifion, the nature of the mode, according to the " refpective rules eftabliihed, is certainly true -, but there wants " fomething more •, for it is not proved, that they are the rules " which the Greeks followed. For the reft, the movement, or " breaking of the notes with a proper ratio, and the profody de- " termined for a certain effect ; the determinate aftlgnment of the " fong rather to a fpecific grave, than to a fpecific acute voice* " and the contrary -, the choice of certain intervals, rather than " others -, the expreffion of the fong, rather in this than in that " manner ; the choice of the inftrument proper for the mode ; all " thefe things from that time were neglected, and have never been " thought of fince. What we have added of our own are, fimul- " taneous harmony, i. e. the combination of many voices toge- '" ther ; the modulation -, and a fine manner or tafte. As to the " effect which our harmony can produce, in refpect to the pur- " fidered. ec I have above diftinguifhed the old Italian modes from our § 115. " truly modern ones. The diftinction was neceffary, in regard Modem modu* " to the modulation, which, as I have obferved in another place> lattm% " and you very well underftand, means the paffing from the tone " propofed to a different one •, but which has relation to the tone " firft propofed. It is not fufficient, for the prefent purpofe, to " give a general explication - 9 it is neceffary to come to partial- " lars, in fuch a manner as to convey a compleat idea of it, and " that too fcientifically ; becaufe it is an effential part of our mo* " dern mufic, and therefore ought indifpenfably to have a place " in this treatife. This then will be a proper place, as being " neceffary here, in order to make a comparifon between the " modes. " The principal foundation of our modes arifes from the very § 116. " three notes of example 3, fig. 1 ; upon which we faw the har- The fame fub- " mony was founded - 5 from whence the common diatonic fcale^ continued, " was deduced. The foundation is the belt poffible, becaufe it " is reduced to the numbers 6, 8, 9, 12, and therefore is a foun- " daticn common to us and the Greeks. The notes expreffed " by thefe numbers are, and all put together " will be r, A, £, B 5 /, D. Thefe fix notes, deduced as was men- " tioned, and underitood as firft bafes, are the whole foundation " of our modulation j which may wander and circulate through [ 8o ] C H A i 5 . V. cc any of the above fix notes, by transferring the fcale and the haf* { v " ' " rnony of C •, which, relatively to the example, is the principal cc tone propofed, and in which the harmony ought to begin and " end 5 to G and F for the harmony of the 3d major, and again, " by transferring the fcale and harmony of A •, the relative note " with a 3d minor to C •, into E and D, for the harmony of the " 3d minor. Hence arifes in our compofitions a prodigious num- " ber of mnfical accidents •, and therefore we deviate from the cc diatonic fcale •, becaufe G and E have a diefis, or fharp, in " the key ; F and Dab molle, or a flat. By modulating in " the afore- mentioned notes, and determining by harmonic ca- " dences the tone arifing from the fcale, and from the harmony " relative to them, the occurrence of thefe refpective accidents, " and the employment of them, are inevitable ; and this the " fubftance of our modulation, The order of it is not eftablifh- " ed by fixed and certain laws, and in general it is regulated " by the fentiment of the compofer -, though, indeed, it may be " faid, that fentiment brings us acquainted with many truths, " which ferve afterwards for laws. § 117. " The paifing, in the modulation, from the principal tone with The paffage " a 3d major, to the 5th of the tone, is pleafing, according to cZal tone to "" common fentiment \ and therefore that is made a rule. This' the 51b natu- " ru } e \ s founded on principle, and confequently can be accounted " for. The tone with a 3d major is by its intrinfic nature har- " monic ; therefore the paffage of the modulation, from the " principal note to the 5th, is conformable to the nature of the " harmonic fcale \ becaufe the paffage is from the extreme to vc the mean. From this moil certain principle it happens, that tc when, by the modulation, the tone, fenfe, and period are once " fettled, all men, by the force of natural fentiment, feel the re- * c pugnance that occurs, in pafling with the modulation from 3 " the [ «« 3 ** the principal note of the tone with a 3d major, to the 4th Chap. V, * c of the tone. This repugnance arifes from the contra- " riety of nature. The 4th of the tone divides the octave c< of the tone arithmetically. If the tone is with a 3d major, " which is harmonic by nature, we ought to feel a repug- " nance : If the tone is with a 3d minor, which is arithmetical " by nature, we fhall perceive no repugnance. It is true, that " this repugnance does not arife from any defect that is in the " original plan, or in the compofer. The tone of C is compofed " of two natures, harmonic and arithmetical ; and therefore the " modulation may rightly proceed through the two means, har- " monic and arithmetical. However, when there are in the " fame tone the two modulations, the comparifon that arifes " necerTarily, from their being near to one another, difcovers " the perfection of one, and the imperfection of the other, and u makes us perceive the repugnance. x< In general, if we attend to the nature of the tone, and to § 118. " the neareil relative notes, fo that the modulation may proceed Modulation " by fteps, and not by jumps ; (it would be, for example,^*? trJnji " a jump, and not a ftep, in modulation, to pafs without a pro-tfw". " per medium from a tone with b molle to a tone with a diefis x, " and the contrary) ; if we attend to the keeping of the modu- " lation more in the principal tone, than in the accefTory and re- " lative tones -, the contrary of which is often feen ; and parti- is clearly true •, but I break in upon him, in order to prove how neceflary it is to make the diftinction he has made, in order to get rid of a very extraordinary innovation, lately introduced, of bringing the Italian manner into our old Englilh ballads ; which I am told, for I did not choofe to hear fuch an unnatural mix- ture myfelf, was praclifed on our ftage j but, abfurd as this may be, Tartini will, foon give us an* inftance, which will mew the rage of good tafte full. as ftrongly ; for he continues, and fays, c - In our churches, the Miferere mei Deus is performed; and § 125. " on the ft age heroes and heroines go to death with the very fin eft Abufe of goorf " mufical graces above mentioned. It is well that cuftom and aJ e ' " habit do not give room for reflexion ; however, very little re~ " flexion is fufficient to turn all the pleafure, that can be re- ** ceived from the moft perfect execution, immediately into its " contrary. The fong adapted to the paffion, the voice adapted u to the fong, both as to its natural quality, and as to the act of " modification, as well as to its pitch, will always prevail, in " every time and in every circumftance. This is all that can " be called general. If we defcend to particulars, I underftand " very well the propriety of adapting our mufical graces to a. " great number of fongs ; but of the adapting of thofe graces " to all fongs, I underftand nothing, nor ever fhall. I am too " much perfuaded and convinced, that, in order to have a fong " truly adapted to the paffion that is expreffed by the words, «* every fong ought to have its individual and particular modes , " of exprefiion, and, in confequence, its individual and fpecific " good tafte. That the Greeks underftood and praclifed in this " manner was abfolutely neceffary for their intent ; a propofi- " tion fo true, in my opinion, that, had they aded otherwife, "■■I. would. [ 88 ] Chap. V." I would deny the fact, the hiftory, and the poffibihty in na- v— — y— •— ' " turc. If we underfland and act otherwife, the reafon is, that " mufic alone, and feparated from any other confideration what- " ever, is become our only aim and intention. This being pro- M poied as genus, fpecies, and individual, and every thing being " referred to that alone, our harmony, our fongs, and our good ^ c tafte do exceedingly well. In this fenfe, we have, here and " elie where, moft excellent compofers and performers, whofe " fkill pleafes and fuits the genius of all Europe ; a mod certain " fign, in general, that this is right in nature, for nemo omnes " fallit. But, if the fame end was propofed as that which the " Greeks had in view, we are very far from a poffibility of ob- cc taining it v/ith the means we ufe. Our harmony is in oppo- " fition, as including different fpecies of grave and acute : In " order to obtain their intention, one fpecies only, individually " belonging to the pailion, muft be employed. Our fong is in " oppofition, as being modulated according to our art ; as being " unconfined by any reference to profody, either in matter or in " form -, as not being obliged to choofe intervals of a greater or " lefs extent, as to high or low, nor tied down to the choice of " a determinate voice. § 126. " If we would therefore purfue the fame end which the Greeks How the paf- " did, we mould act quite contrary to what we do -, we mould ''rioted* ' S " ma ^ e u *" e °f one principal tone only ; we fhould regulate our " mufic by our profody, as to long and ihort fyllables, and " particularly in refpect to metrical feet proper for the paffion - 9 cc a thing as neceflary as it is difficult ; to which feet the fong * ought to correfpond identically : We fhould ufe with precifion " certain intervals chofen with analogy to the nature of the pat ct fion •, (neceffary alfo, but difficult ;) we fliould ufe a determi- " nate extent of notes, as to. grave and acute •, and alfo a fpecific " voice, [ s 9 ] c * voice, rather grave than acute, rather in the middle than the Cm a p. V t " extreme - 3 or the contrary, according to the nature of the V ~**"'V"~ " paflion. But laftly, our good tafle is in oppofition to the end " the Greeks propofed, as being jufl the fame in every fong " whatever, and as being formed of fuch component parts as " carry with them an evident contradiction to nature, when ap- " plied to all circumftances without diftindtion." Whereas good " tafte ought to vary perpetually, according to the different " paffions ; and mould be compofed of fuch minute component " parts, as are fpecific and individual to the particular mode of C£ long required by the paffion, and never transferrable to any " other mode. If the paflion is mixt wi.h other pafiions, as " frequently happens, in that cafe there is one generally pririci- " pal and predominant, and this mufl be the chief object. If " two paffions are equal in degree, which is poflible, then in the " fame long the object of the compofer will be doubled, in pro*- " portion to the force of the two different paffions. " I am entering too far into this affair before I am aware; § 127. ." not too far, becaufe I doubt of the truth of the foregoing pro- The difficulty " pohtions : but becaufe, great as the obfcurity of this affair °f ^ 0 ~" this fi*K&> ?I wiU tel1 y° u ' with m 7 uil]al Sincerity, that by 44 word of mouth I mall have no difficulty to declare my fenti- 44 ments to you in private, as freely as you can defire or command; 44 in writing, certainly not. I know my limits, and obferve them 44 rigoroufly. Nothing is more eafy than the communication of 44 what is written, either by reading or by a copy ; and I blufh 44 already at the thoughts of appearing as a mufician, poet, and 44 philofopher. I have undertaken more than enough, as a mufi- 44 cian only ; infomuch that I am rather confounded, than f.itif- w fled, with what I have already done. Let this be my utmoft 44 boundary ; or, if I prefume to go one ftep farther on this fub- 44 jeer., let it be to make a particular malicious obfervation. It 44 is this : Wherever there is mufic (and mufic there is, of fome 4,4 fort or other, in every nation) it is never found without ♦ 4 dancing. This is a key to difcover and deduce movements, 44 and rnufical breaks, relative to the diverfity of people ; nor is 4 * there any danger of being led into an error by attending to it, 44 as f 99 1 "' as it is the very language of nature. From hence afifes that Ch a p. \ t , * conftancy, for ages, in the ufe of the fame kind of dance* v ~"~^ r "~ w adopted by each nation rcfpe&ively, to fuch a degree, that at 6C laft dances get their name from the nation where they are prac- Ci tiled. In each of thefe dances, we fhall infallibly find the " phyfical movements correfponding with the long and fhort u fyllables, and metrical feet ; it is iuificient to obferve and 6C make ufe of them, which is no difficult matter. You have c * my philofophy- on this point, which I call by a more proper €C name, a malicious obfervation, Do you, illuftrious Sir, judge " whether, in the prefent cafe, it is better to be a philofopher ic or an obferver. Here I put an end to the 5th chapter, much " better pleafed with myfelf for havmg obeyed you, than for "' having written what I have/* Before I enter upori aft examination of Tartini's next chapter, § 142-". I fhall give the fyftem of the 3d minor, which I prorated § 44, *$d.mnm and which I chofe to place here, as the knowledge of it is parti- cularly neceflary for underftanding the remaining part of his book : But as I have not hitherto fully explained the foundation of the fyftem of the 3d major, or, at leaft, have not put it in ir point of light, which will ferve to explain the fyftem of the 3d' minor, I fhall begin firft with that It was obferved, § §^ that Tartini,- in order to fill up die qc~ § 143- tave, made ufe of the mufical intervals C, F, G, Q expreffed bj y major. the numbers 6, 8, 9, 12, which Pythagoras is fuppofed to have firft difcovered, vide § 12. Why thofe notes only can be ufed as bafes, fhall now be made evident. No notes then can be prime bafes, but fuch as have perfect 3ds major and perfect 5ths belonging to them \ for this is the precife and fpecific idea fur- nifhed by the firing of three founds, § 2. With thefe the ear o % '£ 3d, A perfect. \ 3d, B I 5th, D [ ">o ] a r. V. is fatisfied, and with none elfe -, and what Ariftoxenus fays, p. 33, is certainly true, though mifapplied by him, that the fenfation of a mufical ear may be almofl looked upon as a firfl principle in mafic. Let us now examine the notes of the octave by the rule above- mentioned. f 3d, E perfect. C has for i , _ c ~ / 5th, G perfect. D - - 3d, F imperfect. E - 3d, G imperfect. 