[figure]
To Musicks sacred Temple, Mercurie.
And Orpheiis dedicate their Harmonie
From thence proceeding. Whose faire Handmaids an
Myster'ous Numbers: which, if you compare.
The Rat'on of proport'ons you will find.
These please the Eare, and satisfie the mind.
For nothing, more, the Soule and sense contents.
Then Sounds express'd by voice, and Instruments.

Io. Dir. Iohn Chantry [...]

sould by Peter Dring at ye Sun in the Poultry:

TEMPLVM MVSICVM: OR THE MUSICAL SYNOPSIS, OF The Learned and Famous Johannes - Henricus - Alstedius, BEING A Compendium of the Rudiments both of the Mathematical and Practical Part of MUSICK: Of which Subject not any Book is extant in our English Tongue.

Faithfully translated out of Latin By John Birchensha. Philomath.

[...]mprimatur, Feb. 5. 1663. Roger L'Estrange.

London, Printed by Will, Godbid for Peter Dring at [...] Sun in the Poultrey next Dore to the Rose-Tavern. 1664.

To the Right Honourable EDVVARD Lord MONTAGU Earl of Sandwich, &c. Knight of the most Noble Order of the Garter, and One of His Majesties most Honourable Privy-Council.

SIR,

WHen I considered the Excellency of the Subject of this Book, and deserved Fame of the learned Author, I thought it not necessary to crave a Pro­tection [Page] for this Treatise by a Dedication of it unto any: be­ing in it self far above the reach of detracting Calumniators. Yet I have made bold, humbly, to present it to your Honour as a pleasant and delightful Diver­tisement from your many and great Imployments. In all Ages Musick hath been accep­table to the wisest, greatest, and most Learned men, of whom many have been famous for their great Ability and Knowledge in this Science and Art. It was no dispraise to Da­vid that he plaid skilfully on the Harp, and Sang well: the [Page] Compositions of divers Ger­man Princes are extant: neither is it the least of those Virtues which are eminent in your Lordship, that you are both a Lover of Musick, and a good Musician. The renowned Al­stedius in this Compendium (not much differing in his Judge­ment from the Opinion of the Generality of modern musical Classic's) does present the world with a great Light and Disco­very of this Art, with the Sub­ject, Principle and Affections thereof, with the curious Sym­metry of Proportions: the pro­portional Dimensions of [Page] Sounds: the Variety of Dias­tems: the admirable Series of musical Voices: the usefulnesse of Tetrachords: the several Genus's of Musick: and har­monical Moods, which being expressed by Voice or Instru­ment or both, do operate in­eredibly upon the Affections. Wherefore I hope that this Book will be accepted both by your Honour, and all ingenuous Lovers and Professors of this Art, and the Errors thereof favourably pardoned by your Lordship and them. The Rea­son which moved me to under­take this Translation, was, be­cause [Page] I desired a Discovery might be made of some Princi­ples of the Mathematical part of Musick, unto those ingenu­ous Lovers of this Science, who understand only our own Language, to the End that by this means the transcendent Virtue and Excellency that is comprehended in the due pro­portions of musical Sounds may be known unto them; which will give Satisfaction unto their Reason aswell as to their Sence. I do not think this unworthy my labour, because that many skilful Musicians have not thought it any Disparagement [Page] to publish their Translations of the Works of famous Men, who did write of the Art which they themselves professed. As Meibomius Translated some Fragments of Baccheus, Alyp­pius, Nichomachus, and others: the never to be forgotten Fran­chinus, the Commentaries of Briennius, Aristides, Ptolomy, and others: and our English Douland, the Introduction of Ornithoparcus. In the Author's last Edition of his universal En­cyclopaedia, I met with an Ap­pendix to his Musical Synopsis, taken out of the writings of E­rycius Puteanus; but not find­ing [Page] any thing new in it, only an ABCdary Repetition of the first Elements of Musick, formerly but more judiciously and large­ly handled in this Compendium: and also some few Questions started by Cardanus, which are, for the most part more fully and Satisfactorily resolved by the Author; I did forbear the Translation thereof; not being willing to weary the Reader with the unnecessary recital of those things, nor your Lord­ship with too tedious an E­pistle, which I here conclude, humbly craving pardon for my boldnesse, and your Honours [Page] favourable Acceptation of this Mite from your Lordships

Most humble and devoted Servant, JOHN BIRCHENSHA.

