portrait of Christopher Simpson 
Christophori Simpson Effigies.    

The Division-Violist: OR AN INTRODUCTION To the PLAYING upon a GROUND: Divided into Two PARTS. The First, Directing the HAND, with Other Preparative Instructions. The Second, Laying open the Manner and Method of Playing Ex-tempore, or Composing Division to a GROUND. To which, are Added some Divisions made upon Grounds for the Practice of Learners.  
By CHR. SIMPSON.  
LONDON, Printed by William Godbid. 1659.   

THE PREFACE.  
IT is not unknown, that He who exposes a Book to Public View, doth also expose it to Public Censure: Nor can I expect a Privilege denied to better Authors. Some will dislike the Matter; Others the Method. Some again, will except against This; Others against That particular Part or Passage; every one censuring according to his Judgement or Fancy.  
As for the Matter or Subject; though in itself, it might deserve acceptance from all that pretend to Division, upon what Instrument soever; yet I offer it only to Those that affect the Viol. The Method is such as I thought might render the Matter most easy; as well to the Hand as to the Understanding. If in This, or That, particular Part, or Passage, I differ from the Judgement of any Master in Music, I am ready to submit to better Reasons, when I shall hear them, pretending to no more than the delivering my Own Opinion.  
True it is; the first Essay of this Treatise was not intended for the Press, but for a private Friend, who desired some Instructions for Playing Division to a Ground. After I had considered what might be said upon That Subject; and committed the Heads to Paper; I found as powerful Motives, to take also into consideration what was necessary to be known in order to those Instructions: (even from the first handling of the Viol) and, thereupon, drew all up into a Compendium, to the end, that what was chief intended for One, might also be useful to Others.  
How far I have acquitted myself herein, must be referred to the Book itself; which, (encouraged by the approbation of Competent Judges) hath now put on the confidence to appear in Public.  
And now I must tell my Reader (if he know it not already) that This Playing Division to a Ground, of which we treat, is the Highest Degree of Excellency that can be aimed at upon the Viol; and includes what else is to be done upon That Instrument.  
All I have to say more, is; that if This which I now expose, prove useful; (be it in the least degree) as either by improving the Knowledge of this kind of Music, in laying the Way more open than it was; Or by serving, and assisting such as be Lovers, or Learners of it; Or if my failings herein may prove an Incitement to some more able Genius to make a better Discourse upon this Subject, I have then attained my desires.  
Chr. Simpson.   

To Mr. Christopher Simpson, upon his Excellent Treatise of Playing Division upon a Ground.  
I Stand not here, your Merits to proclaim,  
Which will be done, by, both your Book, and Fame:  
But, as concerned for our great Art, I may,  
To you, my Thanks, though not my Praises pay.  
To Praise, is to bestow; but what can we  
Give him who has obliged all Harmony?  
For you have drawn her from her gloomy Pit  
Wherein so many Ages she did sit;  
Obscured, either by Design, or Chance;  
By too much Wit, or too much Ignorance.  
You have her inward Beauties now revealed,  
Thinking them Injured, while they were Concealed.  
For, things, that are thus rationally good,  
Are more Admired, the more theyare Understood.  
Her roughest Descants, you have made so clear,  
'Tis as much Pleasure now, to Learn, as Hear;  
For you enlighten all by your own Beam;  
And in a Style, as Charming, as your Theme.  
What then to you (brave Friend) does Music owe,  
Who, in untrodden Paths, hath ventured so,  
To bring to Light, that her Illustrious Birth,  
Derives from all that's great, in Heaven, and Earth;  
And by such certain Scales, her Rules to try,  
As shows both how she conquer's Souls, and why:  
From whence, men may Judiciously invent,  
And bring even Discord into Ornament.  
Your great Desert hath all requital barred;  
We may acknowledge it, but not reward.  
Music herself, with all her Concord's fraught,  
Adorned with every Grace which you have taught;  
And helped by all whom Numbers do inflame  
To Sing a Panegyric to your Name:  
Would only tell the World, That Consort met,  
Not to Repay, but to Confess her Debt.  
For all th' eternity she can confer,  
Is short of that, which you have given her:  
Be this your Glory, to make Music Live;  
'Tis much to merit Fame, but more to Give.  
CHARLES COLMAN, Dr. in Music.   

To his Excellent Friend Mr. Christopher Simpson, upon his most accurate Treatise of Division to a Ground.  

GReat Soul of Music, who shall Sing thy Praise  
Give thee loud Plaudits; circled thee with Bays;  
Crown thy soft Numbers; who, at least, incline  
To treat or descant on this Treat of Thine?  
For he that speaks thee home, 'tis fit he be  
Familiar with thy Soul, thy Work, and Thee.   

Some happy few that know, some that know not  
Thy Worth, promiscuously throw in their Vote;  
And why not I, who by Inspection see,  
My Opticks clear by a Reflex from Thee.  
Mix me i'th' Chorus then, since to thy Praise  
I bring no Flattery; Truth's my only Baise.   

Thou art no God, and yet thou seem'st to be  
A near Resemblance of some Deity.  
Witness that Excellent Scheme, thy Music Sphere,  
And those thy well composed Months o'th' Year;  
Which Months thy pregnant Muse hath richly dressed,  
And to each Month hath made a Musick-Feast,  
Wherein the Graces do so subtly Play  
As they conclude twelve Months within one Day.   

And having raised this handsome Frame of thine  
Thou also givest, Method and Design  
To work by: Rules so perfect, that 'twil be  
Styled Simpson's Grammar unto Harmony;  
By which the Ingenious Scholar is both taught  
To Play, and imitate what thou hast wrought.   

Pack hence ye Pedants then, such as do brag  
Of Knowledge, Hand, or Notes: yet not one Rag  
Of Music have, more than what got by Theft,  
Nor know true Posture of Right Hand or Left:  
False fingered Crew, who seem to understand,  
Pretend to make, when you but mar a Hand.  
You may desist; you'll find your Trade decay:  
Simpsons' great Work will teach the World to Play.   
John Jenkins.   

To Mr. CHRISTOPHER SIMPSON, on his Excellent INTRODUCTION, etc.  
NOr can I silent be, Dear Friend! but must  
Offer my Sacrifice of Praise; as Just,  
And due, to your Great Merit; though it be  
Clad too too meanly in bad Poetry.  
How have the Learned Theoricks of their Ages  
Burdened the World with Volumes; When Three Pages  
Formed by your Nobler Muse, have given Us more  
Than They, or Knew, or Saw, or Herd before!  
How humbly have you stooped to th' Fingers, Hands,  
And Genius of the Weak! what sweet Commands!  
How facile your Examples! Full and Plain,  
Your Rules for Composition! and your Vein  
Of Breaking Descant on The Instrument  
Our Nation Glories in; how excellent!  
Yet here you cease not; but Conduct him, till  
By an Admired Demonstration you fill  
His Heart with Holy Thoughts, his Will with Fire  
Kindled on th' Altar of th' Angelic Choir;  
By which he doth, in Music's Concord's, see  
What he Adores; An Unity in Three.  
Since Than you Thus have taught, and made our Isle  
Justle for Honour, with the World's Vast Pile;  
No more let the Large Continent commend  
Only its Own; no more let it pretend  
To Sole Invention; nor no more our Own,  
Who stride both Sea and Alps to slight their Home,  
Adhere to their past Follies: for they'll find,  
Heaven, Earth, and Art, have here their force Combined,  
To raise a lasting Monument, to your  
Great Name; whilst Time, and Harmony endure.  
MATTHEW LOCKE.   

To my Worthy Friend, Mr. Christopher Simpson, upon his Excellent Treatise of Division.  

YOu common Dabblers, Mercenary Crew,  
That sell your raw, and undigested Strains:  
Which (like your wretched selves) poor and untrue,  
Fall flat, and perish with your bootless gains;  
Cease here your Malice and foul Obloqui,  
Since this great Work detraction doth defy.   

And all you sullen Stoics, full of years  
As are your grosser Rules, sordid and harsh;  
Custom has made you obstinate, as appears  
By your self-willed, or e-grown, and formal Trash;  
Thus dull d by use, you see with affectation,  
Or falser Heresies of Speculation.   

As you renounce the Sense, so 'tis your Fate  
Not to discern, until familiar grown:  
And as your stupid Ears, if pleased; 'tis late;  
The Vulgar so learn Tunes about the Town;  
Unsympathizing Natures, what is Art,  
When such sad Drones her Mysteries impart?   

I would not be mistaken in my Sense;  
You Nobler Souls, Masters and Patrons too,  
With many such like Worthies, that dispense,  
And, in your Spheres, bravely perform, and do;  
All you I honour, as whose Intellects,  
Stored with large Gifts, do merit all Respects.   

No; 'tis those base Professors, insolent,  
As scandalous Pretenders; These alike,  
(As in their Manners ruin all Content)  
Against all Art their Ignorance doth strike;  
But these lost things I neither hate, nor scorn,  
Since 'tis themselves do make themselves forlorn.   

If then thy Cedar Branches, thus out-grow  
The greatest Plants, what are the smaller Shrubs;  
The Sun, as they ne'er saw, so cannot know  
By what strange Rules, thou'st passed the stranger Rubs;  
For hitherto, in this Mysterious Ground,  
None like thy Noble Self this Way has found.   

Brave Friend, with what a modest charge, and mild  
Hast thou now routed all Antagonists;  
Thy Innocence, and Art, so reconciled,  
Thy brighter beams break through their darker mists;  
And generous like thy purer Harmony,  
Thy Virtue triumphs in thy Victory.   

The latitude (extent stupendious)  
Of this great Art, by all uncomprehended,  
Cannot yet limit thy vast Genius,  
But thy unbounded Soul, as being led,  
(Or else inspired) by some mere Godlike sense,  
Thou more than humane natures dost commence,   

As if thy wrestling in thy labours past,  
Were blessings not enough, thou strivest still more;  
And yet thou show'st this cannot be the Last,  
Thy Airy Spirit so aloft does sore;  
Thy pregnant, and unimitable heart,  
Seems greater in thy contemplative part.   

And sure some Angels waited on thy Muse,  
So rare's that Piece, so Moral, so Divine;  
No Mortal such like Similes infuse,  
Nor could another reason do't but thinc;  
Inspired thus, what Fancy dares pretend,  
Or Carp, or Censure, what they ne'er can mend.   

But this rude Age is now so savage grown,  
That only studying Principles of Earth;  
They not discern, nor know what thou hast shown,  
And that this Plenty was so great a Dearth;  
But (when in vain) these shall for mercy cry,  
Their Zeal wants Heav'nly-musicks' sympathy.   

For as these live, so are they living dead;  
Whilst thus thy happy thoughts do upwards climb,  
Thy firmer Soul these lost things cannot dread,  
Corruption's only subject unto them Jime.  
Thy Towering Trophies great with Praises spread,  
(By all good men) shall Crown thy virtuous head.   

And as thou liv'st so shall thy living Fame,  
Raise Monuments, t'eternize thy great Name.   
JOHN CARWARDEN.   