5 3 / 5th, C perfect, perfect, perfect. A 3d, C imperfect. B 3d, D imperfect. From hence it appears, that there can be but three prime bafes, viz, C, F, and G, in the diatonic octave. § 144. From the foregoing obfervation it appears alfo, that all other t^d major. notes befides C, F, and G, when ufed as bafes, muft have fome figure or figures belonging to them \ which figure or figures, when put over them, fhew that fuch bafes are not prime or fun- damental - 9 and at the fame time give the true bafe ; fo that all of them together make 3d and 5th. Thus to go through the notes of the octave, C, F, and G, have no figure over them ; be- caufe 3d and 5th are played with them of courfe. D ought to have I over it, which fhew that it is not prime bafe. Now, the 4th to D is G, and the 6th to D is B ; fo that, as it appeared be- fore, that B cannot be a prime bafe, G muft be fo in this cafe. Now, B, D, make 3d and 5th to G. Next, E ought to have « over it •, therefore C, which is 6th to E, is prime bafe ; and thefe two iiotes, along with the 3d to E, which is always fup- foied [ ioi ] pofed when the 4th is not marked, give the 3d and 5th to C. Chap. V. G ought to have \ over it for the fame reafon that D has : For *■** ^V~"— ' though it is fometimes a prime bafe, yet as in regularly afcend- ing through the notes of the octave, it goes immediately before a clofe in F, it muft be confidered here as 5th of C. Next, A ought to have 6 over it, for the fame reafon that E has. Laftly, B ought to have 6 over it, for the fame reafon ; fo that the notes of the octave, ufed as bafes, Hand thus, along with the corre- fpondent prime bafes : t 6 I 6 6 CDEFGABC. C G C F C F G C Let us now proceed to the inveftigation of the fyftem of the § 145, 3d minor, which I fhall do in a way different from what Tartini $d minor. takes, but ftill making ufe of his clue. lie obferves, that there is a note arifing in the hexachord, which he marks E ", fig. 1. ex. 3". This note is a 3d minor to C, the fundamental and nniverfal bafe to all the notes in the hexachord. Here then is a beginning given to a fyftem very different from that of the common diatonic fcale. I have lhewn § 40, that this note is a confonance, as every note in the hexachord, whether it be arithmetical or harmonic, muft be ; as they all arife from aliquot parts of 60 •, and I have befides given, § 41, fome reafon to think that all thefe notes do, poten- tially at leafr, if not actually, exift as founds, upon finking a mufical firing \ nay, that they do fometimes exift actually, I fhall endeavour to prove afterwards. But, however this may be, we certainly have got a beginning for the fyftem of the 3d minor, in the moil natural, and, I may fay, the only natural, way : For whatever fyftem, as Tartini obferves, does not arife from the harmonic, muft be arbitrary. To which 1 will add, that, to fuppofe any thing to be arbitrary, which is univerfally pleafihg, [ »«* 1 Chap. V. pleafmg, Ts to uippofe that our fenfes were franud without any , ~*~~'y~~' fpecific adaption to the objects that affect them ; and that in fome particulars only, v*hen in others of the fame kind we can trace the utmoft regularity •, which is a fuppojition too wild to be admitted. § 146. But to quit theory 4 , arid come to experiment. Let any mu~ bi-vefii^atkn fician, after having fully fettled the tone of C with a 3d major* of the \dmi- c kf cen d from C through G, F, E, to E^, and he will find, that he is brought out of the fyftem of the 3d major into that of the 3d minor imperceptibly and agreeably ; and that he may, if he pleafes, by playing D after E *>, make a clofe in C. In this cafe, lie is got full into the fyftem of the 3d minor ; but how to con- tinue in it is the difficulty. This difficulty, great as it is, I will now endeavour to folve, expecting the indulgence of the reader, if I fail, in a point which has never, as far as I know, been cleared tip fatisfactorily j not even by Tartini himfelf ; though he has eftablifhed the true fcale, and the right ufe of it, by a very inftructive example, and alfo furnifhed every prin- ciple I make ufe of in this intricate affair. In order to un- derstand it, I defire the reader to recoiled: what was faid, § 143, about the fleceffity of having 3ds major and 5ths to every prime bafe j but we muff except the 3d to C, in this cafe, from the very nature of the thing. We have got therefore C, E K G ; but, in order to make a full clofe upon C, its 5th, or G, mud have 3d major and 5th ; i. e. B and D. We have therefore got B, C, D, E ®, G. Again, the 3d found to C, E^ is A* 3 ; vide fig. 3 : Therefore only one note, viz. between E ^ and G, is wanting to compleat the octave. Let us fuppofe it to be F,.then the 3d found to F, A k, will be D^- but D was fettled, as well as A b : Therefore, fince A b , which, along with F, produced D •, (which cannot belong to the fcale) cannot be [ *° 3 3 be altered, F necefiarily mufL Let us make F * 3d major to Crap. V. D, and the 3d found to F*, A**, is B, which belongs to the } ^ 000 ^ mmmJ fcale. I might as well have determined F * by the 3d founds to D, F and D, Ff. In the former cafe, it is B", which cannot belong to the fcile § in the latter, it is D, which does belong to it. I mull obferve 3 upon this occafion, that though the 3d founds, belonging to the fyftem of the 3d minor, if heard, would be ex~ tremely difagreeable, as being double* and their progrefnon auk- ward, yet they always belong to the key - 9 as will be evident at once, to any one who examines them. We have now got all the notes belonging to the fyftem of the 3d minor ; becaufe, by changing any note, we change the relation it bears to every other note, and confequently change the fyftem : Therefore F and B & are excluded. Let us next examine, which notes of this fcale can be prime § 147, bafes. D cannot, becaufe D, A " makes an imperfect 5th ; E Bafts in the cannot, becaufe B makes a fuperfluous 5th with it - F^ cannot, & «w*w» becaufe it makes a defective 5th with C -, G may be prime, becaufe it has a perfect 3d and 5th -, A" may be alio prime, for th^ fame reafon •, B cannot, becaufe it makes a 3d minor with D ; C is prime of courfe : So that all the prime bafes are C, A % G, I have by means of this theory, which is chiefly borrowed from Tartini, and by the help *sf his mufxcai example in the 3d minor 5 given a fcale with the bafe, vide fig. 9. It appears by that fcale, that the pafiage from 1 to A 5 , G 9 F& 3 ^nd from A b td G, F *, E*^, are perfectly regular. It will be fiid, by way of objection to the fcale above-men- | j^g; tioned, that no piece of in uric is to be found, where the notes, ofyttw!, therein fpecifed as belonging to the fyftem of the 3d minor, are alone employed. I readily own that it will be difficult to find 4 fuch [ io 4 ] Chap. V. fuch a piece : but yet pafTages of that kind are to be met with w " - w_ here and there in the bell Italian compofers, though the practice is not ileady and uniform. This is not extraordinary when there is a want of principles to direct : Nor would it be extraordinary if no fuch paiiage, was to be met with at all : fince, as Ptolemy rightly obferves, Harm, page 2 : 6 the fenfes difcover what- is nearly c true, and receive from reafon what is accurately fo ; whereas c reafon receives from the fenfes what is nearly true, and dif- c covers what is accurately fo.* And afterwards, page 3 : c A ' man might think a circle made by the eye only to be very accu- c rate, till he has feen one made by a pair of compaiTes - s fo it is 4 with the ear in mufic' For this reafon too much pains and ftudy can never be employed in order to difcover principles in every branch of knowledge - 9 I mean when the pains and ftudy are pro- portioned to the dignity of the fubject. § 149. But the deviation from the fcale above-mentioned, is not always Deviations in owing to want of principles ; on the contrary it is frequently prattue. ow j n g to a change of key, which, though not attended to, is real. The tone of the 3d above, and that of the 3d below, i. e. of E^ and A", are fo clofely connected with it, that we are per- petually led by nature to touch upon one or other of them ♦, and whenever that happens, the 4th or 7th muft be altered reflectively. But that happens whenever the 3d or 6th of the principal is in the beginning or middle of the bar : i. e. when they are accented. I will not. affirm, that no change ought to be made in any other cafe •, but I do not at prefent recollect one, where there ought to hz any \ and leave that point, as well as many others, to be de- cided by proper judges. I will fay thus much, however, from my own feeling, that by fubftituting B and F *, in the room of B " and F, in many places, in fongs and other pieces, the effect, was greatly improved. I mail t * e 5 ] I mall make a few obfervations on the aforefaid fcale. i&Chap. V. then, there are no two whole tones, following one another, v — -"^ -^ throughout the octave. This was one of the characteristics of § 150. the antient chromatic,, vide §83. 2dly, There are two tetr%- Ohfirvation chords; viz. from F* to B, and from E b to A b ; confifting °^ ^ mi ~ each of two diefes ; which, both together, are lefs than the un- compounded triemitone. This is another characterise of the antient chromatic; Ariftid. p. 18 ; Euclid, p. 10. gdly, The nature of the 3d minor is foft and melancholy, which is another characteriftic of the antient chromatic. Many teilimonies might be produced in proof of this afTertion ; but I fhall content myfelf with two only at prefent : Ariftides, p. in, fays, the chromatic is very pleafing and plaintive ; and Plutarch, Vol. II. p. 109, puts this query, Why does the chromatic foften the mind ? But I do not conclude, from thefe refemblances, that they are the fame ; on the contrary, I am certain they are not, both from what Tartini has faid, and from o:her reafons. 