To all ingenious LOVERS of MUSICK.

GENTLEMEN,

IT was for your Profit and Bene­fit that I undertook this Translation: and that you might thereby understand the Rudiments and Principles both of the Mathematical and Practical Parts of this Sci­ence. We know that there is some light into the Mathe­matical Part of all other Arts; but little discovery of that Part of the Theory of Musick hath been made in our Language; therefore I did suppose that this work would be gratefully accepted by you, the Author having more fully discovered the Precepts, Rules, and Axioms of this Science, then any other whose Works I have seen.

Since the Rumour of this Translation hath been spred abroad, I have by diverse been demanded, What Benefit and Advantage the Knowledge of the Ma­thematical Part of Musick does contribute to the completing of a Musician? To which I answer, That it is as necessary for a perfect and complete Musician to [Page] understand the Proportion of Sounds, as for a curious Painter, exactly to know the Symmetry of every part o [...] a Body: that so he may rightly understand the ground and foundation of the Art he does profess, which is, the nature of Sounds, and their due Pro­portion, in respect of their Ration, Habitude, Qua­lity, Difference, Excess, Dimension, and Mag­nitude. For this I dare boldly affirm, and if [...]c­casion be offered: undertake to prove it: That such Rules may be yet further, and are already, in part, contrived (drawn from the Mathematical Principles of Musick, by which, musical Consonants and Dis­sonants (artificially applied and disposed, according to the nature of their Proportions, and by the foremen­tioned Canons) may afford, in 2, 3, 4, 5, 6, 7, or more parts, as go [...]d Musick, that is, as agreeable, artificial, and formal, as can be composed by the help of any Instrument. Yet until such Rules be known, it is commendable in any to use such helps as may Ad­vantage their Compositions. But for any Musician to unde [...] value or speak slightly of the Mathematical part of Musick, is to repro [...]ch the Common Parent from whom the Art h [...] professeth rec [...]ived a Being. I k [...]ow that all Ingenuous persons who are Artists, will ac­knowledge that it is a more noble way to work by Rules and Pr [...]c [...]pts in any Art, then mechanically; And so to work in this Art. i. e. to compose regularly, will be found m [...]re advantagious then any other way in these Respects. For by such a way of Operation the Com­poser shall work more certain [...]y, firmly, readily, and with more facility then by any other way.

If Musick be an Art, then it may be contracted [Page] and collected into certain Rules which may discover all those Mysteries that are contained in that Science, by which a man may become an excellent Musician, and expert, both in the Theorical and Practical Parts thereof. To the Completeing of such forcible Rules I have contributed my Mite, whose Certainty and Rea­lity has been Experienced by divers, and may likewise be further known unto others, if they please or desire to understand them.

I know that all Virtuoso's will encourage those things which conduce to the Improvement of any ingenious Art: but what shall be spoken against such things by persons rude, envious, or that do pass their Judge­ment rashly upon things which they know not, having neither seen, heard, nor understood them, is not to be valued. And I do assure my self that there is not any person in this Nation, that is a true Lover of this Science; or a Professour thereof, who does truely ho­nour and understand this Art, but could cordially wish such an Improvement thereof, that those things which in Musick are concealed and mysterious, might be fully discovered: those which are imperfect, completed: those which are doubtful and disputable, cleared by evident Demonstration: those which are not to be done without great trouble, facilitated: those many Obser­vations which burthen the Memory, made few and plain: and those whose Operation and Experience do's require the study and Expence of many years, might be performed without any difficulty in a few Weeks, or Months at the farthest. And that this way is found out and effected in a great measure, I say, many per­sons of Worth and Quality are able experimentally to testifie.

[Page]Musick hath already flowed to a great [...]eighth in this Nation, for I am perswaded that there is as much Exc [...]llency in the Musick which hath been, and is now c [...]mposed in England, as in any part of the World for Ayre, variety and Substance. [...]ut I heartily wish, that af [...]er this great Spring and [...]lood, there be not in our succ [...]eding Generations) as low an Ebb. For if the serious and substantial part of Harmony be neg­lected, and the mercurial only used: It will prove vo­latile, evaporate, and come to nothing. But, Gen­tlemen, I woul [...] not willingly weary your patience, and sinc [...] [...]he Temple is so small, I will not make the [...]ate too bigg; But subscribe my self as it is known I am) a true Lover of Musick, and

Your Servant J. B.