Ad Authorem in Introductionem suam ad Chelyn ex plano cantu Diminutione Modulandam.  
MVsica qualis erat tulerit cum Graecia laurum, &  
Pars reliqua ingenuis artibus orba fuit?  
Luserat in plano cantu pueriliter aetas  
Pristina, & ignavam praedicat usque Lyram.  
Orpheus agrestes animos lenibat & iras:  
Saxea Thebano maenia struxit agro  
Amphion: Sic Diva potens sua munera gestit,  
Eximia & Graios dona referre juvat  
Verùm haec monstra aevi lactentis adultior aetas  
Ridet, & antiquam prodiga fama Lyram  
Dum laudare studet, quanta heu mendacia finxit!  
Commentumque placet queis Vetus omne placet.  
Nos nova miramur meritò, Simpsonus inertes  
Graecorum numeros ocyùs ire dedit,  
Et Testudineos fugit indignataque gressus  
Docta Chelys celeri nunc pede carpit iter.  
Non sic Pythagorae Sphaerarum motibus aures  
Demulsere modís somnia Vana suis:  
Non sic Sirenum Voces adulantur Vlyssi  
(Quem tua Victrici ceperat arte manus)  
Quàm tuus ense truci pollentior imperat arcus,  
Concordesque animas grata tyrannis habet.  
Aemula quae Citharaedi olìm Philomela sepulchrum  
Nacta est in Cithara quam superare velit,  
Si tecum invictam decertans senserat artem  
Quàm placidè fatum sustinuisset avis!  
Invidus angusto tua nec mysteria condis  
Pectore, sed cunctos instruere arte paras.  
Quam dignum aeterno te praestas nomine, terris  
Musica qui tecum regna perire Vetas.  
Musica qualis erat? submisit Graecia laurum:  
Simpsoni ingenio tradita qualis erit?  
Quàm latè regnabit enim tua gloria, cujus  
Arte Chely aeternus conciliatur honos.  
Edu. Gelsthorp.   


CONTENTS of the First Part.  
WHat kind of Viol is fittest for Division, and how to be accommodated. Page 1  
What kind of Bow. Ib.  
How to hold the Viol. p. 2.  
How to hold the Bow. Ib.  
The Posture of the Left Hand. Ib.  
How the Viol is Tuned, and applied to the Scale of Music. p. 3  
An Observation for Playing Notes upon another String. p. 4  
A Rule for the Motion of the Bow. p. 5  
An Observation for Fingering. Ib.  
The Motion of the Right Arm and Wrist. p. 6  
How to gain the Motion of the Wrist. p. 7  
The Motion of the Bow in Double Stops. Ib.  
Of Tripla's. p. 8  
Of Gracing Notes. p. 9  
Of the Concord's in Music; with an easy Way of Joining Parts together. p. 10  
The use of Discords. p. 15  
Reflections upon the Concord's of Music. p. 16   

CONTENTS of the Second Part.  
Of Division to a Ground, and the manner of performing it. p. 21  
Three Sorts of Division, viz. Breaking the Ground, Descanting upon it, and a Mixture of these One with the Other. Ib.  
Of Breaking the Ground. Ib.  
Five Ways of Breaking a Note. p. 22  
How Division is made Harmonious to the Holding-Note of the Ground. p. 24  
How Division is brought off to meet the Next Note of the Ground. Ib.  
How Division is to move below the Ground-Note. p. 25  
An Example of Breaking the Ground. p. 26  
An Observation for Playing Flat or Sharp in the Seventh above, or Second below the Standing-Note. p. 27  
How to Break a Cadent-Note at a final Close, and How, Elsewhere. Ib.  
Of Descant-Division, and how it differs from Breaking the Ground. p. 28  
Concerning a Sixth. Ib.  
Of Mixt-Division. p. 29  
Cadences of two Sorts Ib.  
Examples upon the first Sort of Cadence. p. 30, 31  
Examples upon the second Sort of Cadence. p. 32, 33  
Consecution of Fifths or Eighths; How allowed, or not allowed in Division to a Ground. p. 34  
An Example of a Cadence upon a Breve. p. 35  
Concerning Rising, or Falling, in Thirds, or Sixths; and in what Cases, This, or That is better. p. 36  
Of a Close without a Cadence, and an Example thereupon. p. 37  
Examples of Dividing upon Crotchets, Rising, and Falling, by Degrees. p. 39, 40  
An Example of Dividing upon Crotchets, moving by Leaps or Intervals. p. 41  
Quavers; to be Considered, whether they be not the Minute Parts of some Longer Note. p. 42  
An Example of Dividing upon Quavers, Rising, and Falling by Degrees. p. 43  
Of Notes being made Flat, or Sharp, in relation to the Fourth above, or below. p. 44  
An Example of Quavers Moving by Leaps. Ib.  
How to Play Ex-tempore to a Gronnd. p. 45  
Concerning the Ordering and Disposing of Division. p. 47  
Of Composing Division, for One Viol, to a Ground. Ib.  
Of Two Viols Playing together to a Ground. p. 48  
Some Observations in Composing Division-Musick of Two and Three Parts. p. 49    

Part. I. THE DIVISION VIOLIST: OR An Introduction to the Playing upon a Ground.  
BEfore I treat of Playing Division to a Ground, I suppose it convenient to speak of some things which must be known and prepared in order to that Design. As first, a Viol fitted for that purpose: Next, Hands enabled to Play upon it; and then, some Knowledge in the Concord's of Music. With these therefore I will begin, in assistance to such as are not already sufficiently informed therein: And first, concerning the Viol.   two viols 
What kind of Viol is fittest for Division, and how to be accommodated.  
I would have a Division-Viol to be of something a shorter since than a Consort-Basse, that so the Hand may better command it; more or less short, according to the reach of his Fingers who is to use it: but the ordinary size, such as may carry a String of thirty Inches from the Bridge (duly placed) to the Nutt. The Sound, quick, and sprightly, like a Violin; and Viols of that shape (the Bellies being digged out of the Planck) do commonly render such a Sound. It must be accommodated with six Strings; and seven Frets, like those of a Lute, but something thicker. The Strings, a little bigger than those of a Lyra-Viol, which must be laid at the like nearness to the Finger-board, for ease and convenience of Stopping. The Bridge, as round as that of a Consort-Basse, that so each several String may be hit with a bolder touch of the Bow. The Plate or Finger-board, exactly smooth, and even. It's Length, full two parts of three from the Nutt to the Bridge. It must also be of a proportionate roundness to the Bridge, so that each String may lie at an equal nearness to it.   finger-board 
As for Example.  
If the roundness of the Bridge be as the Arch A. B. then I would have the low end of the Finger-board, 
Let Viol-makers take notice hereof.  to be as C. D. and the top of it as E. F.  

The Bow.  
A Viol-Bow for Division, should be stiff, but not heavy. It's Length, (betwixt the two places where the Hairs are fastened at each end) about 27 Inches. The Nutt, short. The Height of it, about a Finger's breadth, or little more.  
The Viol and Bow thus prepared, I must now teach you how to use them; and, in order thereto, first,   

How to Hold the Viol.  
Being seated, place your Viol decently betwixt your Knees, so that the lower end of it may rest upon the Calves of your Legs. Set the Soles of your Feet, flat on the Floor; your Toes turned a little outward. Let the Top of the Viol be erected towards your left Shoulder; so, as it may rest in that posture, though you touch it not with your Hand.   

How to Hold the Bow.  
Hold the Bow betwixt the ends of your Thumb and two foremost Fingers, near to the Nutt; the Thumb and first Finger fastening upon the Stalk, and the second Fingers end turned in shorter, against the Hairs thereof; by which you may poise and keep up the point of the Bow. If the second Finger have not strength enough, you may join the third Finger in assistance to it; but in Playing Swift Division, two Fingers and the Thumb is best in my opinion.  
Holding the Bow in this posture, you may stretch out your Arm, and draw it first over one String, and then another; crossing them in right-angle at the distance of two or three Inches from the Bridge. Make each several String yield a full and clear sound; and order your Knees so, that they be no impediment to the Motion of your Bow.   

The posture of the left Hand.  
When you are to set your Fingers upon the Strings, you must not grasp the Neck of your Viol like a Violin; but rather, (as those that Play on the Lute,) keep your Thumb on the back of the Neck, opposite to your Forefinger, so, as your Hand may have liberty to remove up and down, as occasion shall require.   man playing a viol 
How the Viol is Tuned and Applied to the Scale of Music.  
It is supposed you understand Song, and consequently the Scale of Music which known, the Tuning of your Viol appears in such order as you see the Six Semibreves, which stand one over another in the first part of the following Scale: Where note, that all the degrees of rising above the highest of those Semibreves, are expressed on the Triple, or highest String, by Stopping it still lower and lower upon the Neck of the Viol.  
 
When you have Tuned your Viol according to the Six Semibreves, your next business is to Play those other Notes, which you see ascend and descend by degrees; over which I have set Figures to direct you with what Fingers to stop them; 1, 2, 3, 4, is set for first, second, third, and fourth Finger. Those which have no Figures are Played on the open Strings.   

Observation for playing Notes upon another String.  
You must know that sometimes Notes are not Played on Those Strings to which they seem properly to belong; but for ease or better order of Fingering, are Played upon some Other String; an instance whereof you have in those two Notes marked with little Stars over their Figures; which Notes are Played upon the second String, though a little before, Notes standing in the same places were Played upon the Triple: and therefore, when any difficulty shall occur in Fingering, you must try which way the same Notes may be expressed with most ease and convenience to the Hand.  
The Example before-going, was set in the whole Scale, that you might better perceive where every Rule and Space take their places upon the Viol: but those that follow, must be set down in the common way of 5 Lines; and when Notes exceed that compass, they are still reduced into 5 Lines, by setting another Cliff.  
This which follows I would have you practise; first, in a slow measure, increasing the quickness by degrees, as your Hand advanceth in readiness; but be sure to make all your Notes sound clear, and full; stopping the Strings firm and hard with the very ends of your Fingers: Also, give as much Bow to every Quaver as the length of it will permit. But before you set upon it, read the two Rules which follow.  
 
Here you must observe two general Rules; one is for Stopping the Strings; the other, for the Motion of the Bow.   

A Rule for Stopping.  
Which is; that when you set any Finger down, you are to let it rest there, (Playing the following Notes with other Fingers) until some occasion require the removing it. This is done, both for better order of fingering; and that the Fingers may pass more smoothly from Note to Note, without lifting them too far from the Strings; as also, to continue the sound of a Note when the Bow hath left it. Instances of these Holding you have where you see such a Stroke as this ✓ marked for a Hold, and drawn from one, to some other distant Note. As for Example; The first four Quavers of the second Bar, have such a Mark under them; which signifies, that the third Finger, which stops the first of them, must be kept on, until you have also played the fourth Quaver; because, in playing the two middle Quavers, there is no necessity of taking it off. The like is to be observed in the rest.   

A Rule for the Motion of the Bow.  
Concerning the Bow, observe; that when you see an Even number of Quavers, Semiquavers, etc. as 2, 4, 6, 8. You must begin with your Bow Forward: Yea, though the Bow were employed Forward in the next Note before them. But, if the Number be Odd; as 3, 5, 7. (which always happens by reason of some Pricknote or odd Rest) the first of that odd Number must be played Backward. And this is most properly the Motion of the Bow; although not absolutely without exception.  
When you can Play the last Example, you may practise This following.  
 
It is now requisite your Hand be accustomed to Play Notes which ascend above the Fretts; (above I call it, in relation to Sound; being lower, as to the Neck of the Viol) to which purpose, I propose unto you the following Example; with which, I must also give you   

An Observation for Fingering.  
Here you may observe, that in any Point of Division which reaches to the lower Fretts, or beyond them, the Highest Note thereof is always Stopped, either with the Third, or with the Fourth Finger. If with the Third; the First and Second Fingers take their orderly places in Stopping the two Notes gradually ascending to it, or descending from it. If the Highest Note employ the Fourth Finger; then the next Note under it, is Stopped, either with the Third, or with the Second Finger; according as the said Under-Note is either Flat or Sharp: If Sharp; with the Third: If Flat; with the Second Finger. But whether the highest Note employ the Third, or Fourth Finger, you may be assured that the 3 d. below it must be Stopped with the First Finger; which always serves as a Guide unto those two Notes which are above it. And whereas you will see sometimes two Successive Notes, Stopped one after the other, with the same Finger; it is always done, either to prepare the Fingers to this Posture, or to remove the said Posture to some other Place. This Order of Fingering, holds good throughout the whole Finger-board, (in Stopping three Successive Notes upon any one String;) with this only difference; that, where the Stopps are Wide, (as amongst the Fretts,) the Fourth or Little Finger, is of more use, then Lower down, where the Stopps are more Contract.  
As for the Posture of the Fingers, in moving from one String to another; (which for diversity of Circumstances cannot so well be reduced to Rule;) I must refer you to your Own Observation; in making use of those Fingers which offer themselves the readiest and aptest for stopping any succeeding Note.  
 