4thly, This fyftem, when practifed in all its purity, is adapted to exprefs not only foftnefs and melancholy, as I obferved above, but peculiarly alfo the conflict of jarring pafllons of the plaintive kind •, as love mixed with defpair, jealoufy, &c The perpetual contrail: of great and fmall intervals, contributes, I imagine, very much to produce this effect. I fhall now give what I promifed %6o^ viz. the method of § 151* tuning the Harp for the 3d minor ; which is as follows : From Tuning the C to G, and from G to D, perfect 5 ths ; from G to B, upwards, y ^/' a perfect 3d major; from B to F*, upwards, a perfect 5th; from G to E , downwards, a perfect 3d major ; from E " to A° , downwards, a perfect 5th : For accidental notes., from C to F, downwards, a perfect 5th ; from E b to B b , upwards, a perfect P 5th. [ io6 ] Chap. V. 5th. Thefe are the principal accidents; the reft mull be ma- w '^> "" J naged as fhall be found moft expedient upon trial. I mull ob~ ferve, upon this occafion, how neceffary it is for harpers to be particularly careful about tuning their inftrument accurately; as the poflibility of doing it is the chief circumftance that gives it a fuperiority over fome other inftruments -, and a great advan- tage that is. § 152. I quoted before, § 62, many paffages from Englifh writers, Pinedo on the that feemed to put the Harp on a very refpectable footing. I az *' fhall now quote an exprefs proof in its favor from a foreigner, and one who I fhould imagine was no bad judge of fuch matters, both as a theorift and a practitioner. His name is Thorn., de Pi- nedo. Of his fkill in the theory of mufic, he has left us a very fufficient fpecimen, in his notes upon Stephanus de Urbibus y where he has inferted a ihort differtation on mufic, which is very well put together ; in which are thefe words : ' I was incited to * give an account of mufical intervals, by the learned differtation 4 of Joan. Albert. Bannus -, in which he defires fome one will * give a new conftitution of mufic, by placing hemitones between * all the tones, fo that the art of mufic may be rendered com- * pleat, and fit to move the paflions. I will gratify his defire, ' which I am enabled to do by my fkill on the Harp with two ' rows of firings,, the Queen of all mufical inftruments \ in which, c on account of the number of its firings, viz. 39, may be feen, 1 as in a glafs, all the mufical intervals ; and by whofe fweet c harmony,, arifing from the difcordant agreement of firings, "* ftruck with the fingers inftead of a plectrum, I have long not c only amufed. myfelf, but have alfo relieved the mifery attend- * ing an undeferved banifhment from my native country.' Artie. Timoth. Lpro, [ «7 1 I promifed likewife, § 65, to fay fomething more of bolus's Chap. Y. Harp, that extraordinary inftrument invented by Father Kircher, *""" -"V"** as extraordinary a man, who was made np of whim and genius. § 153. The wonderful effedt of this inftrument has been felt by all who iEoIusV have heard it, and have an ear for mufic. It has produced two ar ^ elegant poems in our language, and afforded an opportunity for ^imagination" to difplay itfelf in terms though ilrong, yet not exaggerated. I mail quote one of them at length -, and I pitch upon it, in preference to the other, becaufe it gives a compleat idea of the great variety of mufic produced by a few fimple unifon firings, and becaufe it tends very much to illuftrate and confirm my theory > vide § 39, &c. ODE on lOLUS's HARP: Dods ley's Mifcell. Vol. III. p. 211. 1. JEthereal race, inhabitants of air ! Who hymn your God amid the fecret grove ; Ye unfeen beings, to my Harp repair, And raife majeflic flrains, or melt in love. 2. Thafe tender notes, how unkindly they upbraid, With what foft throe they thrill the lover's heart ! Sure from the hand of fome unhappy maid, Who dy'd of love, thofe fweet complainings part. 3- But hark ! that drain was of a graver tone ; On the deep firings his hand fome hermit throws -, Or he, the /acred bard ! who fat alone In the drear wafle, and wept his people's woes. P 2 4. Stich [ J08 J Chap. V. 4. S ~* ~v mm - J Such was the fong which Zion's children fung, When by Euphrates' flream they made their plaint % And to fuch fadly folemn notes are flrung Angelic Harps, to footh a dying faint. 5- Methinks I hear the full celeflial choir Through heav'n's high. dome their awful anthems raife;. Now chanting clear, and now they all confpire To fwell the lofcy hymn from praife to praife. 6. . Let me, ye wand'ring fpirits of the wind, Who, as wild fancy prompts you, touch the firing, . Smit with your theme, be in your chorus join'd ; For till you ceafe, my mufe forgets to fmg. § 154. In the foregoing Ode, effects are defcribed, and I think very Its effea not truly, which cannot be accounted for by the common fyflem : vcuuntedfcr. p or ^ harmonic notes are only %d T 5th, and 8th to the principal; which feem to make but one found, as appears by adding 12 th and 17th to the pipes of an organ •, vide § 6. It is true, other intervals are produced, as 6th major and minor, 4th and 3d mi- nor. But thefe will not account for the phenomena •,, whereas, if we add the arithmetical notes, the number and nature of the intervals is greatly altered. The number is 19 ; among which are . 7ths, 6ths major and minor, 5ths, 4ths, gds major and minor, a tone major and a minor, a hemitone major and a minor. But it will be afked, How mould thefe notes be heard in zEolus's Harp, when they never have been heard on a fingle firing ? I anfwer, That the lower or arithmetical notes may want to be ex- cited to vibrate didincTly, by a greater power of harmonic notes than C 109 ] than what a Tingle firing furnifhes. There is an obfervation, in Chap. V. Lord Keeper North's trad on mufic, which illuftrates and con- Kmm ^^"^ firms my reafoning. He fays, p. 20, ' An organ-pipe of a * very deep bafe will not fpeak fuddenly, when it is alone ; but c if an o&ave be in play at the fame time, it will anfwer the quick- * eft touch." I v/ill alfo obferve, that the double bafe, when played upon alone, gives the moil languid tones imaginable \ whereas, when accompanied, its tones are firm and vigorous. But I can go one flep farther flill, and prove, that the arith- § 155. metical notes not only may be founded as I have fuppofed, and An illuftra- m part rendered probable, but that they actually have Deen ^7;iv# founded; It is notorious, that the German horn has the fame notes as the trumpet marine, and no other. Now, I remember to have heard Charles, the famous performer on the German horn, found fome low notes, which furprifed me, and made me fufpect that all the theory about that inftrument was falfe. This idea remained with me for many years, and I never could hit upon any folution, till the foregoing theory occurred to me, which feemed to take away all the difficulty. Charles was reckoned an admirable performer, and when he blew the low notes above- mentioned, he ufed no artifice whatever, but what arofe from his conftant experience and genius. I afked him, at the time, what the notes were which he founded-, he told. me,, but I; have now totally forgotten them : thefe particulars however I remember, which are very much to the purpofe, viz. that they were four defending notes, and two of them, as he told me, and as I heard, were what we vulgarly call hemitones ; from whence I conclude, that the notes muft be G, F, E, E^ ; for there are no other low notes but thefe, that can pofTibly be founded. If other performers would learn to found them, the ufe and effect of the horn might be much extended. The clofe and, [ no ] Chap, V, $nd in timsM connexion between the arithmetical and harmonic *•-— V"- J fyftems appears from this, that if you take away F, you deftroy all our mufic at once, but that on the German horn, trumpet marine, and common trumpet -, all which inftruments have pre- cifely the flume notes. From the whole, I conclude, that no one has hitherto Untwifted all the chains that tie The hidden foul of harmony. But I return to Tartini, v/ho begins his 6th and laft chapter thus : Chap. VI. "I am now gotten into a fafe harbor, being returned to the s ^^^^ mmJ « prefent fyftem, relying upon which, I proceed to the examina- § 156. tc t i on f thofe particular intervals and modulations, which are Modern inter- u commonly ufed in modern mufic, but were not known in the delations. ' " I5 tn century. If there was any particular compofer who ufed* " in thQfe times, fuch intervals, of which I am going to treat; " or whether the ufe of them began afterwards, I neither know, " or is it of importance that I fhould know ; it being a fufficient « reafon for me, that they are ufed at prefent, to examine their u foundation and nature. 55 He then fhews the modern method of managing the fuperfluous 2d, the diminifhed 3d, the di- minished 4th, the diminifhed 7th, the fuperfluous 6th, and the fuperfluous 5th. But befides the intervals, which he has parti- cularly confidered, other methods are practically deduced from them ; but thefe, he -fays, are fufficient to give an idea of them. Then adds, " All thefe intervals are included in the pre- " fent univerfal fyftem ; they are the very intervals in the mu- " fical example 4, fig. 1, with which the cpmmon diatonic fcale is r**- J of great confequence, as follows : " I grant, that fuch a kind of mufic may be practifed ac- § 157. " cording to the foregoing fcale ; viz. D, E, F, G*, A, B b, C *, Firft bafes in tc D \ and with the utmoft rigor, according to the foregoing in- * ' 3 minor, " tervals, both in the harmony of the fundamental bafe, and (i. e. that kind of harmony) from whence the diatonic fcale is de- duced, can be fir ft bafes. For the diatonic fcale was deduced from the %ds and 5ths to the prime bafes ; vide § 53 : Therefore e converfo, where a 3d and 5th cannot be had to any note, that note cannot be a iirft bafe. So much as to his firft rule, in re- lation to what he calls chromatic : In relation to his enharmonic, I need fay nothing, having fhewed before, article 84, that it is moft probably built on a miftake. I proceed now to his fecond rule. § 159. « There is," fays Tartini, " no room left for any fapple- firft bafes m « mental rnufical accidents ; becaufe the fecond rule ought to " be the inalterability of the fcale, both in the harmony and in Second rule, « the finging part, otherwife nature itfelf v/ould be changed; " and therefore, if you had a mind to make F firft bafe, in the '" key of D, taking away # from C, it would be an error. Like- " wife, if you were to make C natural, G natural, &c. firft bafes, " it would be an error, becaufe it would be an inverfion of nature. " In fine, as the common fcale is unalterable, in relation to the " nature of the diatonic genus, fo ought this new fcale to be " unalterable, in relation to the particular genus of the prefent " fyftem ; and .the more fo, becaufe thefe two fcales ought to " have certain properties in common. From the fame univerfal " principle, the diatonic fcale was demonstratively deduced ; and " the prefent fcale is alfo deduced demonftratively ; therefore " both of them are unalterable." I have obferved above, § 149, that if you change fome of the notes belonging to the fcale of the 3d minor, you go into the 3d major almoft infenhbly •, which, I imagine, has occafioned all the confufion in theory relating to the [ "3 1 the fyftem of the 3d minor ; and confequently in the doctrine of Chap. VI. practical writers. But to return to Tartini. *-" — *r^~* " From thefe two rules we may practically treat this kind of § 160. " mufic j (i. e. with a 3d minor) and with an excellent effect, as p fa aical ex* " far as my own feeling, and that of other unprejudiced people, am P^ e in tf?t " can determine. See here an example which colt me but little " fludy and pains : The tone is transferred out of D, into A, c * for the convenience of the instruments." This example confifts of a piece in four parts in the 3d minor, where there is not a note which does not belong to that fyftem, and is therefore, I fup- pofe, not to be paralleled out of all the immenfe quantity of mufic which has been compofed fince the revival of arts in Europe. As to the chord which Tartini makes ufe of, viz. F, A, C, D^, which, he fays, contains no difcord, I cannot help being of ano- ther opinion. D * is no note of the hexachord, and therefore, if my theory is right, it mud be a difcord \ but any note belong- ing to the fcale may be ufed, if it can be refolved properly as D* is here upon E. What he fays afterwards, that if you put the harmony thus, D *, F, A, C, it will be harfh and awkward, is mort likely to be true, beeaufe the chord is entirely reverfed. As to what he obferves alfo about the 7th of F, that it ought not to be exprefTed by the letter E ", he is certainly in the right, if E & is taken for the 3d minor of C ; beeaufe there is not the fame interval between E^, F, in the key of B^, with a 3d major, as between F, G, in the key of C 3d major, which there ought to be •, for from E b, 3d of C, to F, is a tone minor -, whereas from F to G, is a tone major. Tartini thus goes on. " I have four things to add in relation to the above-mentioned § 161. " mufical example ; the firfb is, that I have defignedly difpofed Obfewations "the harmony of the four notes, F, A, C, D*, in different Z^phf^ Q^ " manners, [ iH ] Chap. VI." manners, fo that the effect^ the ufe and management of w-"""V— — ' " fuch intervals might appear. The 2d is, that this particular " fyflem is capable of many diflbnances, without any alteratibn " ■•■{ the given fcale, which is eafy to obferve. The 3d is, that c ..io^gh I have called this leak and .his fyflem chromatic and " enharmonic, I do not therefore pretend that it ought to " he called fb, rigoroufly (peaking ; however, what I mewed in tC the diatonic infpiflated fcale is certain, viz. that it is analo- " gous to the chromatic and enharmonic. — —But not to give " myfelf any trouble about names, it is fuffrcient for me, that " the difference of the two fcales is obvious, and alfq cf the two " harmonies -, fo that the diyerfity of the fyflem eafily appears. " I am fatisfied with having reduced to their genus, nature, and " principle, thofe intervals that we fparfedly and indifferently " ufe in praclife, without rule, and without category. The 4th " thing to be obferved is, and a thing of importance, that the " four notes, D, F, G s , B ", which are the foundation of this " particular fyilem, and which are precifely the diflbnances fet " forth in example 4, fig. 1, in relation to the diatonic fcale,, " in this fyflem are employed as confonances. Obferve therefore, " on one fide, the perfection of their principle, which is the " circle ; and, on the other fide, the falfe idea that muficians " have hitherto had, that diffonances are intervals difagreeable " to the ear. I am perfectly fure, that many people will be un- " commonly pleafed with this particular harmony, although " compofed of mufical notes that are to all appearance dhTonant ; " I am almofl certain, that no one will be difgufled with " them." § 162. I mud obferve, upon this occafion, that what Tartini jufl now Dijfhnaucct. faid, that the above-mentioned diflbnances are treated as confo- nances, is a confirmation of what I maintained above, § 48, that [ "5 ] that there are no dhTonances belonging to rriufic, but what arife Chap. . VI, from altering the harmony in fome parts, while in others it re-" % *** ; ~ a V~* mains the fame, Sec. This idea is perfectly clear and precife, and, I believe, perfectly true. This far is, I think, at leaf! certain, that my author gives no m&mte to the contrary, though he has fo fully treated this point. This is an idea I have long had, and am pleafed to fee I have no reafon to alter it. We are now draw- ing towards a conclufion : But before my author finifhes, he has fomething to offer, that will fully mew the ufe, and indeed the necefnty, of principles in mufic. It will ihew that ingenuity will not fecure a mufician from wandering out of his way, when he has not a proper guide to direct him. He will be like a pilot, who has neither fun, moon, nor (tars, to look up to. I mud ob- ferve, that the inflances hitherto given by Tartini, of modern intervals and harmonies, are what properly belong to the fyilem of the 3d minor, though by fome looked upon as licenfes -, but we are coming to fomething of another nature ; for he fays, " From the particular intervals mentioned above chiefly arife § 163. " particular modulations, which many at this time make ufe Extras agant " of. I fay chiefly, becaufe, as will be feen, there may be f onie ^<^^- u few modulations not dependant on them. I fay alfo many? be- " caufe not every one, who yet knows very well what he is about, " choofes to employ them •, nay, I have obferved, that thofe cc diltinguifhed artifts, who have exquifite fentiment, joined to " great know! ledge in their art, never ufe them at all. Thefe " particular modulations are, in reality, mere artificial deceits •, " btcauie, where the modulation ought topafs, by the nature of " the tone in which the compofition is diflinctly ihftituted, to •" futh a determinate and relative tone, it is made by artifice to " and they are adapted to proper words, which will always of- " fer themfelves in fome part or other of a drama. After all " that has been faid relating to practife, it remains to be con- " fidered, whether fuch notes of double ufe can demonftra- u tively ferve for that purpofe. It is evident in the higher! de- " gree that they cannot by any means, becaufe the difference be- " tween the hemitone minor and hemitone major is too great. " It is true, the lame touch of the harpfichord ferves for " D* and E^, but reafon makes a great difference between " them ; and therefore it is demonflratively impofiible, that the " two above-mentioned notes may be ufed interchangeably for " one another. The fame reafon may be applied to all other notes " of double ufe: therefore, demonflratively, fuch notes cannot " ferve for fuch a purpofe, for which they are practically made to uuaj>e, v *""" - < myris and Linus to play upon it -, and Linus taught Hercules* c by whom he [Linus] was killed. Orpheus alfo taught Am- * phion, who built Thebes, with feven gates, to the founds of ' his feven firings. When Orpheus was killed by the Thracian * women, it is faid, his lyre was thrown into the fea, and car- ' ried to AntifTa, a city of Lefbos, and that fome fifhermen hap- * pening to meet with it, gave it to Terpander ; who, having * adorned it very finely, took it with him into iEgypt, and * fhewed it to the priefts there, and gave himfelf out as the in- * ventor.' I chofe to give this account at length, as it exhibits a ftriking fpecimen of the genius of the Greeks, who had full as much vanity as ingenuity ; which is faying a great deal of both. In fpite therefore of this ridiculous claim, we muft allow the ^Egyptians to have been the inventors of the heptachord -, and if this was the cafe, nothing more is necefTary to make good my afTertion, that the art of mufie was begun in iEgypt, &c. : For, as furely as the Greeks learned it of the ^Egyptians, fo furely did the Romans learn it of the Greeks, and the reft of the world of the Romans, § 171. But it will be objected, that the mufic propagated over Europe Probably the has not been that confiding of feven firings only, which is iEgyp- taachordafo. t - an , ^ ut tna t confifting of eight, or more, which is Grecian, as being invented by Pythagoras. To this objection I anfwer, that I mentioned, § 13, fome fufpicions why I think his claim not quite clear : Amongft the reft, I cited a paffage out of Plutarch, about the divifion of the feafons of the year, which plainly alludes to the numbers of the octave. This divifion. is faid, by Arift. Quint, p. 145, to have been the invention of Pythagoras ; but he is certainly miftaken •, for making fpring as 6, autumn as 8, winter as 9, fummer as 12, we ihall have 62, 83, 93, 125 4 days, [ * 2 5 1 days nearly for thofe feafons refpectively •, which may probably Appendix. be right for iEgypt or Chaldasa, but certainly not for Greece; **- ""^ -* where, according to Euripides, and the concurrent teftimony of the old writers, fpring and autumn confifls each of 60, winter and fummer each of 120 days nearly. But Pythagoras, who was, if not 22 years, as Iamblichus fays, yet certainly a long time, among!! the /Egyptians, and being initiated in their myiteries, v/as better acquainted with their learning than any other foreigner whatever, in all probability flrft taught his countrymen the oc- tave expreffed by 6, 8, 9, 12 $ and from thence the very inven- tion of it was attributed to him. However, to fupport my afTer- tion, it is not neceffary to fuppofe the ./Egyptians to have in- vented the two disjunct tetrachords. We may have a great va- riety of very fine mufic with feven notes only 5 at leafl the Greeks thought fo ; for no more notes were ufed in the Dorian, Phry- gian, andLydian modes practifed by Anacreon -, vide Athenssum, p. 635 ; and Pindar mentions his lyre as having only {even firings, Pyth. 2, 130, et Nem. 5, 43 : Yet both thefe poets, who were nearly of the fame age, lived after the fuppofed difco- very of Pythagoras \ and Pindar, particularly, wrote the fecond Pythian ode above 60 years after that philofopher was famous. So much for my afTertion, § 54. I will take this opportunity of obferving, that the advantage § 172. arifing from the octachord of Pythagoras confuted in this, xh-ox Advantage/ whereas in the heptachord, where two tetrachords were joined*' together without an intermediate tone, you could not add ano- ther fimilar tetrachord, without going out of the key \ in the oc- tachord, on the contrary, you may add as many fimilar tetra- chords as you pleafe, and ftill keep in the fame key. This will become evident by confidering fig. 10 ; where B, C, D, E - 9 E, F, G, A, are two fimilar conjunct tetrachords s for from B to C k [ 126 ] Appendix, is a hcmitone, and from E to F is alfo a hemitone ; from C to D, as from F to G, is a tone, &c. ; and the key is C. Add now another fimilar conjunct tetrachord, viz. A, B, C, D, and it is clear that B muft be lowered, in order to get the hemitone re- quired •, and thus the key is altered •, for we are now got into F. B, thus lowered, is called B fa, and the fcale, fcala mollis ; as the other in C is called fcala dura ; but they are both in the 3d major. § 173' Egyptian jculpture painting. Norden, We have no method left of getting any idea of the old Egyp- tian mufic, but by fuppofing (what I believe is always the cafe, taintlZ" an d t0 tne difgrace of conceited ignorance has hitherto proved to be fo) a proportional degree of perfection in arts of a fimilar na- ture, as mufic, painting, and fculpture, may truly be faid to be. If this fuppofition may be allowed, there are remains in Egypt of the two laft-mentioned arts, fufficient to enable us to form a judgment of their mufic ; and fuch remains as will furnim us with a very favourable idea of it. Many teflimonies might be pro- duced on this occafion -, but I mail confine myfdf to two only, who, from their known character, are fully adequate to my pur- pofe. Norden, Voiage en Egypte, p. 102, mentions c obelifks c adorned with hieroglyphics, that one beholds with admiration •/ p. 170, fpeaking of fome hieroglyphics, c agreeable,' fays he, c to behold at a diftance ■, and when one is near, the colours c have a charming effect :' Again, ibid. c It is furprifing to fee c how the gold, the ultramarine, and other colours, have pre- c ferved their brilliancy to this time. Perhaps I fhall be afked, c How all thefe lively colours could be fo blended together ?. I « own, I cannot tell.' Again, p. 173, 'A coloffal head, dreffed c in the antient Egyptian tafle, finifhed with a great deal of art c and patience, with a fimplicity that is charming •, which makes c me believe it came from the hands of a great mafter.' M. 1 [ 127 1 M. le Comte de Caylus, Antiquities ^Egyptiennes, &c. Vol. I, Appendix. p. 4, fays, c It muft be owned, the Egyptian fculptors felt and ^^-V"-— > ' expreffed grandeur ; and it is in this that the chief and moft ef- § 1 74. * fential part of their art confifts \ becaufe this alone raifes the JEgyptian * mind of the fpectator.' Such a teftimony, from fuch a judge/™ 7/ ^ m is a fuflicient anfwer to any objections about the excellence of Caylus. the /Egyptian tafte in the fine arts ; and I might leave every un- prejudiced reader to draw his conclufions. But there is another paffage in Caylus,. which I cannot omit producing on this occa- fion, as it confirms what I cited out of Plato, § 169 ; and as the paffage in Plato folves a difficulty which Caylus feems at a lofs how to account for : c Arts,' fays he, c being progreffive in all c other countries, we cannot but fuppofe that they were fo amongft 4 the /Egyptians ; yet their works, fo far from favouring fo na- * tural a prefumption, have always offered me hitherto an equality c of tafte, form, and workmanfhip, which fnrprifed me. I ima- ' gined, therefore, that I ought to attribute this uniformity to a 4 prodigious antiquity, which hindered their firft works from < coming down to us. I imagined, afterwards, that the propor- c tions being once known and admitted, fuperftition and fcruplc * had laid an obftacle in the way of that fuccerTive progrefs, to * which nature and practife lead, in a country efpeci ally, which, c knowing nothing in general but its own productions, was an- c tiently deprived of the afliftance that arifes from coiilpafifon. ' "With this idea, which was formed upon objects that I had under c my eye, I have more than once mentioned with an eiogium the * equality of proportions obierved by the ./Egyptians.'" He then gives an account of a figure of the higheft antiquity, without beauty or proportion ; and this he takes for a proof, that art had, in /Egypt as well as in other countries, its progrefs towards per- fection. No doubt it had : But that degree of perfection, which fatisfied [ «8 ] Appendix, fatisfied the ./Egyptians, had long been obtained, though not *— — v*- -J 10,000, yet perhaps above 2000 years, before the time of Plato ; and this paffage out of Caylus confirms Plato's account. § 175* Tartini barely mentions, vide § 91, the names of Plato and Greek mufic, Ariftotle, as vouchers and witneffes of the effect of antient mu- ' e ^ e ' fie on the paflions. I intend fio go farther, and not only give ibme account of what thefe two philofophers fay, but alfo to add the teftimony of other grave and credible witneffes 5 in order to confirm what has been doubted of, even by men who had no pre- judices againft mufic in general, or that of the Greeks in particu- lar. But that what I fhall have to fay on this fubject may have its proper weight, in relation to the merit of the antient mufic, it will be neceffary firft to remove fome difficulties, ftarted by one of great authority •, I mean, that moft acute mathematician Dr. Waliis •, who, I fuppofe, knew more of the antient mufic than any modern, except Meibomius. The former, in Philofophical Tranfactions abridged by Lowthorp, Vol. I. p. 618, fays thus : * I take it for granted, that much of the reports concerning the * great effects of mufic in former times, beyond what is to be < found in latter ages, is highly hyberbolical, and next fO fabu- « lous; and therefore great abatements, &c.' This firft article is merely taken for granted, and prefatory. The fecond article gives