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The Place 
 
 OF 
 
 SCIENCEin music 
 
 BY 
 
 HENRY SAINT-GEORGE, 
 
 {Author of "The Bow, its History, Manufacture and Use,** etc.) 
 
 \ 
 
 ; 
 
 I 
 
 LONDON: 
 
 WILLIAM REEVES, 83, Charing Cross Road, W.C. 
 
PUINTKC By 
 
 \VIi-LlAM EE 5VES, 83 , CHAPaNG CROSS ROAD, 
 LONDON, W.C. 
 

 m 
 
 PREFACE. 
 
 HE views embodied in the following pages 
 first appeared serially in Sept, 1901, and 
 were addressed to advanced students of 
 that branch of musical knowledge com- 
 monly called Harmony. In re-issuing 
 them in the present form I am inclined 
 ^ to add young teachers also in this appeal for a return to 
 simplicity. 
 
 The fundamental principles of Harmony are extremely 
 simple; the rules few and clear. While it certainly may be of 
 interest to the advanced student to look into the nature of the 
 various theories that have been super-imposed thereon, there 
 is no necessity for him to do so, and, in the case of novices the 
 
 
 
 
IV 
 
 Preface, 
 
 study of hypothetical principles can only bring confusion, and 
 cause him to join the vast army who vote Harmony “dry.” 
 
 When we remember that most of the greatest master-pieces 
 the musical world has ever possessed were produced by men 
 who had never heard of Day, Macfarren, Prout or Riemann, 
 to name no others, one perceives how unessential their theories 
 are, no matter how interesting. 
 
 For these reasons I would urge Harmony teachers to con- 
 tent themselves with imparting a knowledge of the plain rules 
 in their simple purity without reference to any of the theories 
 relating thereto — theories which may or may not be accurate. 
 
 I fear the reader may find the title of this brochure some- 
 what of an hibernianism seeing that I am disinclined to allow 
 Science any place at all in Music. But on page 15 it will 
 be found that a tiny niche is reserved that will afford ample 
 accommodation. 
 
 Goethe said : “ Art is called Art because it is not Nature.” 
 He can hardly have been thinking of music for, while it is a 
 supreme art, music is Nature — throbbing human nature — all 
 the time. 
 
 London, March, igo^. 
 
THE PLACE OF SCIENCE IN MUSIC 
 
 HERE is an inexplicable tendency on the 
 part, not only of theorists, but of practical 
 musicians, to treat all the principles of 
 musical combination forming the ground- 
 work of composition as being scientific 
 rather than artistic in character. 
 
 It will be my purpose in the following 
 pages to show how unnecessary and illogical such an idea is. 
 Unnecessary by reason of its redundancy, and illogical from 
 the fact that, whereas music can be completely treated from an 
 artistic standpoint, when an attempt is made to treat it as a 
 science many gaps have to be filled up, either by reference to 
 aesthetic feeling, or by pseudo-scientific “facts” of extremely 
 doubtful authenticity. So far from being one of the exact 
 sciences, music is, perhaps, the most intangible and illusive of 
 the arts. He who would make it an' exact science would be 
 equally well employed in chasing an Ignis Fatuus with a bui- 
 terfly-net in one hand and a two-foot rule in the other. Yet 
 there is an abundance of such men. 
 
6 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 When we speak in convenient metaphor of the “ chemistry 
 of sound ” we must not forget that it is always liable to sur- 
 prising changes from the unexpected infusion of those ingredi- 
 ents so commonly ignored by theorists — personality and 
 genius. 
 
 Music is by origin divine; by development human, and is 
 consequently full of human error (even the piano tuner knows 
 that his best efforts are but an approximation to absolute in- 
 tonation) and possibly it is the presence of these errors that 
 gives the art of music such a transcendant power over, and sym- 
 pathy with human emotion. 
 
 Music pours out of the throats of all nations in gaiety and 
 sadness. Everywhere, in the cradle-song, battle-song and 
 funeral-song, we find music in some form is required to stimu- 
 late and intensify the expression of the passions and emotions 
 peculiar to the occasion. 
 
 As the individuality of persons will show most markedly 
 in such matters, so, to a greater extent, will the individuality 
 of nations show itself in these outpourings, and so strongly 
 that what is harmony to the Oriental is discord to the occid- 
 ental ear. Divesting oneself for a moment of Western “ cock- 
 sureness ” it might be difficult to determine Vv^hich, in the eter- 
 nally abstract, is right. Possibly the Oriental, with his 
 enharmonic progressions, may be in more elemental touch with 
 Nature than are we with our elaborate and arbitrary Western 
 systems. 
 