If you find any difficulty in this Example, Play it the slower, until your Hand shall have overcome it.  
I must now apply your Hand to the Playing of quicker Notes, yet not till I have said something concerning   

The Motion of the Right Arm and Wrist.  
I have already told you, that you must stretch out your Arm, so, that your Bow may cross the Strings near to the Bridge: In which Posture, it is more than probable you will move your Shoulder-Joint: for, in Playing long Notes, necessity will enforce you so to do: But if you stir that Joint in Quick-Notes, it will cause your whole Body to shake; which, by all means must be avoided; as also, any other indecent Gesture. Quick Notes therefore must be expressed, by moving some Joint nearer the Hand: which is generally agreed upon to be the Wrist. The Question then arising, is about the Menage of the Elbow-Joint; concerning which, there are two different Opinions. Some will have it to be kept straight and stiff: Insomuch, that I have heard a very Eminent and Judicious Violist positively affirm, That if a Scholar can but attain to the Playing of Quavers with his Wrist, keeping his Arm straight and stiff in the Elbow; he hath got the Mastery of the Bow-Hand. Others contend, that the Motion of the Wrist must be strengthened, and assisted by a Compliance or Yielding of the Elbow-Joint unto it: and they, to back their Argument, produce, for Instance, a 
* Mr. Daniel ●orcome.  Person, Famous for the Excellency of the Bow-Hand, using a Free and Lose Arme. To deliver my own Opinion, I do much approve the straightness of the Arm; especially in Beginners; because, it is a means to keep the Body upright, which is a commendable Posture. I can also admit the stiffness of the Elbow, in Smooth Division; for which it is most properly apt: But Cross, and Skipping Division, cannot (I think) be Well expressed, without some Consent or Yielding of the Elbow-Joint unto the Motion of the Wrist.   

How to gain the Motion of the Wrist.  
The best way I can advise you, is (upon moving the Bow Forward, and Backward) to carry the Hand, To, and Fro, a little beyond the Motion of the Arm; in such manner, that the Arm Returning, shall (as it were) Draw the Hand after it. When you can do this in Longer Notes, you may Practise it in shorter, by degrees; a little Exercise will effect it.  
I will set your next Example in C-fa-ut, with the Lowest String put down a Note, to make it a Sub-Octave thereunto; as we commonly do, when we Play in that Key. And as I have formerly admonished you to Practise your Examples, first Slow, and then Faster, by degrees; that admonition is most requisite in Playing Swift Division; where you must also have a Care, that the Motion of your Bow, and Fingers, do equally answer one another; Bearing your Bow moderately upon the Strings, at a convenient distance from the Point thereof; by which means, you shall make your swiftest Notes more distinguishable: A thing, in which many fail; either through want of a due compliance of the Bow to the Strings; or by not exactly crossing them at a right distance from the Bridge; or else; by Playing too near the Point of the Bow; which Errors I note, that you may avoid them.  
 
I have added a little Piece at the end of this Example, as an Exception against the Rule of Beginning every Even Number, Forward: 
Exception.  (mentioned Page 5.) in which the Quickness of Motion doth not admit a Change of the Bow; But you must Play them (as necessity will enforce you) some Forward, and some Backward. Also quick Notes, Skipping from the Triple to the Bass, and so pursued; are best expressed with Contrary Bows.   

The Motion of the Bow in Double Stopps.  
Here take Notice, that when 2, 3. or more Notes stand One over Another (as you have in two places of the last Example;) they must be played as One; by sliding the Bow over those Strings which express the sound of the said Notes. Now, There they fell out so, as to be Played by putting the Bow forward; which is the usual way, when there comes but one of them by itself. But if there happen divers of them successively (as in the Passages next following,) then, each other of them must, of necessity, be Played by drawing the Bow back: But whether Back, or Forward, be sure always to hit the Lowest String First; and let the Bow slide from it to the highest, touching the middle Notes in its Passage betwixt them.  
 
The Figures, for more convenience, are here set before the Notes; where mark, that where you have this Figure [1] set before 2, 3. or more Notes in one Stop; the First Finger must be laid straight over all the said Notes. In which, as also in all double Stops, the Posture of the Lefthand is the same as if you Played upon a Theorbo, or the Lute in its Old Tuning.  
I will set you one Example more, and then I have done, as fare as concerns exercising the Hand for Division.  
 
When you have practised these Examples according to the Instructions given, you may then, for variety, look upon some of those Divisions adjoined to this Book: Amongst which some are easy made purposely for Learners; others of them require the Hands of a good Proficient. And because in those (as also in other men's Divisions) you will meet sometimes with Tripla's of divers sorts, I think it not amiss to speak of them in this Place.   

Of Tripla's.  
Sometimes the Grounds themselves are Tripla-Time; consisting (usually) either of three Semibreves, or three Minims, or three Crotchets to a Measure. Sometimes you may meet with a Tripla upon a Tripla; as for instance, when, upon a Ground consisting of three Minims to a Measure, each Minim is divided into three Crotchets, six Quavers, or the like.  
Again; in Divisions upon Grounds of the Common-Time, containing two Minims to a Measure, you will meet, now and then, with divers Tripla's: as, sometimes three Crotchets to a Minim, producing six Quavers, twelve Semiquavers, etc. Sometimes three Quavers to a Crotchet, and sometimes also, three Semiquavers to a Quaver: The Measure of all which will not be hard to find out, where the Quantity of each Semibreve is scored out with Bars.  
It now remains, that in directing the Hand, I speak something concerning the Graceing of Notes. And though it be a thing which depends much upon Humour, and Imitation, yet I will try how fare it may be delivered in Words, and Examples.   

Of Graceing Notes.  
Graceing of Notes is performed two Ways; viz. by the Bow, and by the Fingers. By the Bow; as when we Play loud, or soft, according to our Fancy, 
Graces done with the Bow.  or the Humour of the Music. Again; this loud, and soft, is sometimes expressed in One and the same Note; as when we make it soft in the beginning, and then (as it were) swell, or grow louder, towards the middle, or ending. Some also affect a kind of Shake or Tremble with the Bow, like the shaking Stop of an Organ: but the frequent use thereof (in my opinion) is not commendable. To these may be added, that of Playing 2, 3. or more Notes with one Motion of the Bow, which would not have that Grace, or Ornament, if they were Played severally.  
Graces done with the Fingers, are of two sorts: viz. smooth, and shaked. 
Smooth Graces.  Smooth is, when in rising, or falling, a Tone, or Semitone, we seem to draw as it were, the Sound from one Note to another, in imitation of the Voice; and is expressed by setting down, or taking off the Finger, a little after the touch of the Bow. In ascending, it makes that Grace which we call a Plain-Beat or Rise; 
Plain-Beat, Backfall.  in descending, that called a Backfall.  
Sometimes a Note is graced by sliding to it from the Third below, called an Elevation, now something obsolete. Sometimes from the Third above; 
Elevation. Double Backfall  which we call a Double Backfall. This sliding a Third, up, or down, is always done upon one String. Again; a Note is sometimes graced by joining part of its sound to the Note following; like a Prickt-Crochet: whose following Quaver is Placed with the ensuing Note, but Played with the same Bow of his Prickt-Crochet: This we will call a Cadent. There is yet another plain or smooth Grace, called a Spinger, 
Cadent. Spinger.  which concludeth the found of a Note more acute, by clapping down another Finger just at the expiring of it.   

Shaked Graces.  
The other sort of Graces is done by the Shake, or Tremble of a Finger; 
Close shake.  of which, there are two kinds: viz. Close, and Open. Close, is that when we shake a Finger as close and near to that which stoppeth as may be; touching the String, therewith, so gently, and nicely, as to make no Variation of Tone: This may be used where no other Grace is concerned. Open is, 
Open-shake.  when a Finger is shaked in that distance from whence it was removed, or is to be set down; supposing the distance exceed not the wideness of a whole Tone, or two Fretts; for wider than that we never shake.  
Graces made with open Shakes are these. A Beat; a Backfall; an Elevation; 
Shaked Beat.  a Cadent: and double Relish. The Beat is the same in Nature with the Plain-Beat or Rise; the difference, only a short shake of a Finger, before we fix it upon the Place designed. This, as also the Plain-Beat, is commonly made from the Half-Note, or distance of one Fret. The shaked Backfall is likewise the same in Nature with the Plain Backfall, the difference only a shake of the Finger taken off; 
Shaked Backfall,  which must be done in that wideness whence it was removed. How an Elevation, Cadent, and double Relish, employ an open Shake, will better appear in their Examples. To these may be added the Grappo, Trillo, or any other movement of the Voice, imitated on the Viol, by Playing the like moving Notes with one Motion of the Bow.  
The Marks of these Graces, applied to their proper Notes, and their Explications, are as you see following. Exp. is set for Explication. Those Notes which have an Arch, or Struck, set under, or over them, are Played with one Motion of the Bow.  
Beat. exp: Backfall exp: Double-Backfall exp: esevation. exp Spinger. exp: Cadent. exp: Backfall Shaked exp: Shaked Graces Close Shake. exp: Shaked Beat. exp: elevation exp: Cadent. exp: Double Relish exp: or thus: exp: For these, I am obliged to the ever famous Charles Colman Doctor in Music  
Of these, some are more rough and Masculine; as, your shaked Beats and Backfals; and therefore more peculiar to the Basse. Others more smooth and feminine; as, your Close-shake and Plain-Graces, which are more natural to the Triple, or upper Parts. Yet when we would express Life, Courage, or Cheerfulness, upon the Triple, we do frequently use both shaked Beats and Backfals: as, on the contrary, smooth and swelling Notes, when we would express Love, Sorrow, Compassion, or the Like; and this, not only on the Triple, but sometimes also upon the Basse. And all these are concerned in our Division-Viol, as employing the whole Compass of the Scale, and acting by turns all the Parts therein contained.  
The Hand being thus directed, we will now proceed to the Concord's of Music. Not that I make it here my business to treat of all that belongs to the Art of Composing, (a Subject upon-which so many Volumes have been writ) but in assistance to such as be ignorant therein: to show, at least some Rudiments thereof, necessary to be known in Order to our following Discourse: which (perhaps) I shall deliver in a Method more easy than my Reader shall find in other Authors.   