I Have endevoured fa [...]thfully to translate the Origi­n [...]l, in wh [...]ch I find some mistakes, which I dare not impute to the Author, of which I would have thee take no [...]ice. And also one Erratum in this Impression.

1. Fol. 20. the greater Sem [...]tone exceedeth the lesser by the lesser Diesis: whereas it exceedeth it but by a Comma, as appeareth fol. 18. where the Author saith thus, The Comma is the difference between the Semitone m [...]jor and minus.

2. Fol. 31. almost ten parallel Lines; the Word almost should be left out, for the greater System is ten parallel Lines.

3. Fol. 44 for d moll. read b moll.

TEMPLUM MUSICUM.

CHAP. I. Of the Subject of MUSICK.

PRECEPTS.

MUSICK is the Science of Singing well, otherwise called Harmonical: and Mu­sathena.

The parts thereof are two: the general and the special.

The general part doth treat of the Subject of Musick; and both of the Principles and Affections of the Subject.

The Subject of Musick is an harmo­nical Song. And this is the Subject of Tractation. The Subject of Informa­tion, [Page 2] is the Faculty of Singing: and the Subject of Operation, is the matter to which harmonical Musick may be ap­plied.

RULES.

1. Musick is a Mathematical Science, subalternate to Arithmetick.

For as Arithmetick doth treat of Number, so Musick of the number of Sounds: Or as others of numerous Sound. For as the Optick Science is called a certain special Geometrie, so Musick may be called a certain special Arithmetick: But whereas some contend that Musick is both a Science, Pru­dence, and Art, because it doth instruct both skil­fully, or scientifically, and prudently, and artifici­ally to compose an harmonical Song, it is not so ac­curate. For it is not here Queried, whether Science, Prudence, and Art may concur in Practise: but whether Musick being considered as a Discipline ei­ther habitual or systematical, be a Science, Prudence, or Art. But that it is a Science it doth thus app [...]ar, because it hath Subject, Principles, and Affections; which three thin [...]s are required unto the complete Ration of a Science.

2. An Harmonical Song, is a con­cinnous multitude of Sounds, rightly composed according to the Text.

The Subject of Explication in Musick is a Song, whose chief Force lieth in this, [...] accommo­dated to the Text and Affections [...]

But if the same Sound may be accommodated to divers and contrary things and Affections, then the Musick is inept and irrational; because it is contrary to the Scope and Principle of that most laudable Discipline, which will, That Melodie be applied both to Things and Affections.

If therefore v. g. in any Psalm of David, three Parts do occur, viz. Lamentation, Consolation, and giving of Thanks: there, three Tones ought to be.

3. The Subject of Operation in Musick are Things sacred and liberal. By which it appeareth that the useful­nesse of it is very great.

Things sacred, as the Psalms and Songs in the Bible, and of other things wholly Divine.

Things liberal, as pathetical matters in things Philosophical, and which doth altogether concern the common Life of Man. For Musick doth pene­trate [Page 4] the In [...]eriors of the mind, it moveth Affections, promoveth Contemplation, expelleth [...]orrow, di [...] ­solveth bad Humours, exhilerateth the animal Spirits: and so is beneficial to the Life of Men in general, to the Pious for Devotion, to the Contemplative Life for Science, to the Solitary for Recreation, to the domestick and publick Life for Moderation of mind, to the Healt [...] [...] the temperament of their Body, and to the [...] for Delight; As excellently saith that famous Musician Lippius in his Musical Synopsis. Hence it is that the Divel hateth Musick liberal, and on the contrary is delighted with filthy Musick and illiberal, which he useth as his Vehicle, by which he slideth himself into the minds of men, who take Pleasure in such Diabolical Musick. On the con­trary, the holy Angels are delighted with Musick li­beral, not because corporal Harmony doth affect them, but because all Harmony, especially that which is conjoyned with the Affection of a pious Will, is grateful to those chast Spirits. Hence it is, that the Heroes, holy Men, and Lovers of Virtue of all times, have magnified Musick: as appeareth by these Scriptures; Exod. 15. Judg. 5.1. 1 Sam. 16.23. 2 Sam. 6 5. 2 Kings 3.15. 1 Chron. 23.5. Judith 16.1, 2, &c. Syrach 23.5, 6, & 39.20. & 44.5. Matth. 26.30. Luke 1.46. & 2.13. Eph. 5.18, 19. Col. 3.16. Apoc. 5.9. & 14.2, [...].