for reafon c that mufic (to any tolerable degree) was then, ' (if not a new, at leaft) a rare thing ; which the nifties, on c whom it is reported to have had fuch effects, had never heard 4 before ; and on fuch, a little mufic will do great feats \ as ' we find at this day a fiddle or a bagpipe at a country morrice- c dance.' § 176. To fpeak freely on this occafion, I cannot help being amazed Creek mufic to find fo crude an opinion delivered by a man of Dr. Wallis's vindicated. character, { "9 3 character, on a fubjeft, which, as appears by his excellent edition Appendix. of Ptolemy, employed his thoughts very much. Had he con- w-v~-^ fined this unfavourable judgment of the antient Greek mufic to fome fabulous accounts which we meet with here and there, about its effect on various kinds of animals; as, wolves, elephants, mares, wild boars, deer, dolphins, &c. it would hardly have been worth while to contradict him ; though fome of thofe {lories are moll undoubtedly founded on truth ; becaufe they do not fo much prove the excellence of the mufician, as the exquifite work- manihip of the great Author of nature. Had Dr. Waliis's cenfure gone no farther than this, I fhould have faid nothing about it ; but when I confider that it throws a fufpicion on the teftimony of the greatefl men of antiquity, I cannot but think it deferves fome examination. When I fay the greatefl: men, I mean fuch as had the higher!: reputation in the moll enlightened times of Greece, i. e, the mofl enlightened times that the annals of the world mention. I mall not at prefent cite the opinion of thofe great men about the effect of mufic. This I fhall mention afterwards. I fhall now only confider in a general way what probably mull have been the flate of mufic in the time of Plato and Ariflotle, who are the chief authors that give fuch incredible accounts of its effe£ts. Homer lived above 400 years before the philofophers above- § 177. mentioned, according to the account which brings them the near- Mufic not rare eft together. Does it then appear that mufic, even in his days, '{^^J'™' ° f was a rare thing ? So far from it that we have an account of mufic in various ways, perpetually occurring in his poems, parti- cularly in the OdyfTey, which has been juflly called Kocroif^ov T8 £;y av^pooTTiva ; and which we may therefore fuppofe to give a true picture of what he daily faw before his eyes. In the Iliad and OdyfTey together there are above fifty places where mufic is men- S tioned - 9 [ *3° 1 Appendix, tioned \ in fome or which the tibia and cithara are employed— s- **^*~ In fome Tinging and playing on inftruments are called the compa- nions and ornaments of a feaft — In others refponfive choral finging at a funeral is defcribed — In others finging to the cithara to cheer the labourers at a vintage — In others, Apollo preludes, and the Mufes fmg alternately — In others, Phemius or Demodocus performs a kind of mufical drama, or what ought rather perhaps to be called a cantata, with a regular fubjec~l : from whence I con- clude that the mufic mull at leaft have been tolerable ; for we cannot fuppofe that Homer would have thought it worth while to celebrate even good poetry, accompanied with fuch wretched mufic as a bagpipe can produce. Nay, we cannot, without being extravagant, fuppofe that barbarifm and civility could be fo abfurdly coupled together, whatever feeming proofs, either antient or modern, may have been produced to the contrary. ^ I7 g/ After Homer fome of the fir ft writers were the Lyric Nor after >him. zn ^ Dithyrambic poets, as the two Alcmans, Simonides the elder, Terpander, Arion, Stefichorus, Sappho, &x. and thefe were of courfe practical muficians and compofers •, and we mud necefTarily fuppofe that mufic was rather improved than the contrary, under fuch mailers. Next came the theatri- cal poets, and they too fet their own pieces to mufic ; and that the Greek tragedy was throughout fet to mufic, appears by a pafiage in Ariilotle, which is the only teflimony I mail quote in proof of my aflfertion : * The Hypodorian and Hypophry- c gian modes are improper for the chorus, but more fuitable c for the fcenic perfonages. 5 Vol. 2. 770. problem. I may perhaps have occafion to mention Ariftotle's reafons for this opi- nion afterwards. But r '3* ] But again, mufic was fo far from being rare at the time when Appendix. the authors lived who give an account of its wonderful effects., u " , ~"" v -^ that it was a regular part of education. This is fo well known a § 179. fad:, that to undertake to prove it would be a mere orientation of "Mnfic not ran reading. Every fchool-boy knows what Cornelius Nepos fays of in Gmcg ' Epaminondas; and the ftory of Themiftocles related by Cicero, is almoft as well known. Inftead therefore of citing fuch trite inilances, and fifty others fimilar to them, I will give one from amongil a people who are frequently reprefented as rather averfe to the ftudy of mufic. Xenophon, p. 661. fays> that Agefilaus at the folemn feftival, called Hyacinthia, performed his part ift the Psean fung to Apollo, being appointed thereto by the mailer of the chorus. From hence it appears that mufic muft have made a part of education amongfl the Lacedemonians, otherwife we cannot fuppofe that one of their kings could* with any decency, have been appointed to fing on a public occafiom This ftory would afford many reflections; but I have no room left to wander into all the paths where my copious fubject would lead me. What mail we fay to the paflage cited by Athenaetis out of § 180. Ariftoxenus, p. 632.? c I and a few others, recollecting what Mufic corrupt* * mufic once was, and confidering what it now is, as corrupted e f l ?L e Ume * by the theatre, act like the people of Pofidonium, who annually * celebrate a feftival after the Greek manner, in order to keep up c the memory of what they once were \ and before they depart, * with tears deplore the barbarous ftate they are brought into by c the Tufcans or Romans.' Is not this paflage a convincing proof that mufic muft have been carried to a great degree of perfection as early as the time of Plato and Ariftotle ? What mail we fay about the care of the Greek muficians in adjufting the modes, inftruments, and rhythm together \ and this with a fcrupulous ex- S 2 actitu&le, [ ^32 ] ArrENT>ix. actitude, that favors to us of whim and affectation. Instances of c- * - ^ - / this fort abound in the ancient writers. Is it ufual for arts that are little understood, and only practifed amongfb nifties, to be fo very nice ? What fhall we fay to the cuftom amongft the Athe- nians of erecting monuments with tripods in honor of the tribe which gained the prize in a chorus, where the names of the furnifh- er and teacher, the number of performers, and whether men. or boys, were recorded ? Was mufic rare when a whole people con- tended thus with one another by bodies, which of them could produce the ableft muficians ? Or can we fuppofe the mufic to be ordinary, or even indifferent, when it was ftudied by fo many inge- nious rivals ? Let any one confider all thefe circumftances, and decide whether it is pofTible to reconcile them with Dr. Wallis's opinion ; who, after having obferved that mufic with the ancients took in poetry, dancing, gefture, as well as finging and playing; lays thus : ' Now all this together muft needs operate flrongly on 1 the fancies and affections of ordinary people, unacquainted with * fuch kind of treatments.' § 181. « But,' fays Dr. Wallis, c the antients had not conforts of two, Antienu had < three, four, or more parts or voices.' Maibomius afferts much * f * the fame thing ; and this is, one may almofl fay, the univerfal opinion. Some, however, of the writers on mufic have produced paffages out of the antients, which feem to imply the contrary ; but which are not looked upon as conclufive by others : Such as that out of Seneca, Epift. 84 : * Non vides quam multorum vo- « cibus,' &c. mentioned by If. Voffius de Poemat. Cant. &c. p. 82 ; where perhaps nothing but octaves are implied. Another paflage cited by him, out. of the piece de Mundo, attributed to Ariftode, feems to be more to the purpofe ^vo-iKy o%&? 9 &c. i. e. mufic, mixing together acute and grave, long and fliort founds, forms one harmony out of different voices. Wallis alfo has pro- duced L i33 1 duced a pafTage out of Ptolemy, which he thinks may infer mufic Appendix-, in parts. Ptol. Harm. p. 317. But the ftrongeft paiTage which *-*-v-*^ I have met with, in relation to this long-difputed point, is in Plato -, a pafTage which I have never feen quoted, and which I fhall tranflate : ' Young men mould be taught to fing to the lyre, c on account of the clearnefs and precifion of the founds, fo that c they may learn to render tone for tone. But to make ufe of c different fimultaneons notes, and all the variety belonging to * the lyre, this founding one kind of melody and the poet ano- * ther — to mix a few notes with many, fwift with flow, grave * with acute, confonant with diffonant,, &c. muft not be thought « of -, as the time allotted for this part of education is too fhort * for fuch a work." Plat. 895. I am fenfible, that objections may be made to fome parts of this tranflation, as of the words tfvkvqIw* fJLuvolm* and avltpwvots y but I have not defignedly dii* guifed what I took to be the true fenfe of them, after due con- sideration. It appears then, upon the whole, that the antients were acquainted with mufic in parts, but did not generally make ufe of it. v- But Dr. Wallis enters into particulars, and objects to the flo- § j g 2 . ries about Orpheus, Amphion, Timotheus, &c. Now, what is stories ahem faid about the two firfl of thefe muficians, is fo plainly poetical, Orpheus, that a child cannot miftake it ; and perhaps may only mean, that men were incited and encouraged to work by the power of their mufic ; as Nicomachus indeed feems to fay nothing more 5 in the pafTage about Amphion cited § 170 \ and as the Argonauts are faid, by Apoljonius Rhodius, to have been, incited to row by the lyre of Orpheus. This kind of encouragement was not unufual amongfl the antients. Homer mentions a boy finging,. and playing on the cithara, to the labourers at the vintage * s and Euripides, a mufician, playing on the pipe to the rowers >, Iphig, in Taur. v. 11 25. This, I fay, might pofTibly be the whole that was, [ *34 3 Appendix, was meant by the ftories about Orpheus and Amphion. But we * ~v--"— ' a re not obliged to confine ourfelves to that meaning, as we have iufncient reafon to believe that their mufic v/as uncommonly touch- ing, and capable of producing any effect almofl within the limits of pofllbility. The reafon we have for thinking thus highly of their mufic, is not drawn from theory, which is a moft deceitful guide in cafes of this kind ; though the only one which Dr. Wallis had or could have to follow. No, we (land upon other, and better ground, and fuch as may be firmly relied upon ; I mean the teflimony of fome who heard, if not the mufic of Orpheus and Amphion, yet that of muficians full as old. § 183. Plato, fpeaking of the mufic which remained in his time, of Mufic of Marfyas and his difciple Olympus, fays, p. 567, c that it was moft di- Olympus. ( v j ne ^ anc j ac j a pted. in a very particular manner to ftir and affect c the mind.' This teflimony of Plato, who was himfelf a prac- tical mufician, and lived at a time when mufic flouriihed in an eminent degree, ought to have great weight. Again, Ariftotle fays, p. 455. that the compofitions of Olympus raifed an en- thufiafm in the fouL Laftly, the mufic of Olympus was pre- ferved to the days of Plutarch, who fays, it furpaffed any mufic then known. Now* Olympus was at leaft as old as Or- pheus -, and it was he who compofed the curule fong, Plutarch, p. 1 1 33, which caufed Alexander to catch up his arms, while Antigenidas was performing it ; Id. p. ^5- As to the effect of the recent mufic in the time of Plato and Ariftotle, they both fpeak of it in very ftrong terms. Plato, after mention- ing, p. 906. feveral of the modes then in ufe, excludes fome, and admits others into his republic, on account of their different effects on the morals \ and Ariftotle fays, p. yjo. vol. 2. that the Subphrygian mode affects the mind with fomething like mad- nefs, and drives it into a kind of Bacchanalian ftate. ibid. p. 455* [ 135 J 455- That the Phrygian mode raifes enthufiafm. ' This/ adds Appendix, he, c is rightly affirmed by thofe who are converfant in things of <-**"V— -^ c this kind ; for they fpeak from what they fee actually happen,' It appears then that the two above-mentioned philofophers perfectly agree in their opinion about the power of muflc, and the propriety of making it a part of education ; though the difciple takes every occafion to contradict his mailer, efpecially in relation to his republic. It is curious to obferve the different motives they make ufe of to recommend mufic. Plato, who was given up to the fublime of fpeculation, fays, that mufic accuftoms