Of the Concord's in Music: with an easy Way of Joining Parts together.  
Although our Excellent Countryman Mr. Morley, in his Introduction to Music, doth take his Sight, and reckon his Concord's from the Tenor, as the Holding Part to which he, and the Musicians of former Times were accustomed to apply their Descant; in order to the Gregorian Music of the Church: yet here, for better Reasons, (as to our present Purpose) I must propose unto you the Basse, as the Groundwork, or Foundation upon which the other Parts are to be erected; 
The Basse is the foundation.  and from which, we must reckon or measure those distances, in the Scale of Music, called Cencords', and Discords. Concord's are, a Third, a Fifth, a Sixth, an Eighth; (by these, I mean also their Octaves.) An Unison I do not mention, because it hath no difference of Tone, but bears the same relation to Concord's, as Unity doth to Numbers. All other Distances; as a Second, Fourth, Seventh, and their Octaves (Computing from the Bass) are Discords. Of Concord's, two are Perfect; viz. a Fifth, and an Fighth. The other two, Imperfect; to wit, a Third, 
Eighth & Fifth are Perfect Concord's. Third and Sixth Imperfect. Two Perfects of the same kind not allowed, the Parts rising or falling together.  and a Sixth. Why this, or that, is called Perfect, or Imperfect, is a dispute which doth not here concern us, the use of them being now our Business. And this to a Beginner, is best delivered in Counterpoint; that is, setting and comparing Note against Note. In order to which you must first know, that two Perfects of the same kind, as two Fifths, or two Eighths, are not allowed in Music, unless when the Notes keep still their places.  
Example.  
5 5 5 5 8 8 8 8 5 5 5 8 8 Not allowed, not allowed, allowed, allowed.  
But you may pass from a Fifth to an Eighth, or from an Eighth to a Fifth, when you please: provided, that one of the Parts, either keep still its place, or remove but one degree; for if both Parts skip together, the Passage is less pleasing.  
As for Thirds and Sixts, which are Imperfect Concord's, two, three or more of them, rising or falling together is no Solecism in Music. In fine, you have liberty to pass from any one, to any other different Concord, so you avoid Relation not Harmonical; that is, a harsh and unpleasing Reflection of Flat against Sharp.  
Next; you must know, that every Composition in Music, be it long or short, 
Concerning the Key, Tone, or Mood.  is designed to some one Key, Mood, or Tone, in which the Basse doth always conclude. This Key, or Tone, is said to be either Flat, or Sharp, in respect of the lesser or greater Third taking its place immediately above it. As for Example, suppose the Key to be in G, with a b Flat in B. Then I say, it is a flat Key; because from G to b Flat is the lesser Third. But if there be no such b Flat standing in B, it is then the greater Third, and called a sharp Key. And so you may conceive of the Key, in any other place of the Scale.  
Now as the Basse is set in a flat, or sharp Key, so must all the other upper Parts; for by Key or Tone, is meant, not only that wherein the Basse doth end, but all the Octaves to it.  
These things known, 
How to frame the Basse.  I would have you prick down some short Basse or Ground; concerning which, take these Advertisements. First, that it be natural to the Key; making its middle Closes, (if it have any) in those Keys which have affinity with the final Key. Such are the Fifth and flat Third above it. If the Key be set with a sharp Third, (which, of itself, is not very proper for a middle Close) you may in stead thereof, make use of the Fourth or Second above the final Key.  
Example.  
Key flat Fifth. Third. Key sharp. Fifth. Fourth. Second.  
Secondly that your Basse do move, for the most part, by leaps of a Third, Fourth, or Fifth; using degrees no more than to keep it within the proper bounds and Air of the Key. Lastly that for more ease, you make choice of a flat Key to begin with; and avoid setting sharp Notes in it, for some reasons which shall appear hereafter.  
Let this short Bass serve you as an Example, which hath a middle Close in B the Flat Third to the Key.  
Example.  
Third.  
Having pricked a Bass in this Manner, you may join a Triple thereto, by setting a Third, Fifth, or Eighth over each Note of the Bass. As for the Sixth (properly belonging to sharp Notes) I shall speak of it by and by. 
How to frame the Triple.  Now, as the proper movement of the Bass, (in Counterpoint) is, for the most part, by Leaps, as before mentioned, so the Natural Progression of the Treble is, a rising and falling by degrees; and therefore when you have set a Third, Fifth, or Eighth, over the first Note of the Bass; you may then take for your next (and so from one to another) that Concord) which affords the nearest compliance to that Movement by degrees, thus:  
Example.  
3 5 3 5 3 5 3 5 8  
If you set a Figure under every Note as you Prick it, to signify what Concord it is to the Bass, (as you here see them) it will be some ease to your Eye, and Memory.  
Here take Notice, that in few Parts, Imperfect Concord's are more delightful than Perfect: as affording more variety, and not satiating or cloying the Ear so much as the multiplicity of Perfects do. Hence it proceeds, that in two Parts, we seldom use an Eighth, unless to the Beginning-Note: Ending Note; some Cadent-Note; or when the Parts proceed in contrary Motion; that is, one rising and the other falling.  
When you are perfect in setting a Triple to your Bass, you may add to them a third Part; 
Composition of three Parts.  as for Instance, an Alt; whose proper Region is next under the Triple; and therefore I would have you set it (Note for Note) in those Concord's which are the nearest thereto. Provided that, if you intent your Composition for no more than three Parts, one of the two upper Parts be still a Third to the Bass: for the reason above mentioned.  
Example.  
3 5 3 5 3 5 5 3 5 8 8 3 8 3 8 3 3 8 3 8  
I have made the Triple and Alt both of them end in the Eighth to the Bass; which in my opinion, is better (the Key being flat) then to have the Triple end in the sharp Third; that Concord being more proper to some inward Part, at a Conclusion.  
As for those two Notes you see made sharp in the Alt; take this observation: that when the Bass rises a Fourth, or falls a Fifth; it commonly requires the sharp or greater Third, to that Note from which it so riseth, or falleth.  
Being Perfect and ready in Composing three Parts; you may try how you can add to them a Fourth, which now remains to be the Tenor; concerning which, these things are to be observed. 
Composition of four Parts  (1) That it be set (as much as may be) in Concord's different from the other two upper Parts. (2) That it be set as near as you can, to the Alt; for the Melody is best, when the upper Parts are joined close together. (3) That you avoid the Consecution of two Fifths, or two Eighths rising or falling together; as well amongst the upper Parts themselves, as betwixt any one Part and the Basse. All which is at once performed, by taking the Next Concord (Note for Note) which you find under the Alt, Thus:  
Example.  
3 5 3 5 3 5 5 3 5 8 8 3 8 3 8 3 3 8 3 8 5 8 5 8 5 8 8 5 8 3  
I have broken the last Note but one, of the Alt, into two Crotchets, and joined one of them to the Note before it; making it, by that means, a Binding Cadence: which you may imitate, upon the like Notes, in that Part always which bears the Sharp or greater Third to the Basse, in the next Note before any Close.  
Here you see Three Concord's, viz. a Third, Fifth and Eighth, interchangeably employed by the Three Upper Parts. And, though for ease, and orders sake, I shown you, first, how to join One Part to your Basse; then Two; and lastly, Three Parts; by setting, and adding one Part after another: Yet, now it is left to your liberty, (when you intent your Composition, at first, for three or four Parts,) to carry on all your upper Parts together; disposing them into these three Concord's as you shall think most convenient. It is no matter which of the upper Parts employ the Third, so any one of them have it. And this is as much as I think necessary, for joining so many Parts together as have been here mentioned; such, 
Concerning a Sixth, and what Notes in the Basse  I mean, as wherein a Sixth is not concerned. But if your Bass have sharp Notes in it (such are commonly the half Note under the Key; the greater Third above it: and sometimes also, the less Third under it; Such Notes, I say, standing in these Places, do commonly require a Sixth to be joined to them, as you here see them.  
Example.  
3 6 3 3 3 3 8 3 5 8 8 3 3 8 8 6 5 8 3 8 5 8 6 5 5 3 3 5 8 3  
Here you have three Notes in the Basse, which require the lesser Sixth to be joined to them. The first in E, (the lesser Third under the Key) whose Sixth is in the Triple. The second in F Z (the half Note under the Key) whose Sixth is in the Tenor. The third in B sharp (the greater Third above the Key) whose Sixth is in the Alt. Concerning which, these things may be Noted. (1) That when the Sixth is used, the Fifth must be left out; for, a Fifth and Sixth, must not sound together in Counterpoint. (2) That the half Note under the Key, doth hardly admit an Eighth to be joined to it, without offence to a critical Ear; and therefore have I put two Parts into one and the same Third, as you see in the first Bar, rather than have any Part to Sound in the Eighth to that sharp Note in F. 3) That Bases consisting much of Notes requiring a Sixth, are more apt for few, then for many Parts. (4) That the Basse, in such kind of Notes, doth want a Third of its full Latitude or Compass, as is evident in this; that if you do but remove the said Notes a Third lower, the Sixths are changed into Eighths, and the other two Concord's, viz. Third, and Fifth, take their accustomed Places, as you may see in the following Example.  
Example.  
3 8 5 3 3 5 8 3 5 3 8 5 3 8 8 8 5 8 3 8 5 3 8 5 5 3 3 5 8 5  
And thus you see how Sixths may be avoided, in case, at any time, one desire it.  
Likewise, you may observe, that seeing a Fifth, and Sixth, are never used together, in Counterpoint; it follows consequently, that there can be but Three several Concord's, (which, commonly are, a Third, Fifth, and Eighth) joined, at once, to the Basse. And therefore, if you would Compose more Parts than four; (as 5, 6, 7, or 8.) it must be done, by redoubling these Concord's in their Octaves; and making them pass into different Changes, (where need requires,) to avoid the Consecution of Fifths, or Eighths, Rising, or Falling together.  
Having given you these general Notions of the Concord's; I will now let you see   

