Andreas Ornithoparcus his Micrologus, or Introduction: containing the art of singing Digested into foure bookes. Not onely profitable, but also necessary for all that are studious of musicke. Also the dimension and perfect vse of the monochord, according to Guido Aretinus. By Iohn Douland lutenist, lute-player, and Bachelor of Musicke in both the Vniuersities. 1609.

THE SECOND BOOKE of Ornithoparchus his Musicke: wherein are contained the Rudiments of Mensurall Song. (Book 2)

THE FIRST CHAPTER.

Of the Profit and Praise of this Art.

BOêtius that Romane, (whose wit in Musicke no man euer mended; nay, neuer attained to, in the first Chapter of his Musicke) writes, That there is such efficacie in Harmoni∣call Consents, as a man though he would, cannot want them. For Musicke driueth away those cares which driue away sleepe, stilleth crying children, mitigateth the paine of those which labour, refresheth wearied bodies, refor∣meth appassionate minds. And euery liuing soule is so ouercome with Mu∣sicall sounds; that not onely they which are of the gallanter sort (as saith Ma∣crobius) but euen all barbarous Nations doevse Songs, either such as stirre them vp to an ardent embracing of vertue; or doe melt them in vnwor∣thy pleasures: and so are they possessed with the sweetnesse of Harmony, that by Musicke the Alarum to warre is giuen, by Musicke the Retraite is sounded, as if the Note did both stirre vp, and after allay that vertue of for∣titude. Now of the two, that Musicke which we call Mensurall, doth specially performe these effects. For this (as Isidorus saith) stirreth vp not onely men, but also beasts, serpents, birds, and Dolphins with the sweetnesse of the har∣mony. By this did Arion preserue himselfe in the middle of the sea; by this did Amphion the Dircaean gather together stones for building the Theban walles. By this did Timotheus the Phrygian so enflame Alexander Magnus, the Conquerour of the whole world, that he rise from the table where he sat, and called for his armes; and afterwards changing his Moode on the In∣strument, did cause him to put off his armour, and sit downe againe to ban∣quet. By this did Dauid the princely Singer, helpe Saul the King of Is∣rael, when he was vexed with an vncleane Spirit; by this, not onely the great God, the maker of all things, but also the furies of the Stygian God are delighted, appeased, and mitigated. For this is the Lady and Mistresse of all other Arts; which can delight both those that be in Plutoes iurisdiction, and those that abode in Neptunes fields; and those that liue in Iupiters eter∣nally-lightsome Mansions. This Art onely, leauing the earth, flyeth vp before

the tribunall seat of the highest Iudge; where together with the Instruments of the Saints it soundeth, where the Angels and Archangels doe incessant∣ly sing Hymnes to God, where the Cherubins, and Seraphins, cry with a continuall voyce, Holy, holy, holy. Besides, no Art without Musicke can be per∣fect: wherefore Pythagoras appointed his Schollers they should both when they went to rest, and when they awaked vse Melodies. Besides, Musicke doth gouerne and sharpen the manners and fashions of men. For euen Nero whilst he gaue himselfe to Musicke, was most gentle, as Seneca witnesseth: but when hee leauing of Musicke, and set his minde on the Diabolicall Art of Nicromancie, then first began that fierce crueltie of his; then was he changed from a Lambe to a Wolfe, and out of a most milde prince trans∣formed into a most sauage beast. But least I digresse too farre, and least we proceede from vnknowne beginnings, I will briefly set downe what this Mu∣sicke is. Therefore Mensurall Musicke is a knowledge of making Songs by fi∣gures, which are in forme differing, and hauing the quantity of Moode, time, and Prolation: Or it is an Art, whose Harmony is effected by the variety of figures and voyces.

THE SECOND CHAPTER.

Of the Figures.

WHerefore a Figure is a certaine signe which represents a voyce, and silence. A Voyce, (I say) because of the kindes of Notes which are vsed: Silence, because of the Rests which are of equall value with the Notes, and are measured with Artificiall Silence.

Of the number of the Figures.

THe Ancients obserued onely fiue Figures, as principall Figures, and such as receiue the quantitie of the three Degrees of Musicke: Out of which after ages haue drawne out others for quicknesse sake, accor∣ding to that saying of Ouid:

Ex alijs alias reparat natura figuras.

The bodies of the Figures are of the forme following.

A Large is a figure, whose length is thrise as much as his breadth, ha∣uing on the part toward your right hand a small tayle, bending vpward, or downeward.

A Long is a Figure, whose length is twise as much as his breadth, hauing such a tayle as the Large hath.

A Breefe is a Figure, which hath a body foure-square, and wants a tayle.

A Sembreefe is a Figure, which is round in forme of an egge, or (as Fran∣chinus sayeth) Triangular.

A Minime is a Figure like a Sembreefe, hauing a tayle, ascending or des∣cending.

A Crochet, is a Figure like a Minime in colour varying.

A Quauer is a figure like a Crochet, hauing a dash to the right hand-ward.

A Semiquauer is a figure like a Quauer which hath two dashes, and ther∣by is distinguished from it, as thus:

The Eight Figu∣rall bodies.

• ...Large.
• ...Long.
• ...Breefe.
• ...Semibreefe
• ...
  [illustration]
• ...Minime.
• ...Crochet.
• ...Quauer.
• ...Semiquauer.
• ...
  [illustration]

There is a certaine Figure, in shape like a Minime, but ioyned with the number of Three, which is called Sesquialterata, because three are sung for two.

Besides, a Figure which hath two tayles, is as if it had none; because one doth hinder another.

THE THIRD CHAPTER.

Of Ligatures.

WHerefore a Ligature (as Gaff. writes in the fift chap. of his second Booke) is the conioyning of simple Figures by fit strokes. Or (according to the strokes vpward or downward) it is the depen∣dence of the principall figures in straightnesse, or crookednesse.

Generall Rules for the Ligatures.

FIrst, There are foure ligable Notes, that is a Large, a Long, a Breefe, and a Semibreefe.

2 Euery ligable Note, except a Large, may be figured with a two-fold body, a square body, and a crooked.

3 Euery ligable Note is to be iudged according to the ascension and des∣cension, either of it selfe, or of the Note following.

4 Euery ligable Note is either beginning, middle, or finall.

5 The Accidents of simple Notes, say for example, alteration, imperfe∣ction, and the like (as Franchinus witnesseth) are also the Accidents of the bounden Notes.

Rules for the beginning Notes.