 I say arbitrary, for, despite the tenets of the scientific cult, 
 I must confess that I can find but little, if any, foundation in 
 Nature (in the conventional use of that much abused word) for 
 the system of music as practised in Europe. 
 
 Music is at once the oldest and youngest of the arts. 
 
 Music, soft charm of heaven and earth, 
 
 Whence did’st thou borrow thy auspicious birth ? 
 
 Or art thou of eternal date 
 
 Sire to thyself, thyself as old as Fate. 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 7 
 
 The crude idea has been latent since the beginnings of 
 humanity, but it is only within the more recent historical period 
 that it has been actualised, with a definite system of written 
 symbols lifting the responsibility of its continued existence 
 off the memory and affection of its exponents, and rendering 
 the productions of its masters understandable by all civilised 
 nations, and in all ages to come. 
 
 This lateness in materializing was but the outcome of the 
 aerial, intangible character of the art. The other arts had 
 their beginnings in the definite expression of concrete ideas 
 and objects. Poetry, with the recounting of exploits. Sculp- 
 ture, with the attempt at centralising the idea of a deity in an 
 image of more or less clumsy and terrifying aspect. Painting, 
 with the depicting of various natural objects possibly as a be- 
 ginning of hieroglyphic writing. 
 
 Of sculpture and painting we have remains from remotely 
 prehistoric times. Poetry had to wait for its record for the 
 growth of alphabets, and music, with its indefinite beauty, and 
 more pregnant meaning has had to wait a still longer period 
 for its own particular alphabet. 
 
 To the amateur, living in this age of sixpenny instruction 
 books, the difficulty of starting a musical notation may not be 
 fully apparent, but he should remember that while any reciter 
 can write down a poem he happens to know from memory, there 
 are but few musicians who can do the same with the pieces in 
 their repertoire. 
 
 It will be seen that music, unlike the other arts, exists in, and 
 for, itself, and does not rely on its relation to external objects 
 or circumstances for its effect on the mind. The other arts 
 depict or describe: music expresses, and is content to tell its 
 own wonderful story in its own mysterious way. And, though 
 it may be capable of depicting, as we find in the large mass of 
 appropriately named “ programme music,” it rises to its highest 
 sublimity when it is music and nothing else. For this reason 
 
8 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 a certain class who criticise before understanding, if such are 
 capable of ever understanding, condemn the Wagnerian music- 
 dramas for the alleged secondary part played by the music. 
 They forget that while the other co-operating arts are appeal- 
 ing to our outward tabulated senses, the music steals into our 
 inner selves, communing with us in its marvellous thought-lan- 
 guage until we feel from within the power of emotion we 
 should otherwise merely have observed. 
 
 Thus, as Art in general is more intimate than Science, so 
 music establishes a closer communion with the emotional side 
 of the intellect than its sister arts, thereby standing removed 
 on either hand. 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 9 
 
 CHAPTER II. 
 
 HOSE theorists who waste so much valu- 
 able time and stationery in attempting to 
 substantiate a cut and dried scientific 
 basis for this illimitable, life-breathing 
 art, seek to establish it on that very rock 
 upon which their ill-steered bark is ship- 
 wrecked. This is lio other than the so- 
 called “Chord of Nature” or harmonic series. 
 
 For the benefit of those who may have forgotten for the time 
 being the exact structure of this series of over-tones, and at 
 the risk of boring those who have not, I will as briefly as possi- 
 ble set it forth here. 
 
 If we set in vibration a tube (organ pipe, trumpet, bassoon, 
 etc.), or string (piano, violin, mandoline, etc.), a note will be 
 sounded of a pitch that will be determined by the length of 
 the tube, or the length and tension of the string. This is the 
 fundamental note, and its vibrations are those of the entire 
 string or air-column. These entire vibrations are, however, at 
 the same time broken up into mathematical subdivisions as 
 half, third, quarter, fifth, etc., producing an ever rising series 
 
 B 
 
10 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 of sounds of greater or lesser prominence according to circum- 
 stances. These are the harmonics or overtones, and as their 
 ratios are as i to 2, 2 to 3, 3 to 4, 4 to 5, etc., the intervals be- 
 tween them continually decrease. Thus reckoning from one 
 to the next, the intervals are an 8ve, a 5th, a 4th, a major 3rd, 
 a minor 3rd, less than a minor 3rd, more than a whole tone, a 
 whole tone, etc. Taking the eight foot C as the fundamental 
 note, the series can be approximately represented in musical 
 notation as follows: — 
 
 75s »- 1 
 
 
 
 
 
 Xv*' • 1 
 
 1 ! 
 