The use of Discords.  
Discords, are two Ways admitted into Music. First, in Diminution: that is, 
Use of Discords in Diminution,  when 2, 3, 4. or more Notes of one Part, are set against One Note of a different Part; as thus;  
Example.  
5 4 6 5 6 5 6 5 4 3 3 4 5 6 3 4 3 4 5 6 3 4 6 5 4 5 3  
Where you may perceive; that, if One Part move by degrees, whilst the Other keeps still its place; the moving Part, must, of necessity, pass (sometimes) through Discords, as well as Concord's. In which way of passing, a Discord may be allowed in any Note of the Diminution, except the Leading Note, which must always be a Concord.  
The other Way, in which Discords, are not only allowed, 
Use of Discords in Syncopation, or Binding.  but of most excellent use, is in Syncopation, or Binding: that is; when a Note of One Part, ends, and breaks off, upon the middle of some Note of a different Part; as you may see in these Examples.  
Syncopation in two Parts.  
8 7 6 6 5 4 3 4 6 7 6 8 3 4 3 4 3 4 3 2 3 8 3 2 3 2323 2 3 4 6 43 8 5676 7676 76765 4 3 8 3 4 3 43238 8 7 6 5 5 3656 7 65 4 3 8  
Syncopation in three Parts.  
5 6 7 6 8 5 6765 7 6 8 3 65 365 365 4 3 8 5656 5656 7 6 5 8 323 3 3 3 4 3 3 3 3 3 843 843 8438 3 33 3 434 3 4 3 8  
In this way of Binding, a Discord may be applied to the First Part of any Note of the Basse; if the other Part of the Binding-Note did sound in Concord to that which went before.  
Discords thus admitted; we are next to consider, how they are brought off; to render them delightful to the Ear; for, simply, of themselves, they are harsh, and displeasing; and introduced into Music, upon the account of Variety; Or, by striking the Sense with a disproportionate Sound, to beget attention to that which follows; to the hearing of which, the Ear is carried on, (as it were,) by a necessary Expectation. This Winding or Bringing a Discord off, in Binding-Musick, is always best effected, by changing from thence into some Imperfect Concord; to which, 
How Discords are to be brought 〈◊〉 in Binding.  more sweetness is added by the Discord going before. Yet here, the Ear is not fully satisfied, until, at last, these Discords, and their Succeeding Imperfect Concord's, arrive at One more Perfect; where, as at a Period, we understand the Sense of that which went before.  
Now; the Rule to be observed in passing from Discords, to Imperfects, is this; That we always deflect to that which is nearest, rather than to one more remote. Which Rule, holds good also, in passing from Imperfects to those more Perfect. Thence it is, (as 
* In his Compendium of Music.  Des-Cartes ingeniously observes, that the greater Sixth passes more naturally into an Eighth: the lesser Sixth, into a Fifth. This little remove, by a Tone, or Semitone, connects, and makes smooth the Air of the Music, in passing from one Concord to another, which, by a greater remove, would often seem disjointed.  
Here I must not omit a Discord, not yet mentioned, which is, a Tritone, or Greater Fourth; as also a Semidiapente, or defective Fifth; (both which are but the same thing in proportion of Sound, though they appear different to the Eye;) of all Discords, 
A Tritone, and Semidiapente.  the most Noble, and of most excellent Use in Music. For, though the common Fourth be a Consonant by accident, insomuch that four Voices cannot be joined in Concordance, without admitting it, betwixt some two of the upper Parts; yet a Greater Fourth, or Defective Fifth, hath this privilege above it, (perhaps by its near Vicinity to a perfect Fifth,) as to be joined, sometimes, to the Basse, without Syncope, or Binding; which is not allowed to any other Discord. It's natural Passage, when it appears as a Fourth, is, into a Sixth; and into a Third, when it appears like a Fifth in this manner.  
Example.  
Tritone. Semidiapente.  
Here take notice, that a defective Fifth, doth, naturally require a Sixth to be joined with it; as you see set in its Example: which, perhaps, may seem a contradiction to what I delivered, (Page 14.) that a Fifth, and Sixth, must not sound together; that is, as Concord's, set without Binding: but here, the Fifth is set as a Discord, bound in with a Sixth, and brought off with a Third. For (as I said before) there can be but three Concord's positively joined at once to the Basse: which are always (except when a Sixth takes place) a Third, Fifth, and Eighth. And therefore, if a Hundred, or Hundred Thousand Voices should be joined together, in Musical Concordance; they must all sound in these Three Concord's, or in their Octaves; which is still but the same Species.  
And here I cannot choose but wonder, 
Reflections upon the Concord's of Music.  even to amazement; that from no more than Three Concord's, and a few intervening Discords; there should proceed such an infinite Variety; as all the Music that ever hath, or shall be composed, in Concordance of divers Parts. This puts me upon a Consideration of the Seven Gradual Sounds, or Tones; from whose various Positions, and Intermixtures, those Concord's, and Discords do arise. These Gradual Sounds are distinguished in the Scale of Music, by the same Seven Letters, which in the Calendar distinguish the Seven Days of the Week: to either of which, the adding of more, is but a rendering of the same again. This Mysterious Number of Seven leads me into a Contemplation of the Universe; Whose Creation is delivered unto our Capacity, not without some Mystery, as begun and finished in Seven Days. Within the Circumference whereof be Seven Great Bodies in continual Motion (choose whether you will have the Sun, or Earth to be the Fixed Centre) producing still New and Various Figures, according to their divers Positions One to Another.  
When with these I compare my Seven Gradual Sounds, I cannot but also admire the Resemblance of Their Harmonies: the Concord's of the One so exactly answering to the Aspects of the Other; as an Unison, to a Conjunction; an Octave, to an Opposition; the Middle Consonants in a Diapason, to the Middle Aspects in an Orb; as a Third, Fifth, Sixth in Music, to a Trinc, Quartile, Sextile in the Zodiac. And as These by moving into Such and Such Aspects, transmit their Influences into Elementary Bodies; so Those by passing into Such and Such Concord's, Transmit into the Ear an Insluence of Sound, which doth not only strike the Sense, but even affects the very Soul, stirring it up to a devout Contemplation of that Divine PRINCIPLE, from whence all Harmony proceeds; and therefore very fitly applied to Sing and Sound forth his Glory and Praise.  
When I further consider, that taking any One Sound, if you join thereto Another, a Third above it; and then place Another, a Third above that also; these Three thus conjoined and Sounding together, do Constitute One entire Harmony, which Governs and Comprises all the Sounds, which by Art, or Imagination, can at once be joined together in Musical Concordance: This I cannot but think a Significant Emblem of that Supreme, and Incomprehensible Three in One, Governing, Comprising, and Disposing the whole Machine of the World, with all it's included Parts in a Perfect Harmony.  
I insist not upon things of common observation; as, that a String being Struck, the like String of Another Instrument Tuned in Concordance to it, should also Sound and move; or that the Sound of a Sackbut, Trumpet, or like extended Tube, should by a stronger emissi●on of the Breath, Skip from Concord to Concord, before you can force it into any Gradation of Tones, etc. What I have already mentioned, is enough to persuade me, that in the Harmony of Sounds, there is some great and hidden Mystery above what I find delivered.   

The precedent Discourse of the Concord's of MUSIC, and their Analogy to the Aspects of the Planets, Illustrated in the following SCHEME.  
WHere, you have the Seven Gradual Sounds, in their orderly Progression, represented on the Diameter-Line. Upon which is also described a Diapason, with its included Consonants; according to the Arithmetical Division thereof; as experimentally found upon a Monochord, or the String of any Instrument. The outmost Circle represents the Zodiac, and the Aspects of the Planets; to which you see the Diapason, with its Intersections, exactly agreeing; as, viz. the two Terms thereof, to a Conjunction, and Opposition. The Middle Section (which generates a 5 th'. on One side, and a 4 th'. on the Other) to □. A 3 d. and a 6 th'. completing also the Compass of an Octave; as a △, and ⚹, do a Semicircle; or the two opposite Points in an Orb. To which may be added, that a Diapason, consisting of Twelve Semitones; doth also answer the Zodiac, divided into Twelve Signs.  
The other Figure shows, that all the Sounds, that can possibly be joined, at once, together, in Musical Concordance; are still but the Reiterated Harmony of Three.  
I could be glad, if these my Reflections upon the Concord's of Music, might occasion a deeper search into the Theory and Mystery of Sounds. However; let me commend unto you (if you be not versed therein already) the Practical use of the said Concord's, in joining Parts together, according to the Instructions I have given; by which means, you will become more perfect in the Scale, more knowing in Composition, and consequently more capable of that which follows in the Second Part.  
Tria sunt omnia  
Benedicta sit sancta et individus Trinitas    

Part. II. THE DIVISION-VIOLIST: OR An Introduction to the Playing upon a Ground.  

Of Division to a Ground, and the Manner of performing it.  
DIminution, or Division to a Ground, is the Concordance of quick and slow Notes. The manner of expressing it is thus. A Ground, Subject, or Basse, (call it which you please,) is pricked down in two several Papers: One, for him who is to Play the Ground (upon an Organ, Harpsecord, or what other Instrument may be apt for that purpose;) the Other, for him who Plays upon the Viol: who, having the said Ground before his Eye; (as his Theme, or Subject;) Plays such variety of Descant, and Division, thereupon; as his Skill, and present Invention, do then suggest unto him. In this Manner of Play, (which is the Perfection of the Viol, or any other Instrument; if it be exactly performed;) a Man may show, the dexterity, and excellency, both, of his Hand, and Invention; to the Delight, and Admiration, of those that hear him.  
But this, you will say, is a Perfection, which few attain unto; depending, upon the quickness of Invention, as well as quickness of Hand. I answer; it is a Perfection, which some excellent Hands, have not attained unto; as wanting those Helps which should lead them to it: The supply of which want, is the business we here endeavour. True it is, that Invention is a gift of Nature: but much improved by Exercise, and Practice. He, that hath it not, in so high a Measure, as to Play Extempore to a Ground; may, notwithstanding, give both himself, and hearers, sufficient satisfaction, in Playing such Divisions, as Himself, or Others, have made for that purpose. In the performance whereof, he may deserve the Name of an Excellent Artist. For here, the Excellency of Hand, may be showed, as well, as in the Other; and the Music, perhaps better; though less to be admired, as being more studied. But to our matter in hand.  
The Instrument we here propose, is the Basse-Viol, accommodated as mentioned (Page 1.) The Compass whereof, extends, from a Fourth, or Fifth below Gamut, to as much above Ela. In Playing to a Ground, we exercise this whole Compass; acting therein, sometimes a Basse; sometimes a Triple, or some other Part. From hence proceed Two Kind's of Division. Viz. 
* Three sorts of Division expressed on the Viol. viz. Breaking the Ground Descanting upon it, and Mixture of these together. What Breaking the Ground is. Five ways of Breaking a Note.  A Breaking the Ground, and a Descanting upon it. Out of which Two; is generated a Third Sort of Division: to wit, a Mixture of those One with the Other; which Third, or last Sort, is expressed, in a two fold manner: that is; either in single, or in double Notes.  
These several sorts of Division, are used upon the Basse-Viol, very promiscuously: according to the Fancy of the Player, or Composer: howbeit, for Order, and Method's sake, I must discourse of them severally: and will begin with that   

Of Breaking the Ground.  
Breaking the Ground, is the dividing its Notes into more diminute Notes: As for Example; a Semibreve may be broken, into Two Minims, Four Crotchets, Eight Quavers, Sixteen Semiquavers, etc. This Breaking, or Dividing a Note, admits Divers Ways of expression: according to the divers ordering, and disposing, the Minute Parts thereof, as  
First; 
First way.  when there is made no Variation of Sound; by reason of the Minutes standing still in the same Place; or Removing into the Octave, which I account but the same Sound; as you see in breaking this Semibreve.  
Example.  
 
Secondly; 
Second way.  when the Sound is varied, and yet the Air retained; either by a quick return, or keeping near, to the place of the Note divided; as thus,  
Example.  
 
Thirdly, 
Third way.  when those Minutes, are employed, in making a Transition to the ensuing Note; commonly called the Breaking one Note to another: as you see in these following Examples; where Notes are broken, to all the several distances in an Octave; both ascending, and descending.  
Example.  
Third Fourth Fifth Sixth Seventh Eighth Second Third Fourth Fifth Sixth Seventh Eighth Second Third Fourth Fifth Sixth Seventh Eighth Descending Second Third Fourth Fifth Sixth Seventh Eighth  
 