FIrst, Euery Beginning (whether straight, or crooked) wanting a tayle, when the second Note descends, is a Long.

2 Euery Beginning Note without a tayle, if the second Note ascend, is a Breefe.

3 Euery Beginning Note hauing a taile downe-ward on the left side of it, is a Breefe.

4 Euery Initiall, howsoeuer fashioned, hauing a taile on the left side vp-ward, is a Semibreefe, together with the Note next following; so that you need not care whether it ascend, or discend.

Rules for the middle Ligatures.

FIrst, Euery Note betwixt the first and the last, is called middle.

2 Euery middle Note howsoeuer shaped, or placed, is a Breefe.

3 A Long may begin and end a Ligature, but can neuer be in the mid∣dle of it.

4 A Breefe may be in the beginning, middle, and end of a Ligature very fitly.

5 A Semibreefe may be in the beginning, middle, and end of a Liga∣ture: so that it haue a taile in the left part vpward.

Rules for the finall Ligatures.

FIrst, Euery last Note that is straight, and descends, is a Long.

2 Euery Finall Note that is straight, and ascending, is a Breefe.

3 Euery crooked Finall whether it ascend or descend, is a Breefe.

4 A Large wheresoeuer it is set, is alwaies a Large.

The Examples of these Rules are in the following Tenor set out. 〈♫〉〈♫〉 Tenor Exercise of Ligatures. 〈♫〉〈♫〉 Base Exercise. 〈♫〉〈♫〉 Of Ligatures.

THE FOVRTH CHAPTER.

Of Moode, Time, and Prolation.

THe degrees of Musick, by which we know the value of the principal figures, are three: to wit, Mood, Time, and Prolation. Neither doth any of them deale vpon all Notes, but each onely with certaine

Notes that belong to each. As Moode dealeth with Largs, and Longs; Time, with Breefes; Prolation, with Semibreefes.

A Moode (as Franchinus saith in the second Booke, cap. 7. of his Pract:) is the measure of Longs in Largs, or of Breefes in Longs. Or it is the beginning of the quantitie of Largs and Longs, measuring them either by the number of two or the number of three. For euery Figure is measured by a dou∣ble value.

To wit, by the number of	Two,	and so is called	Perfect,	because we make 3. perfect, and limit the imperfect by 2.
Three,	Imperfect,

Of the Diuision of Moode.

Moode (as it is here taken) is two-fold; to wit, The greater, which is in the Largs and Longs, and the lesser, which is in the Longs and Breefes. And each of these is diuided into the perfect and imperfect.

Of the greater Moode.

THe greater perfect Moode is, when a Larg containes in it three Longs: or it is the measuring of three Longs in one Larg. The signe hereof is a perfect circle accompanied with the number of three, thus; O3. The grea∣ter imperfect is a Larg, comprehending in it two Longs: which is knowne by an imperfect circle, ioyned to the number of three, thus; C3.

Of the lesser Moode.

THe lesser perfect Mood is a Long hauing in it three Breefes. Or it is the measuring of three Breefes in one Long, whose signe is a perfect Circle, accompanied with the number of 2, thus; O2. But the lesser imperfect, is a Long which is to be measured onely with two Breefes. The signe of this is the absence of the number of 2. Or a Semicircle ioyned to a number of 2. thus; C2. O. C. as followeth:

Of Time.

TIme is a Breefe which containes in it two or three Semibreefes. Or it is the measuring of two or three Semibreefes in one Breefe. And it is two-fold, to wit, perfect: and this is a Breefe measured with three Semibreefes. Whose signe is the number of three ioyned with a Circle or a Semicircle, or a perfect Circle set without a number, thus; O3. C3. O. The imperfect is, wherein a Breefe is measured onely by two Semibreefes. Which is knowne by the number of two ioyned with a perfect Circle, or a Semicircle, or a Se∣micircle without a number, thus; O2. C2.

Of Prolation.

WHerefore Prolation is the essentiall quantitie of Semibreefes: or it is the setting of two or three Minims against one Semibreefe. And it is twofold, to wit the greater, (which is a Semibreefe measured by three Minims, or the comprehending of three Minims in one Semibreefe, whose signe is a point inclosed in a signe thus, 〈☐☐〉〈☐☐〉) The lesser Prolation is a Semibreefe mea∣sured with two Minims onely, whose signe is the absence of a pricke. For Franchinus saith, They carry with them the imperfecting of the figure, when the signes are wanting, thus: 〈♫〉〈♫〉 Time perfect. Imperf. time. Greater Prol. Lesse Prolation.

There was one well seen in this Art, that made this vnderwritten Example of these three degrees, reasonable learnedly and compendiously for the help of yong beginners: which (by his fauour) wee will not thinke vnwor∣thy to set downe here. 〈♫〉〈♫〉 The Tenor, in the lesser Moode perfect. The Descant, in the greater Prolation. 〈♫〉〈♫〉 The Base, in time perfect.

THE FIFT CHAPTER.

Of the Signes.

THough there be such dissention betwixt Musitians about the Signes, such confusion of rules and examples, that euen to a per∣fect Musitian they seeme to breed doubts: so that Plutarch (a man furnished with all learning) saith in that Booke, which hee wrote of Musicke: In our time, the forme of difference hath so much increa∣sed, and so farre varied from the Custome of our Auncestors, that there is no mention, no precept, no certaintie of Art left. And also though wee be not to make a definitiue sentence in doubtfull matters, but rather to hold question: yet that yong beginners, which are desirous to learne this Art, may not be either discouraged from proceeding, or misled, leauing those things

which more vnusuall, wee will briefly shew those things which are in vse a∣mongst those Musitians, who now are in credite: by seeking out that doubt of the circle and number, which was among the Theoricks. Therefore a signe is, a certaine figure set before a Song, which sheweth the Moode, Time, and Prolation.

Of the Diuisions of Signes.

OF Signes some be principall, and some lesse principall: The principall are those, which are fit for the vnderstanding of Moode, Time, and Prola∣tion. And they are two-fold, to wit, Extrinsecall, and Intrinsecall: Extrinsecall are those called, which doe outwardly present themselues, and shew the de∣grees of Musicke, as Number, a Circle and a Point.

Rules for the Extrinsecall Signes.

FIrst, A Circle set alone by itselfe sheweth time: if it be perfect it shewes perfect time, if imperfect, imperfect time. When it is ioyned to a num∣ber, it signifies the Moode.

2 A Circle accompanied with the number of 3. doth represent the grea∣ter Moode, but ioyned with a number of 2. the lesser.