 
 ! a 
 
 
 
 
 1 
 
 1 
 
 
 
 
 — a — 
 
 
 I say approximately because the black notes find no place 
 in the musical systems of Europe, our B flat being sharper, and 
 our F being flatter than those of “ Nature’s Chord,” in fact the 
 latter is by some quoted as F sharp. As we proceed higher up 
 the series we find an ever increasing number of sounds which 
 we cannot even approximately represent on lines and spaces. 
 
 It will be apparent that by picking and choosing among the 
 sounds of the harmonic series, a certain number of notes will 
 be found that are agreeable to our cultivated sense of music, 
 but what of those which our aesthetic feeling prompts us to re- 
 ject? Are we to be guilty of the gross effrontery of saying 
 that Nature is out of tune? 
 
 It would seem fitter to approach the Divine mystery of music 
 in a greater spirit of humility ; to confess that it is one we have 
 as yet been unable to unravel — to confess that if there is a basis 
 for western music to be found outside our own personality, our 
 researches have hitherto failed to reveal it. Music in the ab- 
 stract should be looked upon as an element of thought : musi- 
 cal systems as the languages expressing that thought. In this 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 1 1 
 
 way we can begin to comprehend the diversity of languages 
 existing in the diversity of nations. 
 
 In some of the more definite Eastern systems of music we 
 find enharmonic scales and monotony of melody and harmony 
 side by side with religion and philosophy of similarly subtle 
 super-refinement and a parallel conservative monotony of 
 poetic metaphor. 
 
 In Europe we find a bolder, more virile music, according 
 better with the broader western systems of philosophy, pro- 
 gress and enlightenment. 
 
 Great stress is laid by scientists on' the fact that the 4th, 5th 
 and 6th harmonics give the major triad: — 
 
 But seeing that this is such a small portion of the entire 
 series, would it not be more reasonable to consider this a co- 
 incidence rather than a foundation? Even accepting it as a 
 foundation for the major chord, or rather as a demonstration 
 of the reason that the major chord is pleasing to our ears we 
 are not brought any nearer to a basis for our complex system 
 of chords and progressions. In fact the only bearing the har- 
 monic series has on music is the acoustical explanation of the 
 phenomena of concord and discord, and of the different varieties 
 of tone colour characteristic of different instruments and voices. 
 
 In this way we find that the curious identity in difference of 
 the octave is due to the exact coincidence of all the overtones. 
 The perfect concordance of the fifth is due to the large number 
 of overtones that are identical. With the third, an extremely 
 small number of these tones are in agreement, and it must be 
 remembered that this interval was considered a discord in the 
 earlier days of part writing. With the minor second it will 
 be found that nearly every one of the overtones is at variance 
 with those of the other fundamental note, thus producing the 
 
12 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 harshness of discord so characteristic of this interval. And so 
 in varying degree with all other intervals. 
 
 The reason that the tone of the clarionet differs from that of 
 an oboe, violin, etc., is that in each instrument the overtones 
 appear in different degrees of strength. 
 
 Without going deeply into acoustical calculations it will be 
 understood that the difference in tone between the violin and 
 mandoline arises chiefly from the fact that the thicker gut 
 strings of the former, not vibrating readily in small sub- 
 divisions, produce only the lower harmonics with the result 
 that the tone is by comparison dull and soft. The thin metal 
 strings of the mandoline, on the other hand, easily vibrate 
 in almost the minutest fractions, consequently a larger number 
 of the higher overtones are brought into prominence and the 
 tone becomes bright to the extent of shrillness. Of course the 
 two methods of tone production — the bow, and the plectrum 
 — also exert an influence on the tone, but a steel string on a 
 violin is found to give a very harsh and piercing tone. Many 
 violinists and ’cellists unconsciously avail themselves of this 
 acoustic principle. Those whose repertoire consists entirely 
 of pyrotechnical show pieces will choose thin strings and so 
 produce the small, bright tone characteristic of such per- 
 formers. Others who incline to works of a more sympathetic 
 nature will select thicker strings and their tone will be of a 
 graver, nobler cast. 
 
 Thus the twin sciences, optics and acoustics, tell the painter 
 and musician what his materials consist of, leaving it to the 
 art which flows from his inner personality to teach him how 
 to employ them to the best advantage. 
 
 It is astonishing how plausible a system of harmony can 
 be built up on the fallacious basis of the “ harmonic series.” 
 And some of its advocates seem to possess an almost forensic 
 ability in suppressing or mis-stating facts not quite in agree- 
 ment with their theories. Others will even invent their facts 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 3 
 
 in order to advance the great and noble scheme of bottling 
 up this limitless art in their scientific laboratories. One of 
 the most eminent English theorists, starting with the harmonic 
 series, builds up a most convincingly scientific system of 
 harmony embracing all the chromatic notes of the major key. 
 But when entering on the minor mode he naively drops the 
 scientific basis, and frankly tells us that here we must look 
 to aesthetic feeling as our warrant for its use. 
 