the mind to order, and thereby allures it to the love of vertu ; which is nothing but moral order ; and fo raifes it gradually to the contemplation and love of that being, who alone is the fource of all order, both natural and moral. This was the way of reafoning of that great philo- fopher ; and the fame way of reafoning made him recommend the fludy of aftronomy, and of the fciences fubfervient to it, as arithmetic and geometry. He thought, all other views but that, beneath the dignity of man. His difciple, Ariftotle, talks more like a man of the world on this occafion,. as he does in all other parts of his philofophy ; and fays, we fliould not only be taught to do bufinefs with honor, but alfo, to be idle with dignity ; — that it is unworthy of a gentleman to make profit the only view in all purfuits ; — that it is fcarcely pofTible to judge rightly, in. any art which we have not practifed \ and therefore, in order to qualify people to be pleafed with nothing but what is fine in mu- fic, they muft practife it in their youth \ — that, as young folks can never be at reft, their parents ought to provide them with fome innocent amufement \ as Archytas contrived a rattle for children, in order to keep them from doing mifchief. § 184. But to return to my main purpofe, which was to fhew, that q-y p Qrwer j the ftories mentioned, about the effect of the antient mufic, were antimt mu f lc proved from 4 not^i C 136 ] \ppkndix. not owing cither to its fcarcity, or the rufticity of the audience. *- — *~ — ' This point, I imagine, muft appear very evident to any impar- tial reader, by what I have already laid ; but, if it were neceffary, I could with the greateft eafe produce the teftimony of poets, hiflorians, foldiers, flatefmen, lawyers, divines, philofophers, of the higheft character for wifdom and gravity, living in feveral ages and countries, all concurring to confirm the opinion of Plato and Ariftotle ; and, what is extraordinary, I do not remember that Lucian, who takes every opportunity of expofing the philofophers, ever once ridicules them for it. If all thefe circumflances are not fufficient to gain our belief, merely becaufe we moderns have not the fame mufical power ; then have the Kamfchatcans a right to decide, that it is impoflible to foretell an eclipfe ; or to reprefent all the elements of fpeech, by about twenty-four marks. § 1 85. Though I think it unneceflfary to produce the Opinion of any other Laced^mo- private perfon on this fubjec"t after thofe I have already mentioned; man fenatus- y et j t ma y not be amifs to produce the judgment of a nation •, and I the rather produce it, becaufe, befides the weight it muft carry, it contains a curious piece of antiquity. The piece I mean is afenatus- confultum of the Lacedaemonians preferved in Boethius ; and is as follows: Whereas Timotheus, the Milesian, coming to our CITY,HAS DEFORMED THE ANTIENT MUSIC; AND LAYING ASIDE THE USE OF THE SEVEN-STRINGED LYRE, AND INTRODUCING A MULTI- PLICITY OF NOTES, ENDEAVOURS TO CORRUPT THE EARS OF OUR YOUTH BY MEANS OF THESE HIS NOVEL AND COMPLICATED CON- CEITS, WHICH HE CALLS CHROMATIC; BY HIM EMPLOYED IN THE ROOM OF OUR ESTABLISHED, ORDERLY, AND SIMPLE MUSIC; AND WHEREAS, &C. It THEREFORE SEEMETH GOOD TO US THE KlNG AND EPHORI, AFTER HAVING CUT OFF THE SUPERFLUOUS STRINGS OF HIS LYRE, AND LEAVING ONLY SEVEN THEREON, TO BANISH THE I l 3T J THE SAID TlMOTHEUS OUT OF OUR DOMINIONS, THAT EVERY ONE APPENDIX. BEHOLDING THE WHOLESOME SEVERITY OF THIS CITY MAY BE DE- *"^"V* — ' TERRED FROM BRINGING IN AMONGST US ANY UNBECOMING CUS- TOMS, &C. I have not produced the whole, nor do I pretend to have given § 1 8 6. a literal tranflation of this remarkable fenatus-confukum, which Obfewatkm has been very much corrupted by tranfcribers. I have taken the^A^f us ~ fenfe of it as corrected by If. Cafaubon in his notes on Athenaeus. The corrections are highly probable, but not fufEcient to furnifh throughout a grammatical construction ; for which reafon I aimed at nothing farther than the general fenfe, which I mufl obferve for the fatisfaction of the EngLfh reader is clear enough, even with- out Cafaubon's corrections. I mufl farther obferve upon this cccafion, that this is the very Timotheus who is faid by fome to have produced fuch an effect, on Alexander by his mufic — that this was the third time that the Lacedaemonians had in much the fame way put a flop to any innovation in mufic, as thinking it of the greatefl confequence to the flate. Plutarch. Inflitut. Lacon. p. 239. vol. 2. et id. p. y^g. vol 1. That only feven firings were ufed long after the octachord was fettled by Pythagoras ; vide ^ iyi — that the chromatic was looked upon as unbecoming a grave and manly people, vide § 150. — And laflly, that it appears that the very two nations who are fuppofed to have paid very little regard to mufic, viz. the ^Egyptians and Lacedaemonians, in fact are found to have laid the greatefl ftrefs upon it, by making it in fo particular a manner the object of national concern. Vice § 169. Having faid all that I think neceffary, in point cf teflimony, § J $7- upon this fubjecr, I fhall now come to theory, and confider, ^be power of ,11 1 1 r l o- mu f tc prwtd whether that may not tend to prove the fame thing. Suceroy^ theory. T Tufc. [ '38 ] A?t>ENDlfc. Tufc. i, fays, that Ariftoxenus thought the foul was nothing *»— "•"V""*''*' but a certain tuning of the body, as in the voice and on the lyre, which is called harmony •, fo that, from the nature and figure of the body, various motions are produced, as founds are in fmging. To this it is anfwered, that he was fo fond of his darling mufic, that he wanted to transfer every thing to that art; and that we can underftand what harmony means from the intervals of founds ; but how the figure of the body, without a foul, can produce harmony, does not appear. As the works of Ariftoxenus, where this doctrine was contained, are loft, it is not pofTible to know whether or not his fenfe be truly reprefented. Several of the antient philofophers, efpecially of the Pythagorean and Platonic fe£ts, fuppofed the foul to be made according to harmony. This notion was mifreprefented by fome, as if they had faid the foul was nothing but harmony. Both Plutarch and Proclus take notice of this mifreprefentation in relation to Plato. By foul was frequently meant amongft the antients, not the rational principle in man, which is capable of perceiving univerfal truths, but a fubtile kind of matter fpread over the groffer body. This kind of matter man was fuppofed to have in common with the brutes ; it was looked upon, either as itfelf of a fenfitive nature, or pe- culiarly adapted to convey the notices of things to the immaterial prefiding mind. This way of confidering the material foul is well illuftrated by the Stoics, who fuppofed it to confift of eight parts; viz. the 5 fenfes, the 6th the vocal, the 7th the fpermatic, and the 8th the governing or intellectual part ; from which laft all the other parts are fpread through their proper organs like the arms of the cuttle-fifh. Plutar. p. 898, vol. 2. § 188. Ariftides Quint, de mufica, p. 106. exhibits a doctrine fome- Nervous fyf- thing refembling that of the Stoics juft mentioned ; for he talks of the meninges and nervous membranes, like the fpider's web, but 4 hollow ; [ 139 ] hollow; containing a fpirit within them •, by which membranes Appendix. the foul, and not the body, is put in motion. How far anatomy ' — "V—— ' had been advanced in the time of Ariftides, who was contemporary with Trajan, I cannot fay •, but the paffage above-cited feems to fuppofe fome knowledge of the nervous fyftem, which is univer- fally allowed at prefent to be an expanfion of the brain, from the meninges over all the body. It is alfo univerfally agreed, that the nerves are the organs of fenfe and motion, but in what manner is difputed. Baglivi, who was one of the firft confiderable writers on this fubject, once thought that thefe phenomena arofe from ani- mal fpirits which pafs through the nerves. Afterwards he changed his mind, and attributed every thing to ofcillation. But to Hick to the auditory nerves, which at prefent is my only concern, Val- falva, who had made a particular ftudy of the ear, accounts for the effect of founds by the vibrations of the nerves, and compares the nerves to mufical firings. Vide de Aur. humana, cap. 6. This theory, however natural it may feem at firft fight, has § 189. been laid afide by later writers. H'aller in his lineae phyfiologicse, Animal fpi- urges, that the nerves cannot vibrate unlefs they are hard, unlefs tltu they are ilretched, and unlefs they are fixed. But nothing in them appears of this fort. Befides, nerves when cut do not contract *, and fome of them are faftened down, as thofe of the heart to the arteries, p. 193. Haller therefore recurs to the old fyftem of animal fpirits, which furely is a very unphilofophical idea, confidered in any light whatever -> for no man will pretend to fay what thefe fpirits are — whether any fpirits paffing through the nerves do at all exift — or whether any fpirits whatever can an- fwer the purpofes for which they are invented. On the other hand if it is poffible for a nerve to be put into motion throughout its whole length, by means of fome impreffion at either extremity, then every difficulty vanifhes, in relation to that fyftem which T 2 feems [ i4° 1 Appendix. feems fo natural; and thefe fpirits may be remanded back to their native region, where they will be more properiy employed to c tread the ooze of the fait de^p — to run upon the fharp wind of \ the north — and to do bufinefs in the veins of the earth — when c it is baked with froft ;' than to carry intelligence backward and forward between the brain, and the other parts of the body. Let us then fee what probable folution may be found. § 190. But before I enter upon this fubjecl:, I muft obferve that Vibrathns net Haller's objections relate only to vibrations, fuch as are produced muji?!~* on a mufical firing; and not to all kinds of continued motions whatever. The whole bufinefs therefore is, to find fome motion in the nerves that is perfectly regular, may be propagated from end to end, and is not liable to the defects mentioned above. If this can be done, one may have as clear a conception how the foul re- ceives intelligence by means of the nerves, as how a fpiderfi mated in the midfl of its web, may be made fenfible of the flightefl im- prefilon made on any part of its delicate texture. § 191. But to come to what I take to be a folution of the foregoing Harmonic uk- difficulties mentioned by Haller. Galileo in his Difcorfi e Dimof- dulattoKs. trat> M at n em# toward the end of the firft dialogue, has the follow- ing paffage. c We plainly fee the circulation of the medium about c the refounding body to diffufe to a large fpace, by making a c drinking glafs tofound,thathas fome water in it, by rubbing the c rim or edge of it with the tip of one's finger ; for we mall thus c fee the water in the glafs to undulate in a mofl regular order; ' which effect will yet be more clearly feen if we put the foot of ' the glafs in the bottom of a veffel of reafonable bignefs, and fill c it with water nearly to the glafs's rim, and then make it found by c rubbing it round as before, with the tip of one's finger : for ' then we fhali fee the circulations in the water to be moft regular, and [ Hi ] £ and with great velocity to fpread to a great diftance round about Appendix, c the glafs : Nay, I have often happened to fee, in making a *"— *"V— ' 'pretty big glafs almoft full of water to found as before, the € waves formed with an exact equality : but the tone of the glafs 4 happening fometimes to rife an eight higher ; I have feen at that ' very inftant every one of the faid waves to divide thcmfelvts c into two : which accident moft plainly proves the form of the c octave to be double.' From this phenomena it follows that harmonic undulations may take place where vibrations cannot ; and I think what we fee happen in animals of the ferpent kind will help to explain how the nerves may be affected. When animals of that kind move in their natural way, you fee regular undulations throughout their body. Thus Milton, fpeaking of the ferpent, B. ix. v. 496, c Not with indented wave, prone on the 4 ground as now :' and v. 502, c Spires that on thegrafs/^ta/.' If what happens to animals of the ferpent kind, may hap- § 192. pen to the human nerves, i. e. that they may be put into har- Soul har- monic undulations by the agency of external objects, then was the mom opinion of Plato, that the foul was made according to harmony, not without foundation ; which opinion he might perhaps be led into, by feeing the extraordinary effects daily produced by mufic, partly owing to a more favourable climate, and partly owing to a fuperior fkill in the artifts of thofe days. To the fame purpofe, Ariftid. Quint, p. 107. fays, « If our minds are affected by the < vibrations of mufical firings, where