3 Wheresoeuer is the greater Mood, there is the lesse, but not contrarily.

4 The number of three ioyned to a Circle, is a signe of the perfect time: but the number of two, of the imperfect.

5 A point inclosed in a signe of time noteth the greater Prolation, thus:

Of Signes, some be

• ...

  O3	of the greater Moode	Perfect	of the perfect time.
  C3	Imperfect

• ...

  O2	of the lesser Moode	Perfect	the time imperfect.
  C2	Imperfect

• ...

  〈☐〉〈☐〉	the greater Prolation	Perfect	Time.
  〈☐〉〈☐〉	Imperfect

• ...

  O	Time	Perfect	in the lesser Prolation.
  C	Imperfect

But when out of the mingling of three principall Signes, to wit; of the number, circle, and point, there be diuers signes made, that you may the easi∣lier haue the knowledge of them, and euery figure may haue his value, I thought good in this forme following to set downe a Table, by which you might at first sight iudg of the value of any figure, thogh placed in any signe.

A Resolutorie Table, shewing the value of the Signes, by the beholding of euery figure.

[illustration]

Of the Intrinsecall Signes.

THe Intrinsecall signes are those, by which the perfection of Musicall de∣grees in the figures is shewed, without the adioyning of any of the Ex∣trinsecall Signes. Of these there are three, to wit;

1 The inuention of a rest of three times. For when in a Song, there is found a Rest which toucheth three spaces, it signifies the lesse perfect Moode. If it touch two, it sheweth the greater perfect. For saith Franchinus; It is not vnfit, that two Rests of three Times be adioyned to the greater Moode, if one be adioyned to the lesser.

2 The blacking of the Notes. For as oft as you find three Longs colou∣red, the lesser perfect Mood is signified. When three Breefes, the perfect time. When three coloured Semibreefes, the greater Prolation.

3 The doubling of certaine Rests. For as oft as two Semibreefe Rests are placed with a Semibreefe, the perfect Time is signified. So by two Minims with a Minime Note, the greater Prolation, thus; 〈♫〉〈♫〉 The greater Moode. The lesser Moode. Time perfect. The greater Prolation.

Of the lesse principall Signes.

THe Signes lesse principall are those, which are not necessary for the knowledge of Moode, Time, and Prolation. And these are diuers, as you may plainely see in the quadrate following. 〈♫〉〈♫〉 Repetition. Conueni∣ence. Concordance Aspiration. b Moll. Dealbation. Cardinalis.

THE SIXT CHAPTER.

Of Tact.

WHerefore Tact is a successiue motion in singing, directing the e∣qualitie of the measure: Or it is a certaine motion, made by the hand of the chiefe singer, according to the nature of the marks, which directs a Song according to Measure.

Of the Diuision of Tact.

TAct is three-fold, the greater, the lesser, and the proportionate. The greater is a Measure made by a slow, and as it were reciprocall motion. The writers call this Tact the whole, or totall Tact. And, because it is the true Tact of all Songs, it comprehends in his motion a Semibreefe not dimini∣shed: or a Breefe diminished in a duple.

The lesser Tact, is the halfe of the greater, which they call a Semitact. Be∣cause it measures by it motion a Semibreefe, diminished in a duple: this is allowed of onely by the vnlearned.

The Proportionate is that, whereby three Semibreefes are vttered against one, (as in a Triple) or against two, as in a Sesquialtera. Of this we shall speake more at large in the Chapter of proportions.

A Rule for Tact.

A Semibreefe in all Signes (excepting the Signes of Diminution, augmen∣tation, and proportions) is measured by a whole Tact, as in the example following appeareth:

[illustration]

The Table of Tact resolued.

THE SEVENTH CHAPTER.

Of Augmentation.

BEcause in the Chapter before going, we haue made mention of Augmentation and Diminution, therefore least we proceed from vnknowne things, we will shew what each is.

Therefore Augmentation is the making of more Notes in a Song: or it is the excrement of some Note. For in it is put a Minime for a Semibreefe; a Semibreefe for a Breefe; a Breefe for a Long.

By what signes you shall know Augmentation.

OF Augmentation therebe 3. Signes. The first is, the fewnes of the Notes in one part of the Song.

The second is, the adioyning of the Canon, by saying, Let a Breefe be a Large, let a Semibreefe be a Long, let a Minime be a Breefe. Or let it increase in Duplo, Triplo, vel hexagio, &c.

The third is, a point in the Signe of time, found onely about one part of the Song: One I say, for if it be found about all, it is not a signe of Aug∣mentation, but of the greater Prolation.

Rules of the Augmention.

FIrst, Augmentation is the contradiction of Diminution.

2 In Augmentation the Minime figure is measured with an whole Tact.

3 Betwixt Prolation and Augmentation, there is this difference, Augmen∣tion sounds one Minime to a Tact; Prolation sounds three, that is a perfect semibreefe: which then is measured with a proportionate Tact.

4 The Rests are diminished and augmented, as well as the Notes.

5 Augmentation must seldome be, but in the Tenor.

6 A Large is not augmented, because it hath none greater than it selfe, whose value it may assume. Therefore they are in an errour, which say there are 81. Tacts in a Large which is set vnder such a signe ☉3: because a Large neither growes to aboue 27. Tacts, nor admitteth any thing greater than it selfe, because it is the greatest, than which there is nothing greater. Besides as in nature, so in Art it is in vaine to place a nothing: therefore should a Large be in vaine augmented, because no Song was euer found of so long time, that 81. Tacts might be Sung in an Vnison.

7 Augmentation comprehends vnder it selfe all the kinds of Notes ex∣cepting a Large, for which point marke the example following: 〈♫〉〈♫〉 Augmentation. The greater The Bariton or Base, Prolation.

〈♫〉〈♫〉 vnder the signe of Semiditie. The greater Prolation.

What a Canon is.

BEing we haue made mention of a Canon, least I hold the learner in a mammering, I will shew what a Canon is.

A Canon therefore is an imaginarie rule, drawing that part of the Song which is not set downe out of that part; which is set downe. Or it is a Rule, which doth wittily discouer the secrets of a Song. Now we vse Canons, either to shew Art, or to make shorter worke, or to try others cunning, thus;

THE EIGHT CHAPTER.

Of Diminution.

DIminution, which is more truely called syncopation, is the varying of Notes of the first quantity, as writeth Fran. li. 2. Pr. 14. Or it is a cer∣tain cutting off of the measure. For as in Grammer we say saecla for saecula, so in Musicke we do curtall the naturall and essentiall mea∣sure of the Notes by this syncopation. Therefore generally it shall be called syncopation, not Diminution, because it is a kind of syncopation.