 Herein is to be discovered the redundancy of the scientific 
 theory complained of in my opening chapter, for, whereas 
 the artistic basis covers the whole field of music, the scientific 
 basis only goes half way. 
 
 The most preposterous attempt at deluding musical 
 students into the belief that their art can be tabulated side 
 by side with chemistry, geology, etc., comes from Germany. 
 
 The author of this work, which rejoices in the title “ Har- 
 mony Simplified,” following the example of his legendary 
 compatriot in the case of the elephant, has evolved a system 
 of harmony out of his inner consciousness. 
 
 I will not enter into the occult mysteries of this simplified 
 system further than is necessary. His derivation of the major 
 key from the harmonic series is similar to the usual one. He, 
 however, with laborious ingenuity, derives the minor mode 
 from the arithmetical “undertones.” Taking the intervals 
 of the harmonic series as they proceed upwards from a low 
 note, we have an 8ve, 5th, 4th, major third, minor third, etc. 
 Now, if we start from a high note and proceed downwards 
 by the same intervals, we get this series : — 
 
 This is a mathematical reversal of the ratios of the har- 
 monic series, and it is a remarkable coincidence that the 4th, 
 
14 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 5th and 6th notes give the minor triad. But the coincidences 
 of mathematics, such as form the bases of card tricks, “think 
 of a number ” riddles, etc., while possessing a certain interest 
 of their own, are not worthy of being pressed into the service 
 of supporting an art not in need of any such aid. 
 
 It is like propping up the dome of St. Paul’s Cathedral 
 with a bamboo fishing rod. 
 
 And as for these arithmetical undertones : the author of 
 “ Harmony Simplified ” maintains that they actually exist, 
 the proof being, presumably, that he says so, at least I can 
 find no other in any of his writings save where he tries to 
 take the low harmonics discovered by Tartini as such proof. 
 These sounds are, however, only clearly explained on the 
 theory of “ difference tones,” of which I may have something 
 to say later. Consequently in the quaint jargon he has in- 
 vented for the simplification of matters, the chord of C major, 
 being derived from C upwards, is called the “ C over-clang,” 
 and the chord of A minor, being derived from the E down- 
 wards, is called the “ E under-clang.” 
 
 This laboured seeking after an explanation or excuse for 
 the minor mode is a marked feature of the scientific craze, 
 and is one than which nothing could be more superfluous. 
 The raison d'etre of this most sublime dialect of musical 
 language lies in ourselves and not in the calculations of 
 acoustical science. Take the music of the Irish, Scotch, 
 Scandinavian and Slavonic races : the untutored, un-“ com- 
 posed ” outpourings of human inwardness, and we find the 
 bulk of it to be minor in tonality. 
 
 Here is what I take to be the true explanation of the matter. 
 The real harmonic series, responding to the minor and major, 
 the grave and the gay, arises from the pulsations of human 
 emotion rather from those of stretched catgut. 
 
 Yet there are men of learning and alleged discernment who 
 waste time in attempting to bolster up the Art of Music with 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 15 
 
 a few coincidences borrowed from the Science of Acoustics. 
 Surely we are not to suppose that the length and capacity of 
 their ears is such as to render music as it stands insufficient 
 for their adequate delectation. 
 
i6 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 CHAPTER III. 
 
 S the imperfections of human vision are 
 largely responsible for the beauty of the 
 painter’s art, so the imperfections of 
 human hearing have influenced the out- 
 ward expression of the inward soul of 
 music. A painter cannot paint things as 
 they are, but as he sees them. And 
 similarly the notes and harmonies of the musician are not 
 true sounds acoustically, but the approximations best appre- 
 ciated by the ears of Western nations. 
 
 As a machine for recording vibrations our aural apparatus 
 is extremely faulty from an acoustical point of view. This 
 everyone can prove for himself by means of the following 
 simple experiment. Set an ordinary tuning fork in vibration 
 by striking one of the prongs smartly on the knee, and hold 
 it to one ear for a fractional period, then pass it to the other 
 ear and back again, repeating the process so long as the fork 
 continues in vibration. The student will be surprised to find 
 a distinct divergence in pitch perception between the two ears, 
 the tone of the fork appearing to rise and fall slightly as it 
 passes from ear to ear. 
 