is the wonder ? fince the c mind has a body belonging to it, refembling a mufical inflru- c ment \ and fince we know that if a light body be placed on a c firing while an unifon to it is founded, the light body will move. 9 And thus Lord Bacon, either induced by Platonic notions, or by what he faw and felt himfelf, even in this unfavourable climate, fays, Advancem. of Learn, b. 2. ' This variable composition of • man's body hath made it as an inflrument eafy to diftemper ; c therefore [ *4* 1 Appendix. c therefore the poets did well to conjoin mufic and medicine in u " v tmmJ * Apollo, becaufe the office of medicine is but to tune this curi- 1 ous harp of man's body, and to reduce it to harmony.' But fomething elfe is required belides a mufical inflrument and a mu- fician, in ordtr to produce the proper effedts of mufic. Nobody, I think, will fcruple to call bolus's harp a mufical inflrument ; yet every gale will not fhew the power of it ; nor can every voice nor every hand, though mufical, raife thofe undulations in the nerves, which are capable of infpiring rapture and enthufiafm. Perhaps, if every circumftance befides was juft what it ought to be, want of fimplicity alone might render the effect imperfect. This appears to be Tartini's way of thinking; and even Dr. Wallis lays fo much flrefs upon fimplicity, that he almofl feems to have been inclined to believe the relations of the effects of antient mu- fic, at leafl amongfl the ruflics, on this account chiefly. § 193. So much for the human foul as far as harmony is concerned* Beafts affcactlBux. are the effects of mufic confined to man only ? By no j mujic. m eans : I will produce a few inftances of the power of mufic over the brute creation -, and fuch inftances as cannot be difputed. It has been mentioned by feveral writers, Clemens Alexandrinus, TElian, Martianus Capella, that deer are affe&ed by mufic ; and Waller, in a poem addreffed to lady Ifabella playing on the lute, alludes to this notion in the following lines : There Love takes Hand, and as me charms the ear, Empties his quiver on the lift'ning deer. I believe this allufion has generally been looked upon as a poetical ornament, built upon a fabulous piece of natural hiflory ; I my- felf looked upon it in that light till I met with the following pafTage in Playford's introduction to mufic, who feems to have been a plain man, and one whofe teftimony might be taken. Thus he fays : < Myfelf, as I travelled fome years fince near Royflon, ' met [ H3 1 * met a herd of flags, about 20, upon the road, following a bag- Appendix, 4 pipe and violin ; which while the mufic placed, they went * forward ; when it ceafed they all Hood Hill ; and in this manner * they were brought out of Yorkfhire to Hampton-Court.' — That fheep are affected by mufic, is no lefs certain. Apollonius Rhodius, lib. 1. v. 574. fays, c As when a flock of fheep returning c at evening to the fold, croud about the heels of the iliepherd, * who walks before, and plays a delightful paitoral air upon his *■ fprightly pipe.' — And fcripture evidently alludes to this cuftom in more places than one, as Numbers xxvii. 17. May lead the peo- ple, that the congregation of the Lord be not as iheep which have no fhepherd. Again, Pfal. Ixxx. 1. Thou that leadeft Jofeph like a flock. If I am not much miftaken, this cuftom itill prevails in fome parts of the Earl, and certainly gave rife to the fhep herd's pipe, fo frequently mentioned in the fcenes of paftoral life. — Bees, I think, may be put amongft the animals that delight in mufic. Ariftotle, vol. 1. p. 948. fays, what is very well known, that they are drawn together into the hive by the tinkling of brafs, but doubts whether from fear or pleafure. However others, as Pliny > areofopinionthatitisfrompleafure. Lib. 11. § 22. And Varro calls bees, the birds of the mufes ; de re ruftica, lib. 3. § 16. What to fay of horfes, I am not altogether without doubt. They are repre- fented by fome writers as delighting merely in the noife and clafli of arms 5 fo Pindar calls the Sicilian horfes mf^s%&ffJL-&ii Pyth. 2. 4. and Virgil Georg. 3. 82. Turn fi qua fonum procul arma dedere, &c. But I am apt to think the account given in the book of Job is more natural, where the horfe is defcribed as faying among the trumpets, Ha ! ha ! or, as the Septuagint gives it, Euge ! which tranflated according to our prefent way of expreflion, means, Bravo ! This is fine ! It is added indeed, that he fmells the bat- tle, as appears by his prancing and neighing, according to the ver- fion of xhe Septuagint, which feems better than that of our bible ; but t m ] Appendix, but furely his prancing and neighing is accounted for fufficicntly v -"""' >v ~ by the found of the trumpets. Thus Ovid, ' Fremit equus quum 4 figna dedit tubicen.' § 194. I come now to fome inftances of the power of mufic on the Serpents af- brute creation, much more extraordinaiy than any hitherto by me fe t ymujic. ment j onec ^ anc i f u \\ as we ]} a ttefted. It is a common practice in the Eaft Indies, as I am allured, when a hooded ferpent gets into a houfe, to fend for a charmer, who with his pipe tempts him out of his hole, and after fome time lulls him to deep, and fo feizes him. Scripture plainly alludes to fomething of this kind, in Pfal. lviii. 4, 5. Like the deaf adder that ftoppeth his ears : which refufeth to hear the voice of the charmer (cdW-0> charm he never fo wifely. But we have an account in an author of credit ftill more wonderful. NieuhofF, (in Churchhill's Voyages, vol. 2. p. 231.) fpeaking of Malabar, fays, c You meet there with certain 4 vagabonds, who carry ferpents in a bafket, with fome bran for 1 their food, hanging on a ftick, carried on the moulders of tw6 4 fellows ; fome of thefe ferpents are fix or nine feet long, of a grafs 4 green colour, and not above an inch thick ; fome are very large 4 and bulky, with grey fpots •, fo foon as thefe Malabar vagabonds 4 begin to play upon a certain inflrument, like a bagpipe, the 4 ferpents fet themfelves upright upon their tails, twift themfelves 4 in a moft furprifing manner, and foon after raiie their fins or 4 bridles which are near the head, and fall on with fuch fury, as 4 if they would tear one another in pieces, to the no fmall terror 4 of the fpectators.' I defire to know, if any one, after reading this account, can think it reafonable to difbelieve the moft extra- ordinary accounts of the power of mufic over the human mind, related by the antients, who were eye-witnefles of what they relate. Thofe who are verfed in natural hiilory would be able, in all probability, to increafe the lift of animals that delight in mufic : For my part I have none to add but the grafhopper, (different no doubt [ H5 ] doubt from what we call fo) of which there is a pretty fable Appendix. m Plato, vid. Phaed. towards the beginning : and the clafs of ^— *"V"— ^ birds, many of which are fo remarkable for ringing, that Lucre- tius imagined they firit taught mankind the art of mufic ; Et li- quidas avium voces imitarier ante, &c. lib. 5. v. 1378. ■ But this is not the full extent of harmony according to the § l 95* Pythagoreans and Platonicians. They fuppofed the univerfe itfelf Inanimate and all its parts to be formed by the principles of harmony. Nor ;z/Vm do I imagine they meant only to make ufe of a figurative expref- fion. There are traces of the harmonic principle fcattered up and down, fufficient to make us look on it as one of the great and reigning principles of the inanimate world ; and though we have no proof, or indeed any reafon to believe that the Greeks were -acquainted with the foundation of fome of their philofophical opinions; yet what that very fagacious and judicious philofopher Mr. Maclaurin obferves, Phil. Difcov. of Newton, &c. p. 3$. concerning the aftronomy of Pythagoras, feems highly probable. 4 When we find,' fays he, l their accounts (i.e. of the Greeks) < to be very imperfect, it feems reafonable to fuppofe that they 6 had fome hints— only from fome more knowing nations, who c had made greater advances in philofophy, &c.' Thofe more knowing nations I fuppofe to have been the ^Egyptians, from whom the firft and great outlines of every art and fcience originally came. Maclaurin gives us one inftance of the Pythagorean doc- trine which could hardly be fuppofed to be of Greek original, the harmony of the fpheres, and which, in conformity .with Dr. Gre- gory, he explains as follows : 6 If we mould fuppofe mufical chords ' extended from the fun to each planet; that all thefe chords ' might become unifon, it would be requifite to increafe or dimi- c nifh their tenfions in the fame proportions as would be fufficient * to render the gravities of. the planets equal ; and from the fimi- U < Htude I 146 ] Appendix. c litude of thofe proportions, the celebrated doctrine of the har- v«*— "Y^— -'' « mony of thefpheres is fuppofed to have been derived.' Certain as this harmonic coincidence is now become, till Sir Ifaac Newton demonstrated the laws of gravitation in relation to the planets, it mud have parled for the dream of an Utopian phiiofopher. § 196. Befides the above-mentioned inftance, which proves the har- CoJoars bar- mony of the univerfe to be true in a literal fenfe ; and which we fuppofe to have been known to the antients \ there is another initance totally new, difcovered alfo by Newton, equally ftriklng* and equally extenfive. He found that the breadths of the feven original colours, were in the fame proportion as the feven mufical intervals that compofe an octave. The reafon why this law was followed rather than any other, does not appear ; nor has Newton given any the leail conjecture about it : but we cannot avoid be- lieving that it tends fome way or other to the perfection of the univerfe, either as to ufe or beauty -, and that the proportions cannot be altered, without altering the phenomena for the worfe, unlefs we can believe that the proportions of the elements alfo might be altered without any bad effect. § 197* The inftances 1 have hitherto given of the harmonic principle All fubjlanccs prevailing in the inanimate fubflances of the univerfe, have been harmonic much more taken notice of, both as making part of the fublimeft philofophy that ever was invented, and alfo as being found in the greateft and moll interefting objects in nature ; but the fame prin- ciple appears, if not with equal luftre, yet not with lefs certainty on many other occafions, and in a manner more intimately con- nected with mufic, both as to theory and practice ; for all fub- flances elaftic, homogeneous, and continuous, whether animal, vegetable or mineral, yield, upon percuflion, harmonic founds, i. e. they ring according to the common phrafe. This is notorioufly the urt [ H7 ] t\\t cafe of iron, brafs, earthen-ware, glafs, wood, parchment, Appendix, Sec. and this happens, whatever their form may be. Nor is this *— '•V-J owing to the motion produced in the air ; for the fame thing will happen, without any communication between the organs of hear- ing and the air. Fallen a firing to a poker, or any iron bar, hold the firing between your teeth in luch a manner that the poker may fwing freely, flop your ears clofe, make it flrike againfl the fender, and you will hear a loud clear ringing, as of a bell ; nay, even the fire-pan, oddly fnaped as it may feem for fuch a purpofe, will produce much the fame efFect : but the tongs, which are not a continuous body, make only a confufed and in- diftincl: noife. This experiment is fo very common, and well known, that I remember to have diverted myfelf frequently with it when a child. Lord Keeper North mentions an experiment, which proves likewife, that we may feel mufic without the me- dium of air. In his Philof. EfTay on Mufic, p. 16. he fays thus : c Such a continuity to the nerve of hearing will caufe a fenfe of 4 found to a man that hath flopped his ears, if he will hold a * flick that touches the founding inflrument between his teeth.' Since then it appears that it has pleafed the Supreme Being to s jq^ form many of his wondrous works according to the principles of ^ u £ c 0U ^ tt9 harmony, and fince it is certain that fome of our purefl and mofl bsp.died. affecting pleafures arife from harmony, can it be looked upon as unbecoming to give up fome of our time to the fludy of an act manifeflly intended by Providence to allure us to the love of order, &c. according to the doctrine of Plato ? Surely not : and the lefs fo, as mufic has, not without reafon, been thought to con- tribute to the cure of fome difeafes. Baglivi, p. 363, fays 3 Aliis morbis confert mufica, &x. Again, ib. Exercitatio vocis debito cantu ad plures conducit morbos, ut fufe monet Hippo- crates, 3. disc, n. 16. et multo melius de infomniis, n. 3. And U 2 ths [ '4? ] Appendix; the fame Baglivi, p. 390, has a chapter intitled, De methodo cu- ■ w v^~-*- / randi morbos complures mufica, faltatione, &c. I fay nothing about the tarantula, becaufe the facts have been difputed -, how }uftly I know not. It