Of the kindes of Syncopations.

OF this there be two kindes; Semiditie, and Diminution. Semiditie is the middle of the chiefe measure of Notes, which can be placed onely in an imperfect time, which hath these Signes, O2. C2. 〈☐〉〈☐〉. 〈☐〉〈☐〉. 〈☐〉〈☐〉.

For in all these, the halfe of the measure is put off by the dash properly, and by the number, for so much as it hath of Duple proportion. Therefore Erasmus Lapicida doth well in placing one number vnder another in all these signes, thus; O2/1. C2/1.

For proportion is the relation of two quantities, not of one, as elsewhere we will more largely shew.

Of Diminution.

DIminution (as the Ancients thought) is the taking away of the third part from the measure. But the opinion of the Modernes, is more true and laudable, which make no difference betwixt Diminution and Semiditie, as Ioan: Tinctoris, of all that euer excelled in Musicke the most excellent

writer, and Franchinus Gafforus lib. 2. cap. 14, haue positiuely set downe.

Therefore Diminution is the cutting off of the halfe part in the measure, nothing differing from semiditie, but that it is found in perfect Signes, and in figures which are to be measured by the number of 3. Wherefore I can∣not but scorne certaine Componists (for so they will be called) though in∣deed they be the Monsters of Musicke) who though they know not so much as the first Elements of the Art, yet proclaime themselues, The Musitians or Musitians, being ignorant in all things, yet bragging of all things, and doe (by their foolish toyes which contrarie to the maiestie of the Art, they haue gotten an habite of, rather by vse, than wit) disgrace, corrupt, and debase this Art, which was in many ages before honoured, and vsed by many most lear∣ned, (and to vse Quintitians words) most wise men: vsing any Signes at their pleasure, neither reckoning of value, nor measure, seeking rather to please the eares of the foolish with the sweetnesse of the Ditty, than to satisfie the iudgement of the learned with the maiestie of the Art. Such a one know I, that is now hired to be Organist in the Castle at Prage, who though he know not (that I may conceale his greater faults) how to distinguish a perfect time from an imperfect, yet giues out publikely, that he is writing the very depth of Musick: and is not ashamed to say, that Franchinus (a most famous writer, one whom he neuer so much as tasted of) is not worth the reading, but fit to bescoffed at, & scorned by him. Foolish bragging, ridiculous rashnes, grosse madnes, which therfore only doth snarle at the learned, because it knows not the means how to emulate it. I pray God, the Wolfe may fal into the Toiles, and hereafter commit no more such outrage; nor like the Crow brag of bor∣rowed feathers. For he must needs be counted a Dotard, that prescribes that to others, the Elements whereof himselfe neuer yet saw. As Phormio the Greeke Orator (in Tullies second Booke de Orat.) who hauing before Antio∣chus the King of Asia, (in the presence of Haniball) made a long Oration of the dutie of a Generall, when as hee himselfe had neuer seene Campe, not armes, and had made all the rest to admire him, in the end Haniball being as∣ked, what his iudgement was of this Philosopher, his answere was, That hee had seene many doting old men, but neuer any man that doted more, than Phormio. Now come I to the matter, and leaue these vnlearned ridiculous Phormio's, many whereof (the more is the shame) haue violently inuaded the art of Musick, as those which are not compounders of Harmonies, but rather corruptors, children of the furies, rather than of the Muses, not worthy of the least grace I may doe them. For their Songs are ridiculous, not grounded on the Principles of the Art, though perhaps true inough. For the Artist doth not grace the Art, but the Art graceth the Artist. Therefore a Componist doth not grace Musicke, but contrarily: for there be that can make true Songs not by Art, but by Custome, as hauing happily liued amongst singers all their life-time: yet do they not vnderstand what they haue made, know∣ing that such a thing is, but not what it is. To whom the word our Sauiour vsed on the Crosse, may be well vsed; Father pardon them, they know not what

they doe. Wherfore allow of no Componists, but those, who are by Art wor∣thy to be allowed of: now such are Ioan. Okeken, Ioan: Tinctoris, Loyset, Verbo∣net, Alex: Agricola, Iacobus Obrecht, Iosquin, Petrus de Larue, Hen: Isaack, Hen: Finck, Ant: Brummel, Mat: Pipilare, Geor: Brack, Erasmus Lapicida, Caspar Czeys, Conradus Reyn, and the like: whose Compositions one may see doe flow from the very fountaine of Art. But least by laughing at these fellowes we grow angry, and by being angry grow to hate them, let vs euen let them alone, and returne to Diminution.

Whereof we will resolue with Franchinus and Tinctor, that it taketh not away a third part, as the Ancients thought, (for it is hard finding out that) but one part: for as this signe 〈☐〉〈☐〉. is the Duple of this signe C. so is this 〈☐〉〈☐〉 of this O. Wherfore euen approued Componists doe erre, because they mark not that there is a double Progression of measure in a perfect Circle diuided with a dash, besides the Ternarie number of the figures, because they are of a perfect time: singing one Semibreefe to a Tact, when they should sing 2. For in that signe the Song is so to be placed, that keeping the perfection of the Ternarie, it may receiue the Closes, and end in a Binarie measure. For in this Signe 〈☐〉〈☐〉. the Notes keepe the same value, which they haue in this O, but the measure onely, is to be measured by the Binarie number, thus:

[illustration]

A Table for the Tact of Diminution.

By what signes Diminution is marked.

NOw Diminution is marked by three wayes, to wit: By a Canon, by a Number, and by a Dash. By a Canon, saying; It decreaseth in Duplo, Tri∣plo, and Quadruple, and such like.

By a Number, for euery number adioyned to a Circle, or a Semicircle, be∣sides that which essentially it betokens, doth also diminish according to the naming of his figure. As the number of 2, being placed with a whole Circle besides the time, which it betokens to be imperfect, doth also signifie a du∣ple Diminution, the number of three a Triple, the number of foure a Qua∣druple, and so forth.

By a Dash, to wit, when by a Dash, the signe of Time is diuided, thus; 〈☐〉〈☐〉. 〈☐〉〈☐〉. 〈☐〉〈☐〉. 〈☐〉〈☐〉.

Rules of Syncopation.

FIrst, Syncopation belongeth to the measure of Time, not to the figures themselues.