I have set some of these Examples, in higher Cliffs; because, this breaking a Note, by way of Transition, holds good, in higher Parts, as well, as in the Basse.  
Fourthly; when the Minutes, into which a Note is broken, are employed, 
Fourth way.  in Skipping from One Concord to Another; as you see in breaking these four Semibreves.  
Example.  
853 468 8 5 6 3 5 8 5 3 468 8 5 3  
Fifthly; when the said Minutes, 
Fifth way.  make a Gradual Transition into some of the Concord's; (which is effected, by making 3, 4. or more of them, ascend to the said Concord, by degrees;) returning from thence, either, to end in the Sound of the 
* Holding-Note, Standing-Note, Ground-Note, and Note divided are the same.  Holding-Note, or else, passing on to meet the Note following. And though this moving into the Concord's, be the very same with Descant-Division, so long as it is in that Motion; yet, in regard of its returning, either to its Own Note, or to meet the Next Note, in Nature of a Basse, we must here rank it under the Name, and Notion of Breaking the Ground. The manner of it you may see in these Instances.  
These pass up to the 3.d d These to the 5.th These to the 8.th These to a 3.d d higher These to a 5.th higher. These to a 3.d d These to a 5.th These to an 8.th These to a 3.d d higher These pass to the 4.th below These to a 6.th below These to the 8.th below These into Concord's both above and below.  
In this Fifth, and Last way of Breaking a Note, consisteth the chief Mystery of Playing, or Making Division to a Ground: which may be referred to these two Heads. (1) That it be Harmonious to the Holding Note. (2) And, that it come off so, as to Meet the beginning of the Next Note, in a smooth and natural Passage. How it is made Harmonious to the Holding Note, 
How Division is made harmonious to the Holding-Note of the Ground.  was showed in the precedent Example: to wit; by Passing into its Concord's. True it is, that Division doth sometime pass into a Discord, as the proper place designed; as you see in these two Instances:  
This passes into a 4.th This into a 7.th  
But, this is done, upon the same account, that the very same Discords are used in other Composition.  
As for bringing the Division off, 
How Division is brought off to Meet the next Note of the Ground.  to Meet the beginning of the Next Note, it is done much after the same Manner, as passing into Concord's: that is to say; by making the last Three Minute Notes (at least two of them) ascend, or descend, by degrees, unto the said Next Note, as you see here following, where the Semibreve in G, is broken to every distance in an Octave.  
As thus or thus Thus or thus Thus or thus Thus or thus etc.  
This holds good, be the Division Quicker, or Slower; only that in quick Division more of the Minute-Notes will offer themselves in making this Gradual Transition unto the succeeding Note, as you may observe in the Semiquavers of the precedent Instances.  
Now; suppose this Transition, which is made by Two, Three, or more Notes, should in stead of the Unison, meet the Next Note of the Ground in a Third, or Fifth, above; by which means it is changed into Descant-Division; it is still but the same thing, (quatenus Division to a Ground▪) and therefore left to your liberty to use This, or That, as there shall be occasion.  
By this which hath been showed, I suppose you see what belongs to Breaking a Note; but this requires not only a Notion, but Habit also; which must be got by Practice. Wherhfore, I would have you prick down some easy Ground; and break each Note to other, according to what hath been delivered: To the better effecting whereof; I will set you an Example, with which take these Advertisements.  
First; that your Division be natural to the Key of your Ground, in relation to Flatts and Sharps.  
Secondly; you are to consider that a Seventh, or Sixth, Falling, is but the same with a Second, or Third, Rising; and so all other Distances the same with their Opposite Octaves; thus exemplified.  
2d. 3 d. 4 th'. 5 th'. 6 th'. 7 th'. 8 th'. 7 th'. 6 th'. 5 th'. 4 th'. 3 d. 2 d. 8 th'.  
Whence it follows; that you may choose, whether you will meet any succeeding Note of the Ground, in the Unison, or in the Octave; either above, or below it: for, de octavis eadem est ratio.  
Thirdly; in such places, as the Ground doth intimate a Cadence, by 
* Vide Page 13.  Falling a 5 th'. or Rising a 4 th'. all the Notes that hit upon the 3 d. above, or 6 th'. below, must be Played sharp.  
last; as your Division passes into the 3d. and 5 th'. whilst it moveth above; 
How Division is to move below the Ground-Note.  (by which means it is made Consonant to the Ground-Note;) so; in moving beneath, it must pass into the under Octaves of the said Concord's; viz. into the 4 th'. and 6 th'. below the standing Note.  
Example.  
5 3 5 5 3 5 5 3 5 4 6 4 4 6 4 46 4  
These things being known; you may Break your Ground, in such manner as follows: where, you have the Division placed over the Ground; that you may better observe the Breaking of each Note.  
An Example of Breaking the Ground  
Here you see every Note of the Ground, Broken, still, according to some One, or Other, of those five ways before mentioned; (as, indeed, no Note can be broken, but must relate to some of them,) only, in one place, I have made the Division, meet the Ground-Note in the 3 d. in another place; in the 5 th'. both which are marked out unto you, for your imitation; when the Point, or any other convenience, shall invite you thereunto.  
Some other things there are, which offer themselves to observation in this Example. One is; concerning the Second below, and Seventh above, the Divided-Note, 
An Observation for Playing Flat, or Sharp, in the Seventh above, or Second below the Standing-Note.  which you see, sometimes Flat, and sometimes Sharp. Although it be hard to determine, what a Composer may Approve, or Disapprove, in divers Cases concerning Flatts, and Sharps, (in which doubts, the Ear must be chief Umpire;) yet, in This Particular, something, I think, may be delivered, by way of Rule: which is; that if we descend a Second, and immediately ascend to the place of the former Note; the second must be sharp, (The same is understood of the 7 th'. above, in reference to the 8 th'.) as you see in Breaking this Semibreve in D.  
Example.  
 
Here, if you consult your Ear, you will find, that C, Naturally, requires a Sharp, when the next Note immediately ascends again to D. But in the Second Instance, where the Next Note doth not so ascend, no Sharp is required.  
This Rule of Sharp, in case of ascending, admits yet some Exceptions. First; if the Ground do suddenly Rise, or Fall, to a flat second. Secondly; if it fall a 3 d. last; if it rise a 4 th'. or fall a 5 th'. in nature of a Cadence; in These Cases, though the Division rise again, to the place of the former Note, no Sharp is to be added; as thus,  
Example.  
 
Another thing to be noted, is concerning a Cadence; which (as I have said) is intimated, when the Bass falls a 5 th'. or rises a 4 th'. But we must put a difference betwixt a Cadence, at a Close, and in Other places of the Ground. 
How to break a Cadent-Note at a final Close, and how elsewhere.  It the Basse falls a 5 th'. at, or near the beginning of your Ground; or in any Other place where a Close is not signified; you may Break the antecedent-Note, either in Transition, by degrees, or in what manner pou please: But, at a Close, I would always have the Division of the said Note to end in its own Sound, and, from thence, Break off into the Close-Note: retaining still the distance, of rising a 4 th'. or falling a 5 th'. as you did see in the Conclusion of each Strain of the Precedent Example.  
And here I cannot but take notice of an Error which I have observed in some, reputed excellent Violists, who in Playing a Consort-Basse, would sometimes at the very Close, run down by degrees to the concluding Note, which is very improper; for if any Upper Part do Fall from a 5 th'. to an 8 th'. (a thing most frequent) the Basse by such a descent in degrees, doth make two 8 this. to the said Part, as in this Instance.  
Example.  
5 8 5 88 5 88 5 88  
Although this running down by degrees, seem worse in Playing a Consort Basse, then in a Division to a Ground; yet, in This also, it doth not want its bad Consequence: the Organist commonly joining such Parts unto his Ground, as the Composer doth unto his Basse.   

Of Descant-Division, and how it differs from Breaking the Ground.  
Descant-Diminution, or Division, is That, which maketh another distinct, and concording Part unto the Ground. It differs from the Former, in These Particulars. That, breaks the Notes of the Ground; This, descants upon them. That, takes the liberty to wander sometimes beneath the Ground: This, (as in its proper Sphere) moves still above it. That, meets every succeeding Note of the Ground, in the Unison, or Octave: This, in any of the Concord's. But in the main business of Division they are much the same; for All Division, whether Descant, or Breaking the Basse, is but a Transition, from Note, to Note; or from Concord, to Concord; either by Degrees, or Leaps; with an intermixture of such Discords, as are allowed in other Composition.  
The Laws, or Rules, to be observed in Descant-Division, are the same with Singing, or making Descant to a Basse Plainsong: or those I gave you, in joining another Part to a Basse, or Ground. That is to say; you may begin, with a 3 d. 5 th'. or 8 th'. to the Ground-Note, Passing On, to meet the Next Note also, in a 3 d. 5 th'. or 8 th'. and so, from Note, to Note; always provided that you avoid the Consecution of Two 5 'tis. or Two 8 'tis. One after Another.  
Now; for the Manner of this Passage, from Note, to Note, we must have recourse again to the five ways of Breaking a Note, mentioned, Page 21. which are of the same use in Descant, as in Breaking the Basse. For Here, as in the Other, a Note is sometimes Broken, without Variation of Sound; according to the first way. Sometimes Varying the Sound, and retaining the Air; as in the Second way: Sometimes (again) by making a Transition unto that Concord, in which you intent to Meet the Next Note of the Ground; in such 〈◊〉 ●●●ner, as you made it to the Note itself; according to the Third way: viz. by making 2, 3. or more of the Minutes ascend, or descend unto it, by degrees. Lastly, your Division may pass into the Ground-Note's Concord's, either by Leaps, according to the Fourth way; or by Degrees, like the Fifth way, (which as I said (Page 23.) is Descant, so long as it continues in That Motion) and from thence, Return to the place where it begun, or else Pass On, to Meet the Next Note of the Ground in some of the Concord's; according to the Nature of Descant. These several ways of Breaking a Note, are lest to your Liberty, to use This, or That, as there shall be occasion.  
A Discord, (viz. a Second, Fourth, Seventh, or their Octaves) is never to be used, to the beginning of the Ground-Note, unless in the way of Syncope, or Binding▪ as hath been showed.  
A Sixth, is seldom used as the Leading-Note of the Division, to any Note of the Ground, 
Concerning a Sixth.  unless in binding; or, to such Notes of the Ground as require a Sixth to be joined to them, in place of the 5 th'. What Notes those are, was partly showed, Page 13. to wit; such, under which we suppose the Sound of a 3 d. to make up the full Latitude, or Compass of the Basse: not only sharp Notes, as there mentioned, which require the Lesser 6 th'. but sometimes also flat Notes, requiring the Greater 6 th'. as you see in the Middle Bar of this Example; in which the black Notes express the full Compass of the Basse.  
Example.  
6 6 6 6 6 6  
Now, if you do but break this Ground according to the black Notes, you will find that your Division doth, of itself, produce 6 this. to those Notes which stand a 3 d. higher, as thus:  
Example.  
6 6 6  
And here you may perceive a reason, why such Notes affect a 6 th'. more than a 5 th'. because a 5 th'. would be a Discord to the 3 d. below; which, (as I have showed) is the Natural Compass of the Basse.   