is certain, that Baglivi and his father, both of Calabria, (the i'ecne of the fuppofed phenomenon) and both eminent phyficians, did believe them, as appears by the differtation on that fubject written by the former. But however that may be, I have no doubt about fome nervous cafes faid to have been relieved, and even cured, by mufic* § 199. Plato obferves, p. 88 r, that when mothers want to make their \lufic caufes children fleep, the remedy they ufe is not filence and reft, but, on Jkep. the contrary, dancing and tolling them about in their arms, and enchanting them, as it were, by fongs : and people, he adds, who are pofleffed with a bacchanalian fury, are brought to their fenfes by the fame method. The effect of founds is very extraordinary, and very various. The Pythagoreans, of all men, feem to have un- derflood this matter the befb ; and to have made ufe of it, on many occafions, to very good purpofes. The {lories and remains of that noble feet, are full of accounts that appear to us fabulous, but may neverthelefs be true. Lord Bacon obferves, Nat. Hid. Art. 112, that the wind, purling of water, humming of bees, a fveet voice of one that reads, &c. are opiates. Now that thefe founds, though not per- haps in themfelves, ftrictly fpeaking, harmonic, may yet put the nerves into harmonic undulations, appears by the phaenomenon of iEolus' harp. The only difference is, that the air ilrikes upon the ftrings of the harp already tuned j whereas, it (hikes upon the nerves perhaps out of tune. But this difference is of no confequence ; for the foul has a power of adjufting the audi- tory organs to any pitch requifite, as is evident whenever a mu- iician changes the key abruptly -, for in that cafe, it is fome time before the ear can comprehend the harmony. Analogous phe- nomena. [ H9 ] nomena, in relation to the organs of finging and feeing, prove the Appendix, truth of my affertion. It is therefore highly probable, that in u — * r "* w fome cafes, what produces harmonic undulations in the nerves, will produce fleep ; and that was the opinion of Pindar, who, in his fublime Pythic ode, (finely imitated by one of our poets) fpeaking of the eagle, fays : Perch'd on the fceptre of the Olympian king, The thrilling darts of harmony he feels ; And indolently hangs his rapid wing, While gentle ileep his clofing eyelids feals ; And o'er his heaving limbs, in loofe array, To ev'ry balmy gale the milling feathers play. Wefts Pindar. This effect of harmony, the reafon of which is not difficult to affign, were it conflant, would be of the greateft cbnfequerice ; for to produce deep, in fome diforders, is to produce a cure. I cannot omit, on this occafion, to mention the oppofite effect § 200.. of difcordant founds, as contraries illuflrate one another beft. Horrible Charlevoix, fpeaking of the Indians of Canada, lett. 13. {ay$^ ounds ' 1 That their war-fongs are at all times melancholy and doleful .; ' but here they were to the laft degree frightful; occasioned per- c haps, he adds, entirely by the darknefs of the night, and the ap- ' proachcs of the feftival.' I believe Charlevoix is miftaken in his conjecture about the caufe of the effect mentioned; for Anfon's Voyage, p< 30. fays, c That Orellana placed his hands hollow to * his mouth, and bellowed out the war-cry ufed by thofe favages, 4 which is faid to be the harmed and moft terrifying found known '■ in nature. This hideous yell, &c.' And Plutarch, fpeaking of the Parthlans, when they attacked CrafTus, fays, 4 They do not { ufe horns or trumpets in war •, but by means of hollow clubs, c covered with leather, and having bells fattened to them, the 5 Farchians fpread a din far and wide. Thefe inftruments fend 3 ' forth [ *5° 1 App£\ t dix. ' forth a deep and terrible found, fomething between the howling *— -v^-*' < f w ii c | beads and the harfhnefs of thunder. This cuftom the * Parthians ufe, as knowing, that of all the fenfes the hearing is c the moft capable of difordering the mind, and that its operations ' have the quickeft effect. The Romans, upon hearing thefe c horrible founds, threw down their arms.' Plut. Vol. I. p. $57. But to return from the gloomy fcenes of horror and difcord to thofe of cheerfulnefs and harmony. §201. It appears from a variety of conclufive circumftances, that mufic Mufic accom- is the voice of induftry — of content — of fcrenity — of innocence. — - panies content, T n . • , • r . , ~ , tf Cm In inojt, it is the voice or nature, uncorrupted and unoppreiied - 9 and as fuch is heard, and once was more frequently heard, in our fields and villages. When it is confidered in this light, it is of all harmonies the moft delightful ; as fuch, it has ftruck men of the moft delicate fenfations. — The plowman whiftling o'er the furrowed land — the milkmaid finging blithe — the fpinfters, and the knitters in the fun— and the free maids, that weave their thread with bone, chaunting, were objects that drew the attention of two of the greateft poets the world has known. But agreeable as thefe effufions of the heart may be to the ear of every man who has feeling ; yet fince it has pleafed our good and great Creator, to grant us faculties capable of improving the imperfect fallies of nature, I cannot conceive why we ought not to go a ftep farther, and learn mufic as an art, and even make it a regular part of education, as was antiently the cuftom of many wife nations. I would not willingly incur the cenfure of fome grave and fober people, who think we have already but too much of fuch trifling and ufe- lefs amufements : I mult therefore explain myfelf. § 202. My opinion is, that young ladies at leaft, who have a tolerable Young ladies ear, to fay nothing of the other fex, fhould learn mufic. But as mufic. ea ' I do not recommend it to them for the purpofe of parade and 4 oftentation, [ m 3 often tation, fo I iliould not wifh to have them attempt to rival the- Appendix. atrical performers, either in finging or playing. A proper model ^^ ^T mmmi to imitate on this occaiion, may be feen § 181. where thepaflage quoted from Plato recommends only the fimpleft kind of mufic for the education of youth. In his books of laws, p. 893, hepro- pofes, that they fhould begin at thirteen years of age, and continue for three years, and no longer. Something of this fort might per- haps fuit our young ladies in general. It feems fufficient that they learn mufic enough to form their ear, and to be able to pick outaneafy tune, by the help of fome manageable and portable in- flrument, as the guitar ; and particularly that they learn to tune it well. Their bufinefs fhould be to praclife merely for the amufements of themfelves, their own family, and particular friends, or rather for domeftic comfort, which they were by Providence defigned to promote-, viz. To calm the boiflerous paffions— to relieve the anxieties and cares of life — to infpire cheerfulnefs — toappeafe the nerves, when irritated by pain, ficknefs, or labour of mind or body, to footh the peevifhnefs of infancy and old age — and to raife the mind* to a feeling and love of order. She who fhall im- prove the natural talents, with which women are born, of doing all thefe things, will not have mifpent her time by applying three years to mufic. How it ferves thofe noble purpofes, as nowprac- tifed, I leave others to tell. That the divine gift of mufic was in a great meafure intended § 203. for the purpofes above-mentioned, feems clear from the courfe of Uufical dif* nature in other animals. The birds, who, except man, are almoft"""^ the only fongflers in the creation, hardly ever fing but to relieve the tedioufnefs of incubation in the female -, infomuch, that whereever you hear a bird fing, you may be generally fure that there is a neft not far off. It is natural to inquire, on this occafion, why the fongs of various birds finging together are not difagreeable, as being ne- ceffarilv [ '52 ] NDrX. cefiarlly discordant. To this I anfwer, that I do not believe they are difcordant : Why fliould we net fuppofe, that the delicate ear of the birds produces the fame effect as we daily find amengd men, who, however many in number, conllantly fall into cenfo- nant tones in converfing with one another ? I never knew but one in Ranee to the contrary ; and that infbnce proved the truth of my afTertion : for there was fomethingfo unharmonious and harfh in his fpeech merely on that account, that every body was of- fended with his want of ear, and wondtred at it. The fame folu- tion fervesfor Shakefpeare's mufical difcord, as he calls it, fpeaking of the cry of a pack of hounds. Midfummer Night's Dream. Mufic. § 204. I find it difficult to quit this enchanted ground, furrounded as I Religious am by firens on every fide, who are tempting me to quit my courfe -, but reafon feems to beckon me away, and point to the port in view. However, I hear the voice of one who mufl be obey- ed. Urania whifpers me about mufic employed in the pure wor- fhipof God, 1 Chron. xxiii. 5, and 2 Chron. v. 12, 13. — of pro- phets prophefying, with a pfaltery, and a tabret, ant E X. H. Hammers of Pythagoras, 12, 13. Harmonic unity, 6 \ notes, 66. Ha liitnic and arithmetical nctes connected, $g% found toge- ther, 41. Harmony deducible from Tartini's. princioles, 166 -, of the fpheres, 195., Harp, 59. 61 — 63; tuning it in a, third, major, 60 ; in a. third minor, 151, 152. Harp M ol u s *s, 65 . 153 — 1 5:5* 1 99. Harpfichord, 5g> Heptachord invented by Hermes, 170.. Homer, mufic in his time, 177 -, after, 178.. Hooker on mufic, 204. Horfe affected by mufic, 193. Hounds take the tone from one another, 203^ Huygens's famous^paffage, $j, $$> L Idasi Da&yli, 78-. - Intervals mufical, 11. 131, 132. 139; difcovery of them,, 14 •■ by the pendulum, 16. j their caufe, 19 \ afcending and de- fcending, 134—137. K.. Kepler fond of analogies, 2 7 . L. Lacedaemonian- mufic,, 185 ; fenatus-confultum, 106. Lyre, 6 3 . M. Meafure or time, 75. 102. Merfennus difcovered three founds in a ftring r 24. Metre, %?. Mixed fcale, y^. Modes, antient, 72 ; of the Greeks, Sg, 112 5 modern, g^- > old Italian, 89. 94 - 9 their number* 95 $ antient and modern compared, 96. £ Modulation^ INDEX, Modulation, modern, 115 — 11S. 156. 163, 164, Monochord compared with the trumpet-marine, 37. I\ 2 u lie, its power proved by theory, 187-, beads affected by it, 193 •, deer — llieep — bees — hories, ibid; hcrfes, 194 ^ caules deep, 199 ; rultic agreeable, 201 ; ladies ought to learn it, 202; religious, 204 ; deferves to be ftudied, 198; cure^ difeafes, ibid ; perfect, 65 ; Perfian, yy ; principles wanting amongft moderns, 92; old church, 109. ni; corrupted,. no; Greek, 175, 176. 179 5 unknown, 113 ; fimple, bed, 122; /Egyptian, 160, 169; in the time of Homer, 177 -, after him, 178 •, in the time of Aridoxenus, 18a; in parts, 181 ; antient, its power, 184, N. Nervous fyflem, 188. Newton's colours, 196. North, Lord Keeper, an obfervation of his, 154; another, 197; Notes of the octave how found, 46; breaking of, 140. Noting of mufic, 10. Numbers exprefTing the disjunct tetrachord known to the Chal- deans, 13. O. Octachord invented by Hermes, 171 ; its advantages, 172. Octave, 15. 51—53. 139. Old ballads, 122. Old Italian modes, 94. Olympus's mufic, 183. Organ, 4. Orpheus, flories about him, 182* Ofcillation of firings, 5. P. Painting, ^Egyptian, 173, 174. Paflions, how to be imitated, ioi ; how moved, 126—130. Pendulum, 16, Perfect mufic, 65. Perfian mufic, 77, Flapford INDEX. Playford, a ftory about deer, 193. Points of red in a vibrating firing, 21 — 23. Poker, a phenomenon of it, 197. Power of mufic from theory, 187-, of Greek, 9 t~ j 84. Practical treatife on triufic wanting, 165. Principles of mufic wanting amongit the modern^, 92. Problem, mathematical, 32 -, phyfico-mathematical, 43. Profody, 97 — 100 ; Italian, 81 , Enghfh, ibid. Ptolemy's prejudice about the circle, 27 -, true intervals of the o&ave found by him, 15. Pythagoras's ftory about his fettling the disjunct tetrachard*. 12, 13. R. Rameau's enharmonic, 84. Refolution of difcords, 48, 49. Rules deduced from Tartini's principles, i6y, Rythm, 78, 80, S. Seafons of the year harmonic, 13. Senatus-confultum, Lacedaemonian, 186. Serpents, regular undulations of, 191 -, affe died by mufic, 194, Sheep affected by mufic, 193. Simultaneous harmony, 103. 108 -, effect of it, 104, 105, 106^ not ufed by the Greeks, 107. Soul, material, 187; harmonic, 192. Spheres, harmony of them, 195. Strings, ofcillation of them, 5*5 in motion, give 3d and 5th* 16 - 3 obferved firfl by Marfermus, 24. T. Tafle, 123 — 125. Tafto-fermo, 120, 121, Temperament, $$, 56 •, of Valloti, 55. Third major, 143, 144 •„ minor, 142, 145—- i^jf, 157 — 161^ difference between them, 133. 137. Third founds, 7, 8 -, in the third minor, 44, 45, 3 Tone, INDEX, Tone, a good, on the violin, 66. Tritones, 86. Trumpet-marine, 2, 3. 25. $$> 36.67. ! . u. Undulations in air, 17 •, in water, ibid ; in ferpents, 191; V. Vibrations, 190; in wood, 18. W. 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