2 Syncopation doth respect both the Notes, and the Rests.

3 Syncopation doth not take away the value, but the measure of the Notes.

4 The number doth not diminish Prolation, because it cannot work vp∣pon the pricke, whilst a Circle doth keepe it.

5 Betwixt Diminution and Semiditie, there is no difference of Tact, or Measure, but onely of nature.

6 Diminution is the contradiction of Augmentation.

7 It is not inconuenient, that to the same Signe there may belong a dou∣ble Diminution, to wit; virgular and numerall, thus; 〈☐〉〈☐〉2.

8 Virgular Syncopation is much vsed, Numerall seldome, Canonicall most seldome: the Example therefore following is of the first, and the second. 〈♫〉〈♫〉 The Rule of Semiditie in Diminution. 〈♫〉〈♫〉 Syncopation by number.

THE NINTH CHAPTER.

Of Rests.

ARest (as Tinctoris writeth) is the Signe of Silence. Or (as Gafforus saith) it is a figure which sheweth the Artificial leauing off from singing: Or it is a stroke drawne in line and space, which beto∣kens silence. Now Rests are placed in songs after three manners, to wit; Essentially, Iudicially, and both wayes. Essentially, when they beto∣ken silence. Iudicially, when they betoken not silence but the perfect Moode: and then their place is before the signe of Time. Both wayes, when they represent both.

Rules for the Rests.

FIrst, There be as many kinds of Rests, as of Notes.

2 The Rest, which toucheth all the spaces, is generall, where all the voyces cease together, and is onely to be placed in the end.

3 The rest which takes vp three spaces, is called of the Moode, which it betokens, and is to be placed onely in a perfect Moode.

4 A Rest, which doth conclude two spaces, is called an imperfect Long.

5 A Rest, which takes vp but one space, is a Breefe betokening one Time▪ whether perfect or imperfect.

6 A Rest, descending from the line to the middle of the space, is called a Semibreefe.

7 A Rest, ascending from the line to the middle of the space, betokens a Minime, or a sigh.

8 A Rest, like a sigh, being forked to the right hand-ward, betokens a Crochet.

9 The Rests of the two last figures, because of their too much swiftnesse, are not in vse among Musitians. 〈♫〉〈♫〉 Rests generall. Larg. Long. Breefe. Semi∣breefe. Minim. Crochet.

THE TENTH CHAPTER.

Of Prickes.

WHerefore a Pricke is a certaine indiuisible quantity, added to the Notes, either for Diuision, or for Augmentation, or for Certainty sake. Or it is a certaine Signe lesser than any other accidentally set either before, or after, or betweene Notes.

Of the Diuision of a Pricke.

OVt of this Definition, there are collected three kindes of Prickes, to wit: That of Addition, and that is the Augmentation of the figures. Or it is the perfection of imperfect Notes. This is set in the middle on the right side, and is found onely in imperfect Signes, and doth augment the Notes to which it is added, the halfe of his owne value, as in the Example follow∣ing appeareth. 〈♫〉〈♫〉 Tenor point of Addition. The Base is the same.

Of the Pricke of Diuision.

THe Pricke of Diuision is the disioyning of two Notes, neither taking away nor adding any thing, but distinguishing two Notes by reckoning the first with the former, & the second with the following Notes, to the end that the Ternarie perfection in Notes may be had. Here the Pricke in perfect degrees, is ioyned not to perfect figures, but to their neere parts, neither is adioyned to the middle of the side, as that of Addition, but a little higher, or lower about the middle of the Notes, which it diuides, thus: 〈♫〉〈♫〉 The Pricke of Diuision in the Tenor. Also in the Base.

Of the Pricke of Alteration.

THe Pricke of Alteration, was obserued more by the Ancients, than the later Musitians. Yet least it may breed some doubt to the Singer, that shall light on it by chance, it is not amisse to speake somewhat of it. Therfore the Pricke of alteration is the repeating of Notes, which doth accidentally befall them, not as they are perfect, but as their parts neighboring the per∣fect. Now is it set neither on the one side, nor vpward, nor downe-ward, but directly ouer the Note, which it alters, as in this Example appeareth. 〈♫〉〈♫〉 The Pricke of Alteration in the Tenor. Also in the Base.

There are besides these, two other kindes of Prickes; to wit, of perfection. And this is a Pricke set after a perfect Note; neither increasing not dimini∣shing it, but onely preseruing it from being imperfected by the following Note. It is set as the Pricke of Addition, but differs from it, because it is al∣wayes, and onely placed about perfect Notes.

There is another Pricke of Transportation, adioyned to Notes, which it doth translate to be reckoned with figures remooued further off: and this doth direct his force not vpon the precedent Notes, but onely vpon the following ones, thus; 〈♫〉〈♫〉 The Pricke of perfection or Transportation in the Tenor.

〈♫〉〈♫〉 Also in the Base.

THE ELEVENTH CHAPTER.

Of Imperfection.

WHerefore Imperfection is the degrading of perfect Notes. For to imperfect is to make a perfect Note imperfect. Or it is this, to bring itfrom his value.

Of two-fold Imperfection.

IMperfection is two-fold: to wit, Totall, when precisely the third part of the value is taken from the Notes: as when in perfect time a Breefe is imper∣fected by a Semibreefe. Or partiall, when not precisely the third part, but a lesse than that, say a sixt part, or so, is taken from the Notes: as when a long of the imperfect Moode, but in the perfect time, where it is valued at two Breefes, is imperfected by a Semibreefe, in regard of the Breefe in it contai∣ned: and as a Breefe by a Minime in the greater Prolation.

By what Signes Imperfection is knowne.

OF Imperfection there be three Signes, (as writeth Franchinus li. 2. Pract. cap. 11.) to wit, numerall Imperfection, punctuall Diuision, and fulnesse of the Notes.

Rules of Imperfection.

FIrst, There is foure Notes which may be imperfected, to wit, a Larg, a Long, a Breefe, a Semibreefe.

2 Euery figure, which may be imperfected, is alway to be considered in the number of his perfect quantitie.

3 That which is once imperfect, cannot be more imperfected.

4 Euery figure that may be imperfected, is greater than the imperfec∣ting figure.

5 Imperfection is made not onely by the neere parts of the Notes, but also by the remoued parts. As a perfect Breefe can be imperfected, not one∣ly by a Semibreefe, which is the neere part, but also of two Minims, which are remote parts of it.

6 Two neighbouring parts of one perfect figure doe not imperfect it, but onely one: although two remoued ones may doe the same. Wherefore if you finde two Semibreefe Rests after a perfect Breefe, it shall remaine per∣fect, vnlesse punctuall Diuision come betweene.