 By means of calculations, and partly by mechanical con- 
 
THE PLACE OF SCIENCE IN MUSIC. 1/ 
 
 trivances, it is possible to prove many things disturbing to 
 the practical musicians' peace of mind. Those who are 
 steeped in theories do not seem to perceive the beauties of the 
 scheme of tonalities that has been gradually developing in 
 the hands of our greatest masters. Consequently we find 
 many have attempted to overcome the almost insurmountable 
 difficulties that stand in the way of constructing keyboard 
 instruments with perfect intonation. Perhaps the most suc- 
 cessful of these superfluities is Colonel Perronet Thompson’s 
 enharmonic organ. The practical value of this instrument 
 will be apparent, when I remind you that it has no less than 
 seventy-two keys to the octave. By this elaboration he is able 
 to produce twenty-one major scales, and a like number of 
 minors with acoustic accuracy. Such things are interesting, 
 despite the small bearing they have on matters musical. They 
 are a result of the scientific demonstration of the incommen- 
 surability of musical intervals, for acoustics proves pretty 
 fully that a key, or series of intervals, can only be in tune 
 to itself. In other words, that the D of C major is not identi- 
 cal with the D of B flat major, and so on. 
 
 It was felt quite early in musical history that the necessity 
 of breaking down the barriers between the keys was impera- 
 tive. The various attempts at this end resulted in the in- 
 -vention of the system of tuning known as “ equal tempera- 
 ment,” which by well adjusted approximations brings all the 
 twenty-four keys into friendly- inter-relationship. Thus we 
 find science and art opposed. While the one faculty has been 
 seeking a vain thing in the chimera of enharmonic accuracy, 
 the other has displayed a broad-minded content in the simple 
 chromatic system that may justly be called the “survival of 
 the fittest.” 
 
 Beyond this there exists a quasi-enharmonic intonation em- 
 ployed by some vocalists and players of such instruments as 
 leave the adjustment of the intonation in the performer’s 
 
i8 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 hands. But this again is opposed to the teachings of 
 acoustics. If we take the scale of twenty -one notes given by 
 Prof. Haughton in his “ Natural Philosophy ” we will find the 
 order of pitch thus: — C, C sharp, D flat, D, D sharp, E flat, 
 E, F flat, E sharp, F, F sharp, G flat, G, G sharp, A flat, A, 
 A sharp, B flat, B, C flat, B sharp, C. 
 
 But this order of pitch is reversed in almost every case in 
 the practice of the majority of musicians (a practice, be it ob- 
 served, solely depending on the artistic feeling of the per- 
 former) for it is their habit to take chromatically raised notes, 
 full sharp and chromatically depressed notes full flat where- 
 ever such alteration imparts an increased leaning in the direc- 
 tion of its movement. It amounts to a slight exaggeration 
 of any specially marked tendency of progression. 
 
 In this way D sharp as an augmented fifth on G will be 
 taken much sharper than E flat as a minor ninth on D, with 
 an effect that quite justifies the treatment. And this exag- 
 geration is sometimes carried still further by the introduction 
 of variously protracted 'portamenti suitable to the emotion 
 expressed, until the one fatal step from the sublime to the 
 ridiculous is made by the wearisome howl of the small per- 
 former who “ plays with such expression, my dear.” 
 
 It has often occurred to me that it is fortunate for our art 
 that the scientists have not succeeded in foisting on the musi- 
 cians a parliamentary rigid intonation. As matters stand the 
 voices and more expressive instruments give us the artistic 
 intonation just described, and then they join with the fixed 
 keyboard instruments in our so-called enharmonic modula- 
 tions. In these modulations no musician makes any differ- 
 ence between say D flat and C sharp. If a distinction were 
 made all the charm of mystery characteristic of these progres- 
 sions would be lost. The beauty of enharmonic modulations 
 lies in the change in the significance of one unchanging sound. 
 
 It will be seen from the foregoing observations that the 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 19 
 
 science of acoustics stands to the practical musician in a simi- 
 lar relationship to that of instantaneous photography to the 
 painter of race horses. In each case one learns that scientific 
 accuracy is frequently detrimental to artistic effect. 
 
20 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 CHAPTER IV. 
 
 T is remarkable that the modern musical 
 theorists, in constructing their elaborate 
 methods of elucidating the sublime sim- 
 plicity of the art of music, should make 
 such continued reference to the harmonic 
 series. As a matter of fact harmonies 
 have nothing to do with harmony what- 
 ever for the art of combining sounds deals exclusively with 
 fundamental notes. 
 
 If harmonics had the musical value so fondly attributed to 
 them, we should have to include all of them in our practice. 
 This, however, is impossible, for reasons already shown. We 
 are told by one great authority that the departure from just 
 intonation of the seventh overtone is so slight as to be no 
 hindrance to its employment. Against this must be set the 
 fact that on horns, trumpets and other wind instruments 
 whose notes are entirely overtones, this particular harmonic 
 is to our ears so lamentably flat as to be utterly useless, except 
 in the case of the few instruments provided with compensating 
 mechanism, or the slide trombone in which the slide can be 
 made to answer the same purpose. 
 