CHAP. II. Of the Principles of Cognition in Musick.

PRECEPTS.

THE Principles of an Harmonical Song are those things upon which it doth depend: And those are either the Principles of the Cognition or Constitu­tion thereof.

Those are complex: these incomplex.

The Principles of Cognition are those by which an harmonical Song is known. And they are either internal or external. Those are taken from the Science it self, these from Philosophy, partly theoretical, and partly practical.

RULES.

1. The internal or domestical Princi­ples of Cognition are here and there spread through the whole Body of Musick.

Wherefore it were not worth while to treat of them in this place.

2. The theoretical Principles which Musick doth use, or is built upon, are either remote or proximate.

The remote are such as are taken from the Me­taphysicks and Physicks. And indeed from the Me­taphysicks, there are taken Principles of Unity, Goodnesse, Pulchritude, Perfection, Order, Op­position, Quantity, Quality, and the like. And from the Physicks, tho [...]e that treat of the Quantity, Quality, Motion, Place, and Time of a natural Body: Al [...]o of Air, an [...] Sound, and of its propa­gation, multiplication, differences, and percep­tion: And lastly of Affections, as Love, Joy, Sor­row, and the like. The proximate principles are Axioms, Assumptions, Questions, Theorems, Pro­blems, and Consectaries mathematical; and those pa [...]tly arithmetical, partly geometrical: but chiefly a [...]ithmatical; especially those which concern the Pro­prieties [Page 7] of Simple Numbers, and also their pro­portion; viz. dupla, tripla, sesquialtera, and the like, of which in my Arithmeticks: But here let these Axioms be observed. 1. That Proportion of Equality is radically between one and one: And this is the Radix of all Proportion. 2. Dupla Propor­tion is radically between two and one, tripla be­tween three and one, quadrupla between four and one, and so forward. Obse [...]ve, that radical pro­portio [...]s are in Nine Simple Numbers, from 1. to 9. because these are the Radixes of all Numbers. 3. Sesquialtera Proportion is between three and two, Sesquitertia between four and three, Superbipartiens tertias, is radically between five and three, and Su­pertripartiens quintas is between eight and five. And these are simple proportions, in which such an or­der of perfection is observed, that after a proporti­on of Equality, a proportion of inequality follow­eth: First Dupla, afterward Sesquialtera, then Ses­quitertia, afterward Sesquiquarta, and Sesquiquinta, then Superbipartiens tertias, an [...] Supertripartiens quintas. To these succeed com [...]ound [...]d P [...]opo [...]tions, as Dupla-Sesquialtera b [...]tween 5, and 2. [...] Ses­quitertia between 10, and 3. Dupla-Superbipartiens tertias, as between 8, and 3. and so forward. 4. Proportions are numbred by Division logistical, as the proportion which is between 3, 2. appeareth by Division. For if 3. be divided by 2. it will pro­duce 1.½. 5. Proportions are added by vulgar mul­tiplication, as 3/2: 2/1: make 6/2: 2/1: 6. Proportions are substracted by Multiplication crucial; as [...] [Page 8] 7. Proportions are multiplied or coupled when they are written without Intermission, and the an­tecedent number of the latter proportion is multi­plied into the Consequent of the former, or con­trarily. Also when the Consequent of the former is multiplied into the Consequent of the latter. Or lastly, when the Antecedent of the former is mul­tiplied into the antecedent of the posterior. As 2.1, 3, 2. Here, once three, give three: and once two, give two, and twice three, give six. 8. Propor­tions are radicated in greater numbers, and in num­berss compounded one with another by Mediation lo­gistical▪ as 16-8. First they are reduced to 8-4. then to 4-2. lastly to 2-1. And thus radical Proportions by course are easily reduced to their greater Terms by logistical Duplation; as 1-2. to 2-4. thence to 4-8. then to 8-16. and so forward. 9. Every Dupla Proportion doth consist of a Sesquialtera and Ses­quitertia. 10. If a Sesquialtera be taken away from a Dupla, a Sesquitertia will only remain, and so consequently.