7 Euery lesse figure being superfluous doth imperfect the greater going before, not the following one: vnlesse it happen by reason of the Pricke of Diuision, Perfection, or Transportation.

8 A Note of one sort comming before his like is not imperfected, wher∣by euery figure that is to be imperfected, must be put before a figure that is greater, or lesse than it selfe.

9 The greater Note doth not imperfect the lesse, nor an equall Note an other equall Note.

10 The figure which doth imperfect another figure, takes so much from it, as it selfe is valued at.

11 A Rest is not imperfected, but doth imperfect.

12 A Ligature doth neuer imperfect, but is imperfected.

13 A Larg doth nothing, but suffereth onely in Imperfection.

14 A Minime doth, and neuer suffereth in Imperfection.

15 A Long, Breefe, and Semibreefe doe imperfect, and are imperfected.

16 Euery Imperfection is either before or behinde: Before, as when the imperfecting Note doth goe before the Note that is imperfected: Behind, as when it followeth. There be that thinke it is caused both wayes in partiall Imperfection.

17 That Imperfection, which is caused before and behind, is caused not by the neighbouring, but by the remote parts.

18 All Imperfection is caused either by the Note, the Rest, or the co∣lour. By the Note, to wit, when a figure of a lesser kind is placed before or after a perfect Note, and so imperfects it, thus: 〈♫〉〈♫〉 Tenor. Base.

By a Rest, to wit, when a Rest of a lesse kind is found before or after a perfect Note: but the Rest cannot be imperfected, as thus: 〈♫〉〈♫〉 Tenor. 〈♫〉〈♫〉 Base.

By Colour: when in the perfect figures you finde Colour, the Notes are Imperfect; because their third part is taken away, thus: 〈♫〉〈♫〉 Tenor. 〈♫〉〈♫〉 Bassus and his Position.

Of Colour.

WHerfore Colour in this place is nothing, but the fulnes of the Notes: Or, it is the blacking of the principall figures: the force whereof is such, that it takes away the third part of the value from figures placed in their perfect quantitie: and from imperfects sometime it takes away the fourth part, sometimes it makes them of the Hemiola proportion. Where∣fore I thought good to place here a Table of the perfect figures coloured. Wherein note this, that the voide spaces doe shew that that figure, ouer which they are placed, is not to be coloured in that signe. But the Sphaerical figure (which the learned call the figure of nothing) declares that the figures may be coloured, yet that they haue not the value of one Tact.

Colour being in other figures essentiall, induce no accidentall quantity into Notes.

[illustration]

Colour is oftentimes found among most of the learnedst, neither to take away nor to adde any thing: but specially, when to remoue Alteration; it is placed in the neighbouring parts of perfect figures, thus: 〈♫〉〈♫〉 Tenor. Base.

Most commonly the Colour doth cause a Duple proportion in the imper∣fect figures, (as Franchinus saith. lib. 2. cap. 11.) which Henry Isaack in a cer∣taine Alleluia of the Apostles, did thus both wittily, and truely dispose. 〈♫〉〈♫〉 Tenor. Base.

THE TVVELFTH CHAPTER.

Of Alteration.

ALteration according to Ioannes de Muris, is the doubling of a lesser Note in respect of a greater, or (as Tinctor saith) it is the doubling of the proper value. Or it is the repetition of one, and the selfe-same Note. And it is called Alteration, Quasi alter a actio, it is another action, to wit: A secundary singing of a Note, for the perfecting of the number of three.

Rules of Alteration.

FIrst, There be foure Notes, which may be altered, (saith Franchinus lib. 2. cap. 13.) a Long, a Breefe, a Semibreefe, and a Minime.

2 Alteration doth exclude the Larg, and is limitted by a Minime, be∣cause a Larg hath not a greater than it selfe, whose neighbouring part it may be: and the lesse figures are not to be reckoned after the number of three.

3 Alteration happens in numbers which be not perfect, but are parts neighbouring to perfect Notes, because a perfect Note in as much as it is a perfect Note is not lyable to Alteration.

4 Onely the Notes are altered, not the Rests.

5 Alteration falleth vpon the second Note, not vpon the first.

6 Euery altered Note containeth it selfe twise.

7 A like Note is not altered before a like Note.

8 Alteration onely fals out in perfect degrees.

9 Alteration comes for want of one Note, when you haue reckoned af∣ter the Ternary numbring.

10 As oft as two alterable Notes are placed betwixt two imperfectible Notes without a Pricke of Diuision: the second is alwayes altered, as the Example following doth shew. 〈♫〉〈♫〉 Altera. Tenor. Altera. 〈♫〉〈♫〉 Base.

11 If a Rest together with the figure, to which it is of equall value, be enclosed betwixt 2. perfect notes; thē either the rest goes before the figure, or followesit; if the Rest go before, the figure is altered: if otherwise, there is no place for Alteration, because the notes only are altered, & not the Rests. Be∣side Alteration fals alwayes vpon the second, and not vpon the first, thus: 〈♫〉〈♫〉 Tenor. 〈♫〉〈♫〉 Base.

12 Alteration is taken away by the fulnesse of the notes; and by the Pricke of Diuision. In Ligatures also Alteration is kept, as in the following Example is cleere. 〈♫〉〈♫〉 Tenor. 〈♫〉〈♫〉 Base.

13 As oft as three alterable Notes are shut within two imperfectible

Notes, both the imperfectible shal remaine perfect, and none of the altera∣ble Notes is altered: because the Ternarie number is euery where perfect.

THE THIRTEENTH CHAPTER.

Of Proportion.

WHerefore Proportion is the nature of two compared together in one vniuocall thing. Vniuocall I say, because in aequiuocals there is no comparison: for a still and a loud voice are not compared. Whence is it, that proportion is properly called, when it is found in those things, which are equall and vnequall, like and vnlike. Or ac∣cording to Euclide; it is a certaine disposition of two quantities how bigge soeuer, (being of the same next Genus) one to the other. Hence is it that things continuate and discreate, although they be contained vnder the same Genus of quantitie, yet are not compared, because they are remote, not neere.

Of the Diuision of Proportion.

PRoportions are some of equality, some of inequalitie. That of equalitie is the Relation of two equall quantities. For that is equall, which is nei∣ther greater, nor lesse than his equall. That of inequalitie, is the disposition of two vnequall quantities. For that is called inequall, which being in Rela∣tion with another is either greater or lesser than it.

What Proportions is fit for Musitians.