 Even then the seventh harmonic used is in reality one be- 
 longing to a slightly raised fundamental note, so that we 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 21 
 
 cannot strictly be said to employ the seventh harmonic of any 
 accepted fundamental. 
 
 But, in addition to the partial ignoring of a certain number 
 of essential elements of the harmonic series, there exists a long 
 range of harmonics of another variety which, by reason of their 
 scattered paucity of musical coincidence, are fortunately never 
 dragged in by the heels to support any wing-clipping, art- 
 killing theories. These are the “ difference tones ” and “ sum- 
 mational tones ” resulting from the combination of two or 
 more fundamental notes. They are frequently more apparent 
 to the ear than are the overtones of a solitary note, and many 
 are most inharmonious to their generating fundamentals. 
 Thus we see that acoustics offers the musician more material 
 than he makes use of : and, since his selection and rejection 
 are arbitrary, or, at least, prompted solely by aesthetic feeling, 
 it would appear that music is very little, if at all, indebted 
 to science for its being. 
 
 Finding such confusion of ideas on the subject of the 
 genesis of Western music, it is not surprising that when we 
 come to its application a similar state of affairs is found to 
 prevail. This over-elaboration of the supposed “ science ” of 
 music has grown to such a pitch that it is high time the 
 fungoid overgrowth of theory which obscures the simple 
 directness of musical principles were swept away. 
 
 There is a curious tendency to make harmony do too much. 
 The professors of scientific music forget the place harmony 
 takes in the general scheme of musical theories. Harmony is 
 nothing more or less than a convenient generalization of 
 counterpoint. All music is virtually counterpoint of a sort : 
 even the earliest harmony exercises are but counterpoint in 
 the first species with the canto firmo in the bass. And the 
 moment the progression f f is introduced, the style becomes 
 contrapuntal, and suspensions and passing notes make it still 
 more so. It will be apparent, therefore, that there must fre- 
 
22 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 quently arise cases where the elucidation of the problem pre- 
 sented is extremely difficult and complex if limited to a basis 
 of harmony, or the structure of chords, yet will be found 
 quite simple if explained as counterpoint, or the permissible 
 movements of parts. 
 
 It must be remembered, also, that “ harmony,” which by 
 reason of its firm foundation in figured bass, is such an ex- 
 cellent stepping stone to the study of counterpoint, deals ex- 
 clusively with what is actually present. But this is not good 
 enough for our scientist who loves to fill up his pages with 
 recondite theorising as to what certain chords would be if they 
 were quite different. 
 
 It is to this cause that we must assign the invention of those 
 ponderous cacophonies, the so-called chords of the eleventh 
 and thirteenth. It is exasperating to the practical musician 
 to see men in high positions filling the minds of earnest stu- 
 dents with such superfluous absurdities. 
 
 The theories relating to these pseudo chords are illogical 
 with a quaint redundancy that renders Mr. W. S. Gilbert’s 
 wildest phantasies of serious import by comparison. Not only 
 do they teach us nothing new, but they wilfully obscure that 
 which we already know in music. 
 
 It is amusing to note the mixed ideas that have existed con- 
 cerning these two “chords. Albrechtsberger explains the 
 chord of the nth as a chord of the dominant seventh with a 
 note added at a fifth below the root. And the thirteenth he 
 describes as a chord of the diminished seventh with a note 
 added at a seventh below. 
 
 Richter gives them as follows : — 
 
 -o- -c?* 'c?* "cr 
 
 and speaks very strongly against their serious consideration. 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 23 
 
 Rockstro gives the reverse progressions under these names, 
 thus : — 
 
 Titfi. nth. 
 
 O* CJ- 
 
 Those who follow the Day theory, give us these six chords 
 of the eleventh: — 
 
 Tonic lUlis. 
 
 Dom. iiths. Supeitonic I Uhs. 
 
 
 
 ;i} 
 
 iO 
 
 and these twelve chords of the thirteenth : — 
 
 Tonic major. Tonic minor. Dom. major. 
 
 Dominant minor. Supertonic major. Supertonic minor. 
 
 as belonging to the key of C, and so attempting to substanti- 
 ate the preposterous theory that all the twelve semitones, C, 
 D flat, D, E flat, E, F, F sharp, G, A flat. A, B flat, and B are 
 characteristic of and essential to that key. 
 