3. Practical Principles which Musick useth, are chiefly taken from the Ethicks, Oeconomicks, Politicks, and Poeticks.

From the Ethick [...] are taken Principles of Virtue, and moral Beatitude; from the Oeconomicks of Act [...] ­ons [Page 9] domestick; from Politicks Principles of virtue, and civil Beatitude; and from Poetrie Principles con­cerning Rhyme and Verse: which have [...]uch Affinity with Musick, that by some Mus [...]ck is divided into Harmonical, Rhythmical, and Metrical.

CHAP. III. Of the Efficient and End of an Harmonical Song.

PRECEPTS.

THE Principles of Constitution are those by which an harmonical Song is constituted.

And they are either external or inter­nal.

The external are the Efficient and End. The Efficient Cause of a Song is either the first or second.

The first Cause is GOD the Author of all Symphony.

The second is partly Nature, the Mo­ther [Page 10] of all Sounds: partly Art perfecting the Rudiment of Nature.

The ultimate End is GOD that Arche­type of Harmony.

The subordinate End is Motion, and the impulse of Man to the hatred of Uice, and study of Uirtue.

RULES.

1. God is the Author and Maintainer of all Harmony,

Seeing Harmony is Order, and tendeth to Unity; for God is the Author and Maintainer of all Order, and the greatest Unity. Furthe [...]more, God is the chief and unspeakable Joy, therefore they who rightly rejoyce come nigher unto God. Hence the Rabbins say, the Holy Ghost doth sing by reason of Joy. And Philosophers say, That the Soul of a Wise man doth alwayes rejoyce; For joy as it is pure Harmony can­not but be excited and maintained by Musical Har­mony.

2. The Exemplary Cause of Harmoni­cal Musick; is that Musick which is called mundane.

This is discerned in the Order, Disposition, and admirable proportion which doth occur in the Ce­lestial, and [...]ubcelestial Region; partly among the St [...]rs, partly among the Elements, partly among all things compounded of the Elements; and lastly, among all tho [...]e things which are compa [...]ed one with another: of which Musick and Harmony we have spoken in our Physicks. This Harmony being such and so great, when ancient men did diligently con­sider it, they supposed that there was the like Pro­portion not only in Numbers and Lines, but also in the Voice; especially when they did discern that Proportion in the various Sound of various Bodies.

3. Musick receiveth his greatest Perfe­ction from the End.

That Perfection doth not only depend upon mat­ter and Form, but also upon the [...]nd we have for­merly shewn in our Metaphysicks and Logicks. In Musick certainly this is most manifest: for unlesse it be referred to the Glory of God, and the pious Recreation of Man it cannot but equivocally be cal­led Musick. Hence it is apparent that those simple men who abuse Vocal and Instrumental Musick to [Page 12] nourish the pleasures of this World, whilst they si [...]g Songs highly obscene, are nothing lesse then Musi­cians. For although the Form of a Song occur there, yet the End which perfecteth the Instrument, is not there discerned: The [...]efore in such Musick there is the first perfection but not the ultimate; which nece­ss [...]rily is [...]equired in an Instrument, because the Virtue ther [...]of is placed in the use.

CHAP. IV. Of the quantity of a Musical Song.

PRECEPTS.

THE internal Principles of an har­monical Song are Matter and Form.

Matter comprehendeth the integral parts of which an Harmonical Song is made.

Of the parts thereof, the one is Sim­ple, and the other is compounded.

[Page 13]The simple part is called Sound: also a Musical Monad. in Greek Tonos.

A Musical Sound is considered in re­spect of his Quantity and Signs.

The Doctrine of that is called theore­tical Musick, and of this Signatory.

Quantity is threefold, Longitude, La­titude, and Crassitude.

The Longitude of a Musical Sound, is that which is discerned in the motion and duration thereof: and measured by a Musical Touch or Tact.

The Latitude of a Musical Sound is that which is discerned in the tenuous and asperous spirit.

The Crassitude of a Musical Sound is that which is discerned in the Profun­dity and Altitude thereof.

By reason of this Crassitude a Musi­cal Sound is equal or unequal.

The equal Sound is the Simple Uni­son.

The unequal Sound doth bring forth a Distance or an Interval of a sonorous Crassitude: which is called a Musical Interval.

[Page 14]A Musical Interval is seen in Propor­tion and Intention.

By reason of Proportion, an Interval is simple or compounded: that is called radical, this radicated.