BEcause the dissimilitude, and not the similitude of voyce doth breede Harmonie: therefore the Art of Musicke doth onely consider of the Proportion of inequalitie. This is two-fold; to wit, the Proportion of the grea∣ter or of the lesse inequalitie. The Proportion of the greater inequalitie, is the relation of the greater number to the lesse, as 4. to 2. 6. to 3. The Proportion of the lesser inequalitie is contrarily the comparison of a lesse number to greater, as of 2. to 4. of 3. to 6.

Of the 5. kindes of Proportions.

OF the Proportions of the greater inequalitie, there be 5. Kindes, to wit; Multiplex, Super particular, Super partiens, and those be simple: the com∣pounded are the Multiplex Super particular, & the Multiplex Super partiens.

To these are opposed 5. other kindes of the lesser Inequalitie (saith Fran∣chinus) and hauing the same names with the Preposition Sub, onely set be∣fore them: as Submultiplex, &c.

But seeing that Multiplex Proportio hath chiefe force in Musicall Conso∣nances, and next to that the Super particular, and the Super partiens with the two following none, we doe therefore abandon the Super partient with the

rest following, as vnworthy of the Harmonicall Consort, and doe receiue the two formost onely.

Of the Multiplex kinde.

THe Multiplex Proportio, is both more excellent, and more ancient than the rest, as when a greater number being in Relation with a lesse, doth precisely comprehend the whole lesser number more than once, as say, twise, or thrise. The kindes of this will be infinite, if you compare each num∣ber with an vnitie, as in the following quadrate you may see. 〈♫〉〈♫〉 Dupla. Trip. Quadru. Quintu. Sexiu. Septu. Octup. Nonu. Decu.

To this foresaid kinde is opposed the first kinde of the lesser Inequalitie, called Submultiplex. The one of these destroyeth the other; and this kind, making the same Relation of an vnitie to other numbers, doth produce out of it selfe the same Species which a Multiplex doth, and Species of the same names, by adding the Preposition Sub, and is produced in this manner. 〈♫〉〈♫〉 Sub Sub Sub Sub Sub Sub Sub Sub Sub 〈♫〉〈♫〉 dup. trip. quadr. quintu. sextu. septu. octu. nonu. decu.

Of the Superparticular Kinde.

SVperparticular, the second kinde of Proportions is, when the greater num∣ber being compared with the lesse, doth comprehend it in it selfe once, & besides some such part of it. Some such part (I say) which being often taken doth make precisely the whole greater number. Of this kinde the sorts are innumerable, if you reckon each of the numbers, taking away an vnity, with the next lesser, in manner following. 〈♫〉〈♫〉 Sesqui Sesqui Sesqui Sesqui Sesqui Sesqui Sesqui Sesqui 〈♫〉〈♫〉 altera. tertia. quarta. quinta. sexta. septima. octa. nona.

The opposite to this, is Sub superparticular, the second kind of the lesse Inequalitie: which doth produce the same Species, which the former doth, with the same names, the Preposition (Sub) being adioyned: if you will com∣pare each of the lesser numbers (an Vnitie I alwayes except) with the greater neighbouring, as here followeth the manner.

〈♫〉〈♫〉 Subses∣quialte∣ra. subses∣quiter∣ta. subses∣quiquar∣ta. subses∣quiquin∣ta. subses∣quisex∣ta. subses∣quisep∣tima. subses∣quioc∣ta. subses∣quino∣na.

By what meanes Proportion is made of aequalitie, and consequently one Proportion out of another.

WHen you will make a Proportion out of Equalitie, and one proporti∣on out of another, you shall thus truely worke it by this Rule of Boë∣tius, Disposing three equall numbers, say vnities, or any other, let three o∣ther be placed vnder them, so that the first may be euen with the first; the second with the first, and the second; the third, with the first; the two seconds, and the third, and you shall find it a Duple, thus: 〈♫〉〈♫〉 Duplae. Duplae. Duplae.

Now if you wil make Triples, placing the Duplaes, which you haue made in the higher ranke, let three numbers be placed vnderneath, according to the Tenor of the foresaid Rule, and you haue your desire; thus: 〈♫〉〈♫〉 Triplae. Triplae. Triplae.

Now if we place these Triples, which we haue thus found in the vpper ranke, we shall produce Quadruples, by the concordant, and regular opposi∣tion of the numbers vnwritten, of Quadruplaes, Quintuplaes; and also out of Quintuplaes, Sextuplaes, and so forward infinitely. 〈♫〉〈♫〉 Quadruplae. Quintuplae. Sextuplae.

And if out of Duplaes, you will create Sesquialteraes, inuerting the num∣bers of the Duplaes, so that the greater may be first, and the lesser succeed in a naturall order: let there be vnder placed three other numbers, as often as the said Rule requireth, and you haue that, as followeth.

〈♫〉〈♫〉 Sesquialterae. Sesquialterae. Sesquialterae.

Now as of Duples you make Sesquialteraes, so of Triples you may make sesquitertiaes, and of Quadruplaes sesquiquartaes, by conuerting the num∣bers, as was said of sesquialteraes, and so you may goe infinitely, in manner following. 〈♫〉〈♫〉 Sesquitertiae. sesquiquartae. sesquiquintae.

Out of what Proportions Musicall Concords are made.

THe Proportions, which make Musicall Consonances, are sixe, (as Boêti∣us and Macrobius witnesse) three in the Multiplex Kind, to wit, the Dupla, Tripla, Quadrupla: 3 in the super particular, to wit; sesquialtera, sesquitertia, & sesquioctaua. Of which specially the allowed Interuals of Musicke are com∣pounded (as saith Plutarch.) Where relinquishing others, wee thought fit to make plaine by short precepts and examples these only, which consist and are described in Notes. So keeping the naturall order, we will begin with the Dupla, because it is both worthyer and better knowne, than the rest.

Of the Duple Proportion.

DVpia Proportio, the first kind of the Multiplex, is when the greater num∣ber being in relation with the lesse, doth comprehend it in it selfe twise: as 4. to 2: 8. to 4. But Musically, when two Notes are vttered against one, which is like them both in nature and kinde. The signe of this some say is the number of 2: others (because Proportion is a Relation not of one thing, but of 2) affirme that one number 〈 math 〉〈 math 〉 is to be set vnder another, thus; And make no doubt but in all the rest this order is to be kept. 〈♫〉〈♫〉 Tenor Duplae. 〈♫〉〈♫〉 Bassus duplae.