 Tonality is entirely diatonic, and chromatic notes always 
 appear strange and disturbing; sometimes, even, to the extent 
 of suggesting a new tonality as in modulation. One has only 
 to play 
 
24 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 to realize this simple truth. In the first example is the pure 
 diatonic sequence of chords, in the second (which we are to 
 consider as a fragment of a chord of the thirteenth), a foreign 
 element is introduced giving to the melody, which had no de- 
 finite tendency before, a strong yearning for the next note 
 which must be satisfied. We accept it by reason of its fitness 
 and beauty of effect as employed by great composers, but it is 
 futile to say the D sharp belongs to the key, or is character- 
 istic of the C tonality, for, if it were, it could not possess that 
 element of surprise which constitutes its principal charm. 
 
 Nothing characteristic of tonality should surprise, and it 
 will be found that it is only such chromatic alterations that do. 
 
 The D sharp in the last example is considered by these 
 theorists as an incorrect notation of E flat, as in their curiously 
 constructed chromatic scale no D sharp is to be found. Here 
 we see how illogical their principles are, for while limiting the 
 number of harmonics we may employ in a given key, they at 
 the same time give us the rules for finding all others. Ac- 
 cording to these rules we find that D sharp is the 75th har- 
 monic of C. 
 
 [Apropos of the above, I may mention that in one celebrated 
 work on Harmony we are told that A sharp is the 225th har- 
 monic of C, yet, in the same chapter we are told that there is 
 no A sharp in the key, only B flat.] 
 
 Returning again to the D sharp in the next example it will 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 25 
 
 be noted that its character is essentially that of a rising note, 
 whereas, if it were written as E flat it would be a sinking note 
 and its natural movement would be thus : — 
 
 By building up such imaginary chords containing all the 
 notes of a key with a certain series of their chromatic altera- 
 tions, it will be seen that by selecting therefrom groups of 
 notes in threes and fours, a large number of chords formerly 
 treated as existing in their own right, can be referred to as 
 various inversions of these all-containing chords. 
 
 Thus the yth on the supertonic : — 
 
 is to be called the second inversion of the dominant nth, and 
 that on the subdominant : 
 
 the third inversion of the dominant 13th. 
 
 As they adopt this method with so many chords it surprises 
 me that they do not “go the whole hog ” and derive every ex- 
 isting chord therefrom. 
 
 Nothing could be more naive than saying, as many do, that 
 a certain chord is the sixth inversion of the dominant major 
 13th written as a mediant triad! 
 
 C 
 
26 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 > 
 
 CHAPTER V. 
 
 LTHOUGH it is possible to explain many 
 chords, progressions and combinations of 
 notes by reference to those acoustic 
 monstrosities, the iiths and I3ths, I have 
 never yet seen a single example that did 
 not admit of a simpler explanation by the 
 earlier methods. In all the works of har- 
 mony I have examined not one has drawn attention to the radi- 
 cal difference between harmonizing and accompanying a 
 melody. If we take a melody and treat it in the first manner, 
 i.e., harmonize it in four parts, we are bound by all the rules 
 of harmony and counterpoint, for, while adding three new 
 parts, we must bear in mind the unity of the whole four. Thus, 
 if the melody makes the suspension 4 to 3, the 3rd may not be 
 heard in another voice simultaneously with the 4th, and so on. 
 
 Now, instead of giving the melody and its accompanying 
 parts tl)e unity of choral treatment, suppose we treat it as a 
 solo for one voice with an “ accompaniment ” for piano, organ 
 or orchestra. At once there is a difference of effect, arid, con- 
 sequently, a difference of treatment. Instead of one thing we 
 hear two. Instead of a landscape or group of figures, we have 
 a portrait with a background. 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 27 
 
 Here we find it no uncommon thing for the accompaniment 
 to give the general scheme of the harmonic progressions with- 
 out reference to the manner in which those progressions are 
 ornamented in the solo part Thus in the suspension 4 to 3 
 selected above one frequently finds the 3rd in the accompani- 
 ment against the 4th in the melody. I have frequently found 
 the augmented 5th in a solo accompanied by the perfect fifth 
 in the accompaniment with no ill effect : such is the duality of 
 a solo with an accompaniment as compared with the unity of 
 a harmonized melody. By taking this dual basis for the treat- 
 ment of melodic material — the actual practice of all great 
 masters — it becomes unnecessary to say that in the one case 
 we have a suspension 4 to 3 and in the other a chord of the 
 nth. We can now say that it is the same thing differently 
 treated. 
 
 In those cases where the 3rd of the tonic is heard against the 
 dominant chord (with or without the 7th) without resolving 
 on to the 5th of the dominant, we have only to accept it as a 
 feature of that particular note that it may be so treated and 
 at once it is justified in counterpoint without the intervention 
 of any absurdities in the way of overgrown imaginary chords 
 of the 13th. 
 