Of Mixed Division.  
Mixt-Division, I call That, which mixeth Descant, and Breaking the Ground, 
What Mixt-Division is.  One with the Other; under which Term I comprehend all Division, which presents unto our Ears, the Sounds of two, or more Parts moving together; which is expressed, either in Single-Notes, by hitting first upon one Part, and then upon Another; or in Double-Notes, by touching Two, or More Strings at once with the Bow. This; as it is more excellent than the single ways of Breaking the Ground, or Descanting upon it; so it is more intricate; and requires something more of Skill, and Judgement, in Composition; by reason of certain Binding, and Intermixtures of Discords, which are as frequent in This, as in Other Figurate Music.  
I will now give you Examples of This, and Descant-Division: not insisting upon the several distances in an Octave, (now less needful,) but upon such Passages as offer themselves most remarkable in Grounds; such are Cadences. And these, (how numerous soever they seem to be) are, in effect, but Two; that is to say, 
Cadances of two sorts.  either a 7 th'. brought off with a 6 th'. after which the Basse falls a Tone, or Semitone; or else a 4 th'. brought off with a 3 d. after which the Basse commonly falls a 5 th'.  
Example.  
7 6 7 6 4 3 4 3 4 3  
Your first Example shall be upon the First Cadence, and Notes Leading to it; in which, you shall have, First; the Ground broken; Then; Descant; and Lastly; Mixed Division, both in Single, and in Double Notes; by which means, you may better discern how they differ, One from Another.  
Example upon the first sort of Cadence. Ground broken Descant Mixed Mixed  
Here note; that in Playing to a Ground, we sometime (for Humour, or Variety) hold out one Note of Descant, to Two or Three Notes of the Ground, (such as will bear it) as you see in the first Variation of Descant, in this Example; where you may also behold a 7 th'. brought off with a 6 th'. which passeth immediately into its 
* Vide Page 16.  desired 8 th'. In the other Variations of Descant you have This Figure [6] set under Those Notes which Led the Division, answering to That Note of the Ground which requires a 6 th'. last; you may observe, that sometimes, part of the Last, or concluding Note, is also divided; which is left to the Liberty of the Player or Composer.  
Your Next Example, is the same Cadence, in sharp Notes.  
Example upon the first sort of Cadence Sharp Ground broken Descant Mixed Mixed  
Though the Ground of these two Examples, be the same Notes; and consequently, the same Descant, or Division, which serves for One, might also serve for the Other; yet I was willing to set them Both; that you might perceive, how great a difference of Air, there is betwixt the same Notes, Flat, and Sharp; as upon hearing, will better appear unto you.  
We will now proceed to the other sort of Cadence; which is, a 4 th'. brought off with a 3d. And First, upon a Minim, thus.  
Example of the Second Sort of Cadence upon a Minim Ground Broken Descant Mixed Mixed  
Where you see, that if the Notes be Played twice so Long, as they are here set down; the Example is then a Cadence upon a Semibreve. Notwithstanding, I will set you it upon a Semibreve; and that I may comprise something more, under the same Example, I will place Four Minims before it; by which you may see how to divide upon Notes descending by degrees.  
Example of the Second Sort of Cadence upon a Semibreve Ground broken Descant Mixed Mixed  
In This, and also in Other Examples, there is One thing which may Scandalise a Young Musician; and perhaps give Offence to some Old Critic: in prevention whereof, I think it not amiss to speak a little.  
Every Composer knows that the Consecution of 5 this. or 8 this. is not allowed in Music; that is, 
Consecution of 5 this. and 8 this. how allowed, or not allowed in Division to a Ground.  betwixt two Different Parts, or Voices. Now; when we Play Division to a Ground, it is to be considered, whether, or no, we Play a Different Part from the said Ground. I answer; in Descant-Division, we do: But in Dividing the Ground, we Play but the same Part with it; in which doing, if we hit upon the 8 th'. Above, or Below the Ground-Note, (which will produce, sometimes two or more 8 this. together, as you see in the first Variation of the Precedent Example;) yet, This is still to be accounted, as but One, and the same Sound with the Basse; and therefore, if any man except against such a Consecution of 8 this. he may as well except against the Lute, Harpsecord, and other Instruments, which have Octaves joined to their Bases; which being struck one after another, produce the Consecution of so many 8 this. together.  
As for 5 this. they cannot occur in Breaking the Ground; because there we meet every Succeeding Note, in the Unison, or Octave. If they happen in Descant, there is no Apology for them, except that One of them be a False, or Defective 5 th'. which, though not allowed by Morley, and some other Precise Musicians of Former Times; yet Kirker, Mersennus, and most Modern Authors, as well Writers, 
Two 5 this. allowed, if one of them be defective.  as Composers, do both Use, and Approve it. For my Own Part, I do not only allow the Consecution of Two 5 this. when One of them is Defective; but, (being rightly taken) esteem it among the Elegancies of Figurate Music.  
Your Next Example, is a Cadence upon a Breve, with Four Minims ascending by Degrees unto it.  
An Example of the Second Sort of Cadence upon a Breve Ground broken Descant Mixed Mixed  
In the Mixt-Division of these Examples, you have, in some Places, many 6 this. taken One after another: 
Concerning Rising or Falling in 3 ds. or 6 this. and in what Cases This or That is better.  in other Places, many 3 ds. Concerning which, observe; that in Notes where we hit two Strings at once with the Bow, 3 ds. are more easy for the Hand, and also more pleasing to the Ear, than many 6 this. together. But in Mixed-Notes, where we hit One String after Another, 6 this. are better than 3 ds. for the Leaps being greater, a greater diversity of Sound is presented to the Eare. Thence it proceeds that in Skipping-Division, we rather make use of 10 this. then Simple 3 ds. when there follows many of them, One after Another.  
Having spoken of Cadences, I must not omit a Close, which is made, without either of the before mentioned Cadences, and used for a Conclusion to some Fancies, Motets, or other Grave Music; in which the Basse Falleth a 4 th'. or riseth a 5 th'. and part of the final Note is commonly taken in to the Descant in this manner.  
Example.  
 
I will give you One Example of dividing upon it, because if at any time you Play or Compose Division to a Through-Basse, or continued Ground, you may happily meet with it. I will also set down a Long, or Four Semibreves, before the concluding Note, because I have known some Beginners apprehend great difficulty, in Playing upon Notes standing long in the same place.  
When you see any Note with a Tail both upward and downward, (as in the Seventh Line of the next following Example) it signifies the Sound of two Strings in Unison; one being stopped, the other open.  
An Example of a Close without a Cadence  
I have not applied This Example into the several Sorts of Division; because, the Gronnd-Notes standing so long in the same place, do not admit a distinction, betwixt Breaking the Ground, and Descanting upon it: But this, which I have done, may suffice, to show you the way of Dividing upon such Notes, albeit their Continuance were longer in the same place.  
And, whereas in all the other Examples, I have Set the several Ways by themselves; that you might better perceive how they differ, One, from Another; yet, in Playing, or Composing, Division to a Ground, we may either Continue any One way, (perhaps a whole Strain together) or Change, from This, to That sort of Division as best pleases our Fancy; in so much, that sometimes, Part of the same Note is Broken in One Sort of Division, and Part of it, in Another, as you see in this Instance.  
Example.  
 
In which, the First Part of the Semibreve in D, is Divided, according to the way of Breaking the Ground, and the Latter Part of it, in the way of Descant.  
Hitherto, we have treated concerning the dividing of Minims, Semibreves, or Longer-Notes; which, duly considered, might also serve for Notes that are Shorter: but, that I may, as near as I can, omit nothing which may ease, or assist the Young Practitioner, I will give some Examples upon Shorter Notes, as Crotchets, and Quavers; with such Observations, as I think requisite; and First, of Crotchets Rising, and Falling, by Degrees.  
An Example upon Crotchets ascending by Degrees The Ground broken Descant Mixed Mixed  
An Example upon Crotchets descending by Degrees The Ground broken Descant Mixed Mixed  
In these Two Examples, you have had Crotchets, Rising, and Falling, by Degrees. I will now show you them moving by Leaps, or intervals, in a Ground of two Strains.  
An Example of Crotchets rising and falling by leaps The Ground The Ground broken Descant Mixed Mixed  
In This Ground, you have all the intervals, or Distances, which are in an Octave; for in the First Strain, you have 3 ds. Falling, and 4 this. Rising; which include, (as the same thing,) 6 this. Rising, and 5 this. Falling. In the Second Strain; you have, (on the contrary,) 3 ds. Rising, and 4 this. Falling; which is the same with 6 this. Falling, and 5 this. Rising. And lastly, for 7 this. you have Them included (by their Opposite Octaves) in Those Notes, which Rise, or Fall, by Degrees.   

Of Quavers.  
If Quavers occur, 
Quavers to be considered, whether they be not the Minute Parts of some longer Note.  in a Ground proposed unto you, to Play, or Make Division upon; you are, First, to consider, whether, or no, they be not the Minute Parts of some Longer Note; as for Example; when they move by Degrees, in such Instances as These.  
Example.  
 
Here, they signify no more than the Plain-Notes you see in the Next Bars after them: and therefore, if you Play upon Such Quavers, as though they were the said Plain-Notes, making your Division proceed in a contrary Motion, it may pass for current, especially in Playing to a Ground, Ex tempore. But in case you desire to divide the Quavers Themselves, or to Play Descant, or Mixed Division Upon them, I will show you them, according to the Method of our former Examples, both, Rising, and Falling, by Degrees.  
An Example upon Quavers Rising and Falling by Degrees The ground The Ground broken The Ground Descant The Ground Mixed Mixed  
The First Variation of this Example, where the Quavers are broken into Semiquavers, is a little irregular, as to what we have delivered concerning Meeting each following Note in the Unison, or Octave; for Here, each other Quaver is met in a Second. But necessity, and the shortness of the Dissonance, render That excusable in Short Notes, which would not be Allowed in Longer. For as Crotchets, so broken into Quavers are not very commendable, so Minims broken into Crotchets, after the same Manner, would be much worse. But if That, Ascending, or Descending, by Degrees, consisted of Pricked-Notes, Succeeded by Notes of the Next less quantity: Then, that way of Breaking would be both Regular and Commendable; as thus,  
Example.  
Ground Broken Ground Broken  
If you ask me, why I have put a b Flat to that Quaver in B; I answer; because the Division Descends from it to F, which is Flat. Again; in the Other Part which Ascends, 
Of Notes being made Flat or Sharp, in relation to the 4 th'. Above, or Below.  there is a Quaver in F made Sharp, because the Division Ascends from it, to B, which is Sharp: Both which are grounded upon the same Reason; which is, that in four Notes Asccending, or Descending by Degrees, we seldom exceed the distance of a Full, or Perfect 4 th'. lest we produce unto the Ear that harshness, which is called Relation not Harmonical. For though the Less 4 th'. (that is; when the Lower term is Sharp, and the Higher, Flat) be most Frequent, and very Agreeable, in Musical Progression; yet when Both terms are extended, the Higher being Sharp, and the Lower, Flat: the distance is a Trione, which is more by half a Note, than a Perfect 4 th'. and therefore when this happens, we commonly alter That which comes first in compliance To (and preparing the Ear For) that which is to follow.  
As for Quavers moving by Leaps, I have little to say; more than that Grounds ought not to consist of Notes so Short, as Quavers, in such a movement. But if such Notes should be proposed unto you, to Divide upon; you may serve yourself by that Example you had, of Crotchets; in making Them, Quavers, and the Quavers upon them, Semiquavers; or, as you see in this following Example.  
Quavers moving by Leaps The Ground broken Descant Mixed Mixed  
By these Examples, and what hath been delivered, you see in what Manner Notes are divided; either according to the Way of Breaking the Ground; of Descanting upon it; or of Mixed Division: which several Ways, have been set down separately, to give you a more Full, and Perfect Knowledge of each Way; but you are now left to your liberty, to use This, or That, or Mingle One with Another, as shall best please your Fancy.  
And now there remains no more to be said, of Dividing Notes, (as I conceive) but that I give you some assistance, by taking you, as it were, by the Hand, and Leading you into the easiest Way of Playing Ex tempore to a Ground. 
How to Play Ex tempore to a Ground.   
First; you are to make choice of some Ground, consisting of Semibreves, or Minims; or of Semibreves, and Minims; for such ought Grounds to be, that are proposed to be Played upon at Sight. Next; you ought to be provided of Ten, or a Dozen Points of Division; (the more, the better) each consisting of a Semibreve, or Minim; which must be accommodated to the First Note, or Notes, of your Ground.  
Being thus prepared, take the Easiest of the said Points, and, by applying it First to One Note, and Then to Another; endeavour to carry it on, through the whole Ground. When by practice you can do This; take Another Point, and do the like with It; and so from One, to Another.  
I will here for your ease, and encouragement, furnish you with a Ground, and also with some Points; to which, you may add infinite more at your pleasure.  
The Ground points  
Let us now take some of these Points, and apply them to the precedent Ground; that you may, by Example, see how they are to be carried on.  
An Example for carrying on a point upon a Ground  
This driving, or carrying On, a Point, doth much ease the Invention, which hath no further trouble, so long as the Point is continued, but to place, and apply it to the several Notes of the Ground. Besides; it renders the Division more Uniform, and also more Delightful; provided, you do not cloy the Ear with too much repetition of the same thing; which may be avoided by some little Variation, as you see I have done in carrying on some of the before-going Points. Also you have liberty to Change your Point, though in the Midst of your Ground; or Mingle One Point with another, as best shall please your Fancy. Thus much for carrying on Points; and now let me advertise you   