I would not haue you ignorant, that the duple Proportion, and all the o∣ther of the Multiplex kind, are marked by certaine Canons, saying thus, Decrescit in duplo, in triplo, and so forth. Which thing because it is done either to increase mens diligence, or to try their cunning, wee mislike not. There be that consider the whole Proportion in figures, which are turned to the left hand-ward with signes, and crookes, saying, that this C. is the du∣ple of this 〈☐〉〈☐〉. and this 〈☐〉〈☐〉 of 〈☐〉〈☐〉 and in Rests that this 〈☐〉〈☐〉 is the duple of this 〈☐〉〈☐〉 I thinke onely vpon this reason, that Franchinus pract. lib. 2. cap. 4. faith that the right side is greater and perfecter than the left: and the left weaker than the right. Against which opinion neither my selfe am. For in Valerius Probus a most learned Gramarian in his interpretation of the Roman letters saith, that the letter C. which hath the forme of a Semicircle signifies Caius the man, and being turned, signifies Caia the woman. And Fabius Quintilianus in approouing of Probus his opinion saith; for Caius is shewed by the letter C. which being turned signifies a woman: and being that men are more per∣fect than women, the perfection of the one, is declared by turning the Semi∣circle to the right hand, & the weaknesse of the other by turning it to the left. By this occasion the Musitians thought fit to take away the halfe left side from the right, thus; 〈☐☐☐☐☐☐〉〈☐☐☐☐☐☐〉

Rules of Proportions.

FIrst, Euery Proportion is either taken away by the comming of his con∣trary proportion, or is broken by the interposition of a signe. As by the comming of a subduple, a dupla is taken away, and so of others.

2 Euery Proportion respecteth both Rests and Notes.

3 Euery Proportion of the great Inequalitie doth diminish the Notes and Rests with his naturall power: but the Proportion of the lesse Inequa∣litie doth increase them.

4 Alteration and Imperfection are onely in those Proportions, which are in perfect degrees, neither are they in all figures, but in those onely, which those degrees doe respect with their perfection, or to which these accidents besides the Proportion doe belong.

5 The sesquialtera Proportion doth exclude the Ternarie perfection of figures, vnlesse they haue it from a signe. Wherefore when the signe denies it; they receiue neither Alteration, nor Imperfection.

Of the Triple.

THe Triple Proportion, the second kinde of the Multiplex is, when the greater number, being in Relation with the lesse, doth comprehend it in it selfe 3. times, as 6. to 2: 9. to 3. But Musically, when three Notes are vt∣tered against one such, which is equall to it in kind. The signe of this is the number of three set ouer an Vnitie, thus;

〈♫〉〈♫〉 Tenor Triplae. 〈♫〉〈♫〉 Bassus Triplae.

Of the Quadrupla.

THe Quadrupla is the third kind of the Multiplex, and is, when a grea∣ter number doth comprehend a lesse in it selfe foure times, as 8. to 2▪ 12 to 3. But Musically, when 4. Notes are sounded to one: the signes of it are these 〈 math 〉〈 math 〉 as thus: 〈♫〉〈♫〉 Tenor Quadrupla. 〈♫〉〈♫〉 Bassus Quadruplae.

Of the Sesquialtera.

THe Sesquialtera is the first sort of the Super particular, and is, when a great number doth comprehend a lesse once, and some other part of it: as 6. to 4: 9. to 6. But Musically, when three Notes are sounded against two of the same kinde: the 〈 math 〉〈 math 〉 as in the Example following. signes of it are these; 〈♫〉〈♫〉 Tenor Sesquialterae. 〈♫〉〈♫〉 Bassus sesquialterae.

There be, which adde the colour to the figures which are made sesquial∣terate by the Caracters of the numbers: and contrarily sesquialterating the

sesquialteraes. And these men (as Franchinus witnesseth) haue this fault, that they make of two sesquialteraes, not a duple sesquialtera, (as they thinke) but a duple sesquiquarta. Some put Imperfection & Alteration in the sesquialte∣rates of the imperfect time, mesuring a Breefe Rest with one Tact: although in the Notes they set 3 semibreefes in one Tact. But vpon what ground they doe it, excepting of an Asse-headed ignorance, I know none. For Imper∣fection admits not the Imperfection and Alteration of signes, neither doth Proportion exclude Rests.

Of the Sesquitertia.

THe Sesquitertia Proportion, which they cal Epitrite, because it is made by an Epitrite, Macr. saith, it is when the greater number of Notes, doth containe the lesser in it selfe, & besides his third part: as 4. to 3: 8 to 6: 12. to 9. But Musically, when 4. Notes are sounded against 3. which are like them∣selues. The signes of it are these, 〈 math 〉〈 math 〉 There be that ascribe an in∣uerted semicircle to this Proportion, but Tinctor seemes to be a∣gainst that. 〈♫〉〈♫〉 Tenor sesquitertiae. 〈♫〉〈♫〉 Bassus sesquitertiae.

Of the sesquioctaua.

THe sesquioctaua Proportion is, when a greater number being compared with a lesse, doth comprehend it once, and with it his 8 part, as 9. to 8: 18 to 16. But Musically, when 9. Notes are sung to 8, which are like them∣selues. The signe of it is the number of 9. set ouer 8, thus; 〈 math 〉〈 math 〉 〈♫〉〈♫〉 Tenor sesquioctauae. 〈♫〉〈♫〉 Bassus sesquioctauae.

There are besides, who (because the value is diminished by adioyning the colours) doe consider the Sesquialtera by the fulnes of the Notes; which also they call Hemiola. For Hemiola is that, which Sesquialterá is, saith Aulus Gellius lib. 19. cap. 14. Yet this blacking of the Notes, is accidentall to it ne∣uer, but vnder the imperfect quantitie, as Franchinus writeth. 〈♫〉〈♫〉 Tenor Hemiolae. 〈♫〉〈♫〉 Bassus Hemiolae.

Though there be many other kindes of Proportions, which the Musiti∣ans doe obserue in Harmonicall Concent, yet haue I omitted all these for briefenesie sake, least children (for whom this Booke is made) should haue their wits rather clogged than helped hereby. Therefore the learned may pardon me, because this is written for them that are hungry, not for those that haue a delicate mawe. Yet (by the grace of God) all that now for breui∣tie sake, or vpon other occasions I now omit, shall be painefully set downe in a greater volume with more diligence and care. Meane while, I intreat yong men to exercise themselues with these small precepts, that when they are to goe to higher matters they may be fit.

The end of the second Booke.