 Another thing that is against the chords of fhe nth and 
 13th is that they do not fall in with the general scheme of 
 chord nomenclature. The notes in a chord are named by the 
 closest interval to the bass at which they may appear. Hence 
 we have a separate figure for the 2nd and gth. A 2nd may be 
 taken as a 9th, but a 9th may never be taken as a 2nd. But 
 the nth and 13th may be a 4th or 6th respectively. As for 
 the incomplete inversions of the 9th, nth and 13th it is incom- 
 prehensible to me that any intelligent person could waste a 
 moment’s serious thought on them. 
 
 The whole basis of music is essentially four-part harmony, 
 and in this it is unnecessary and therefore illogical to con- 
 
28 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 sider anything not actually present. If a chord is figured 
 or 7 there is very little more to be said about it. But in this 
 scheme of mystification, doubtless highly profitable to its 
 teachers, the iiths and I3ths, being without a figuring of their 
 own, lay claim to all the other figurings in turn. 
 
 The complete material of the art of harmony as practiced 
 by all musicians, however some of them may choose to sur- 
 round it with the doubtful halo of irrational theory, is this : — 
 
 The common chord in three positions. 
 
 The seventh in four positions. 
 
 The ninth in one position. 
 
 These eight chords vary diatonically with the degree of the 
 scale they occupy, and are further ornamented and enriched 
 with suspensions, passing notes and chromatic alterations. 
 
 I repeat that this is the entire musician’s palette, and that the 
 extra four positions of the gth, in which the root, above all, 
 is kicked out as an interloper, and the eighteen barbarous iiths 
 and I3ths give the student nothing more unless, indeed, it be 
 headaches and distraction. 
 
 These men deny the legality of chromatic alteration and in- 
 vent this cumbersome system to justify the use of the chromatic 
 notes. But is not their effect sufficient justification? And 
 have we not by means of equal temperament made all scales 
 so closely related that no laboured apology is needed for the 
 friendly interchange of notes that lends such variety of charm 
 to the result? 
 
 To the man “ with no music in his soul ” the cold interest 
 excited by diving into these pedantries may possibly take the 
 place of that musical enthusiasm so essential to the artist. I 
 can only account for the existence of such inartistic elabora- 
 tion by the assumption that in music, as in other professions, 
 men are ocasionally to be found in every way unfitted for such 
 a walk in life. 
 
 With all this piling up of difficulties and complications on 
 
 wio 
 
THE PLACE OF SCIENCE IN MUSIC. 
 
 29 
 
 the natural simplicity of music, it is strange that one progres- 
 sion is systematically left untouched by all the writers I have 
 examined (with the notable exception of Albrechtsberger, who 
 treats it as a passing note.) 
 
 It is certainly not of frequent occurrence, still is well known, 
 Phil. Em. Bach having had a pronounced partiality for it. I 
 speak of those minor cadences in which the two /ths of the 
 melodic scale are heard simultaneously thus : — 
 
 When one realizes what a beautiful explanation could be 
 made on the lines of scientific harmony by constructing a 
 chord of the “ diminished 1 5th on the leading note ” : — 
 
 or still better, a “dominant minor 17th ” : — 
 
 
 
 
 
 one feels that there is “ mischief still for idle hands to do.” 
 With one or two such chords the whole of existing harmony 
 and counterpoint could be abolished, and every little conjunc- 
 tion of passing notes and ornaments could be called a “ chord ” 
 or inversion. 
 
 There is a strong tendency in this direction shown by the 
 distorted interpretations put upon the examples quoted in some 
 books, but it is a consummation devoutly not to be wished for. 
 
30 
 
 THE PLACE OF SCIENCE IN MUSIC. 
 
 It is a matter for regret, or congratulation as the case may 
 be, that I have not more fully entered into an exposition of 
 some of the dishonest methods resorted to in attempting to 
 substantiate these fallacious theories, but I think I have said 
 enough to set the reasonably minded man thinking, with a 
 result I am assured of. As to the unreasonably minded man, 
 I am convinced that a whole houseful of books would not 
 draw him from the circumambulatory path of his stock 
 arguments. 
 
 The chief points I wish to insist on are that the antagonism 
 between musical practice and acoustical theory is of such mag- 
 nitude as to prove the total independence of the two subjects, 
 and that the modern ' theoretical teachings are an excessive 
 overgrowth; obscuring rather than elucidating the principles 
 of harmony, which are largely self-explanatory. In short, I 
 look forward to a return to simpler methods when I3ths shall 
 cease from troubling, and harmonics be at rest. 
 
 I know that to many this will appear a retrograde movement, 
 incompatible with the general progress going on around us, 
 but to my mind, shaking off the trammels of pedantry, and 
 achieving a higher naturalism would be the true fulfilment 
 of progress. 
 
 THE END. 
 
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