Concerning the ordering, and disposing of Division.  
When you are to Play Division to a Ground, I would have you First Play over, the Ground itself; for these Reasons. (1) That Others may hear what Notes you divide upon. (2) That yourself may be better possessed of the Air of the Ground, in case you know it not before. (3) That he who Plays the Ground unto you may better perceive your Time, or Measure. The Ground Played over, you may Break it, into Crotchets, and Quavers, or Play Slow Descant to it, which you please. If your Ground be of Two or Three Strains, you may do by the Second, or Third, as by the First. This done, and your Ground beginning over again; you may then Break it into Division of a Quicker Motion; driving on some Point, or Points, as hath been showed. When you have prosecuted that Manner of Play, so long as you please; and shown some Command of Hand; you may fall off to Slower Descant, or Binding Notes, as you see cause; Playing also Sometimes Loud, or Soft, to express Humour and draw on Attention.  
After this, you may begin to Play some Skipping Division, or Points, or Tripla's or what your present Fancy, or Invension shall prompt you to; changing still from one Variety to another; for, Variety it is, which chief pleaseth. Without which the best Division in the World still continued would become Tedious to the Hearer; and therefore you must so place and dispose your Division, that the Change of it from One kind to Another, may still beget a new attention. And this is generally to be observed, whether your Ground consist of One, or more Strains, or be a Continued Ground, of which I must also speak a little.  
A Continued Ground, used for Playing, or Making Division upon, is (for the most part) the Through-Basse, of some Motett, or Madrigal, proposed, or selected, for That purpose. This, after you have Played Two or Three Semibreves of it, Plain; to let the Organist know your Measure; you may begin to divide, according to your Fancy, or the former Instructions; until you come near some Cadence, or Close; where, I would have you show some Agility of Hand. Here, (if you please) you may rest a Minim, two, or three, letting the Ground go on, and then come in with some Point: after which you may fall to Descant, Mixt-Division, Tripla's or what you please. In this manner, Playing sometimes Swift Notes, sometimes Slow; changing from This, to That Sort of Division, as may best produce Variety; you may carry on the rest of the Ground; and if you have any thing more excellent than other, reserve it for the Conclusion.   

Of Composing Division for One Viol to a Ground.  
When you compose Division to a Ground, endeavour to make it easy for the Hand; for, of things equally excellent in their Composition, That is always to be preferred, which is more easy to be performed. Hence, we may conclude, that no man is fit to compose Division to a Ground, (how great a Musician soever he be) unless he understand the Neck of the Instrument, and the Method of Fingering, belonging to it.  
This is all I have to say concerning Division for One Viol; more than that I would have you peruse the Divisions which other men have made opon Grounds; as those of Mr. Henry Butler, Mr. Daniel Norcome, and divers other Excellent Men of this our Nation, (who, hitherto, have had the pre-eminence for this particular Instrument) observing, and Noting in their Divisions, what you find best worthy to be imitated.   

Of two Viols Playing together to a Ground.  
After this discourse of Division for One Viol; I suppose it will not be unseasonable, if I speak something of Two Viols Playing together to a Ground; in which kind of Music, I have had a little experimental knowledge; and therefore will deliver it in such order as I have known the Practice of it; referring the Improvement thereof to further Experience.  
Let the Ground be Pricked down in three Several Papers: One, for him who Plays on the Organ, or Harpsecord; and the Other Two, for them that Play on the Viols; which, for Order, and Brevity, I will distinguish by three Letters: Viz. A. for Organist; B. for First Basse, and C. for the Second.  
Each of these having the Same Ground before him, they may all begin together; A. and B, Playing the Ground, and C. Descanting to it in Slow Notes, or such as may suit a Beginning.  
This done; let C. Play the Ground, and B. Descant to it, as the Other had done before; but with some little Variation. If the Ground consist of Two Strains, the like may be done by the Second; One, still Playing the Ground, whilst the Other Descants, or Divides upon it.  
The Ground thus Played over; C. may begin again, and Play a Strain of Quicker Division; which ended, let B. answer the Same, with Another, Something Like it, but of a little more Lofty Air; for the better performance whereof, (if there be any difference in the Hands, or Inventions,) I would have the better Invention Led, but the more able Hand still Fellow, that the Music may not seem to go less in performance.  
When the Viols have thus (as it were) Vied, and revied, to one another; A. (if he have Ability of Hand,) may, upon a Sign given him, put in his Strain of Division; the Two Viols Playing, One of them the Ground, and the Other slow Descant to it. A. having ended his Strain of Division; the same may be answered, First, by One Viol, and then by Another.  
Having answered One Another in this Manner, so long as they think fit; the Two Viols may divide a Strain Both together; consisting of Crotchets, Quavers, or Semiquavers, as they please; in which doing; let B. Break the Ground, according to the Ways mentioned, Pag. 22, 23. and if Necessity, or his own Fancy, move him to fetch a Compass; let it be done in moving to the Octave, upward, or downward; returning back, either to end upon the Note itself, or make a Transition to the Note following. By this, C. knowing B's Motion, he knows how to avoid running into the same; and therefore will move into the 3 d. or 5 th'. according to the Way of Descant. Thus much in relation to the present Note, or Note Divided.  
Now, for meeting the Next Note, let C. take these Observations. (1) That whereas B. in Breaking the Ground, doth meet every Next Note, in the Unison, or Octave; his securest Way is to meet the said Next Note in a 3 d. or in a 5 th'. if their Motions be contrary. (2) That such Notes of the Ground as require a 6 th'. to be joined to them, may be met either in the 6 th'. or in the 3 d. (3) That at a Close, or upon such Notes as signify a Cadence, he may (after he hath divided the supposed Binding Note) meet the Cadent Note of the Ground, in an Unison, or Octave.  
These Directions observed, the Two Viols may move a whole Strain together, in Extemporary Division, without any remarkable clashing in 5 this. or 8 this.  
When they have proceeded thus far; C. may begin some Point of Division, of the length of a Breve, or Semibreve, naming the Word Breve, or Semibreve, by which B. may know his Intention: which ended; let B. answer the same, upon the succeeding Note, or Notes, to the like quantity of Time; taking it in that Manner, One after Another, so long as they please; which done, they may betake take themselves to Another Point, of a different Length, which will produce a New Variety.  
This contest, in Breves, Semibreves, or Minims, being ended, they may give the Sign to A. if (as I said) he have Ability of Hand, that he may begin His Point, as they had done, One to Another; which Point may be answered by the Viols, either Severally, or Jointly; if Jointly, it must be done according to the former Instructions of dividing Together; Playing still Slow Notes, whilst A. Divides.  
When this is done, Both Viols may Play another Strain together, either in Quick, or Slow Notes, which they please; and if the Music be not yet spun out to a sufficient Length, they may then begin to Play Tripla's, and Proportions, answering One Another, either in Whole Strains, or in Parcels; and after That, join together in a Thundering Strain of Quick Division, with which they may conclude; or else, with a Strain of Slow, and Sweet Notes; according as may best suit the circumstance, of Time, and Place.  
I have known this kind of Extemporary Music, sometimes (when it was performed by Hands accustomed to Play together) pass off, with greater Applause, than those Divisions, which had been the most Studiously Composed.   

Some Observations, in Composing Divisions, of Two, and Three Parts.  
Now; in Composing Division for Two Basse Viols, you may follow this Method, 
Two Bases.  more, or less, as you please; moulding it into what form you like best; as making sometimes This, sometimes That Part, move Above, or Below: sometimes answering One Another; and sometimes joining them, in Division, Both together; sometimes in Slow, fometimes in Quick Motions; such, as may best produce Variety: But, after their answering One Another by Turns, I would always have them join Together, in some Strain of Division; with which, or with some Slow, and pleasing Descant, you may conclude your Composition.  
If you make Division for Two Trebles; Both must be in the way of Descant to the Ground: and when they move in Quick Notes, Both Together; 
Two Trebles.  their most usual passage will be in 3 ds. or 6 this. to One Another; sometimes, an intermixture with other Concord's; but such, as must still have relation to the Ground. As for their answering One Another; their several Motions, and Changes, in order to Variety; the same is understood as of the Former.  
In Composing, for a Triple, and Basse, you are to consider the Nature, 
Triple and Basse.  and Compass of either Part: framing your Division according thereunto; which in the Higher Part, will be Descant; in the Lower, a more frequent Breaking of the Ground.  
The same regard, to the Nature of the Parts, must be had in Composing for Two Trebles, and a Basse; or for Two Bases, and One Triple. 
Two Trebles and Basse.   
In Divisions made for Three Bases, every Viol acts the Triple, Easse, 
Two Bases and a Treble. Three Bases.  or Inward Part, by Turns. But here you are to Note, that Divisions, of Three Parts, are not usually made upon Grounds; but rather Composed in the way of Fancy: beginning with some Fuge; then falling into Points of Division; answering One Another; sometimes Two answering One, and sometimes, All joining Together in Division; But commonly, Ending in Grave, and Harmonious Music.  
Howbeit; if, after each Fancy, there follow an Air, (which will produce a pleasing Variety;) the Bases of These, consisting of Two, short Strains; differ very little from the Nature of Grounds; as may be seen in the Basse designed for the Organ, or Harpsecord.  
These Airs, or Allmains, Begin like Other Consort-Aires; after which they Repeat the Strains, in divers Variations of Division; One Part answering Another, as formerly mentioned.  
In these several Sorts of Division, both for Two, and Three Parts, myself (amongst Others more Excellent) have made divers Compositions; which, perhaps might be serviceable to Young Musicians; either for their Practice, or Imitation; but the Charge of Printing Divisions, (which cannot be well expressed unless by Cutts in Copper) doth make That kind of Music, less communicable. But, if you desire Written Copies of Divisions, made for Two, or Three Parts, (a thing most necessary to those who intent to Compose such like themselves) none hath done More in That kind, than the ever Famous, and most Excellent Composer, in all Sorts of Modern Music, Mr. John Jenkins. And here might I mention (were it not out of the Road of my Design) divers Others; most Eminent Men of this our Nation; who, for their Excellent, and Various Compositions, especially for Instruments, have, in my Opinion, far outdone those Nations so much cried up for their Excellency in Music: but my naming them would signify little, as to any Addition to their Reputations; they being sufficiently known, and honoured, by their own Works: neither had I taken upon me, to nominate any Person, had it not been upon the necessary account of Division-Musick; the peculiar Subject of my now ended Discourse.    

ADVERTISEMENT.  
Having this opportunity, I cannot but advertise my Reader; that in the year, 1655. a little Book of Doctor Campians was Printed, with some short Annotations, which I had formerly added thereunto, at the Request of a Worthy Friend; to solve such doubts as occurred to him in reading the said Book. These, I should scarce have thought worth owning, though they had been set out to their best advantage; but in that manner they are Printed (the Letters and Marks being left out, which pointed to what words of the Text they had relation) I was much troubled and ashamed at the sight of them. Besides, there are some words misprinted, others quite left out; which destroys the Sense of what I intended. As for Instance, In my short Exposition of the Gamut, or Scale of Music, which follows the Doctor's Preface, (in the tenth Line after the Title) where (speaking of the Cliffs) I said, they open the meaning of the Song unto us, it is Printed Longs unto us. Again; In the same Page (Line fourteenth and fifteenth) where I said, when you look upon any Song or Piece of Music, you commonly see five Rules, etc. the words you commonly see, are quite left out. Moreover; at the end of the said Exposition of the Gam-ut, there is set an Example of Notes, and their value, different from that which my words do there explicate. This I thought fit to Publish, as well for my own Vindication, as Correction of the said Faults.  
As for the Faults of this Present Book, whether relating to the Text, or to the Figures, I hope they are not remarkable. Only, that the Examples (being cut and engraven by those not accustomed to that kind of Work, nor acquainted with Music-notes) are, in some places (though true) not so fair and formal to the Eye as I could wish. What failings may appear in the Discourse itself; which, perhaps, by a longer consideration, might have been avoided, Importuned Hast must plead a pardon for them.   

Divisions for the practice of Learners