A Simple Interval is either Just, or not Just.

A Just Interval is that which is nei­ther defective nor redundant: as an Octave Fifth, &c.

An Interval not Just is that which is defective or redundant: as a Semioctave, &c.

A compounded Interval is that which doth consist of simple Intervals: as a double Octave, a triple Octave, a qua­druple Octave, and so ad infinitum.

By reason of Intention it is a Scale, called Musical; and it is the various dis­position of acute and grave Sounds.

RULES.

1. Every Sound is Quantus.

For in every Body that hath Quantity, there is an audible Quality. That Quantity is numbred by Di­vision, and not barely considered, as it is a magni­tude. So that the most accurate Lippius might rightly say, every Sound is continual or discrete, or explain­able by number. But a Sound is Quantus, by com­plete Quantity. i. e. So that it have a trine Dimen­sion, and therefore Longitude, Latitude, and Crassitude.

2. Every Sound is long numerably.

For seeing every Sound doth continue so long, or not so long, this temporal duration thereof may be numbred. And it is numbred by a Musical Touch, which, according to the motion of the Heart, in this Science ought to be observed. This Touch doth consist of Depression and Elevation, according to a certain Proportion, but especially a Dupla: And it is either more simple, more natural, and more [...]om­mon, which is finished in two equal parts, and may be called Spondaic, as [...]: or lesse simple, and more unusual, which doth consist of unequal parts, th [...] one greater, and the other lesser, and may be call [...]d Tr [...]chaic. as [...]

3. Every Sound is numerably broad.

For every Sound besides the length thereof, is also tenuous or gentle, flat, submi [...]s, small; or sharp, ha [...]sh, clear, full, as consisting of a tenuous and a [...]perous Spirit.

4. Every Sound is numerably thick.

Besides the length and breadth, every Sound is al [...]o thick; and so it is either deep or high. That, is called grave, and this, acute. And we measure this magnitude of a Sound by Proportions of num­bers, especially ra [...]ical, as they are applied to the Monochord.

5. The Simple Vnison is the Principal and Radix of all Musical Intervals.

As in numbers there is one proportion of Equality, and another of Inequality: So also in Sounds, one is equal, and another is unequal. And again as in numbers, the Proportion of [...]quality is the Radix of all the rest: So in Sounds, the Simple Unison is the principal and Radix o [...] all Musical Intervals. For the Simple Uni [...]on doth consist of a proportion of Equality, which is radical [...]y between 1. and 1. as may be seen in a Mon [...]ch [...]rd. Therefore a Simple Unison is not a musical I [...]terval, but the original thereof.

6. Vnequal Sounds do make a Musical Intervall.

Unequal Sounds do make a Diastem or Distance, which is called a Musical Intervall, in which the grave Sound is profound and greater: and the acute, high and lesser. Of this Intervall these Theorems are noted. 1. He that knoweth a simple Intervall, may easily know a compounded Intervall. That, as they say, is radical: this, radicated. 2. There are seventeen simple Intervals or Diastems in this order. The first, an Octave, to wit, a voice, in Greek a Diapason, which is of a Dupla Proportion, between 2. and 1. where one Sound as the greater and graver, doth contain another, as the lesser and acuter, twice in it self; Therefore is the Unison composed from Let­ter to Letter, v. g. from G. to g. &c. The second, a Fifth, or Diapente, which is of a Sesquialtera Proportion; between 3. and 2. The third, a Fourth, or Diatessaron, which is of a Sesquiter­tian Proportion between 4. and 3. The fourth, a greater Third or Ditone, which is of Sesquiquar­ta Proportion, between 5. and 4. The fifth, a Third minor, or Hemiditone, which is of Sesqui­quinta Proportion, betwe [...]n 6 a [...]d 5. The sixth, a Sexta ma [...]or [...]or greater Sixth] or fourth with the greater thi [...]d, which is of a Superbipartiens tertias Proportion, as between 5. and 3 7. A Sexta minor or fourth with the lesser Third, which is of a Supertri­partiens quintas Proportion, between 8. and 5. The eigth, is the major Second, or whole Tone, which [Page 18] is of a Sesquioctave Proportion, between 9. and 8. The ninth, is the minor Second, or minor Tone, of a Sesquinona Proportion, between 10. and 9. The tenth, is the major Semitone, of the Proportion of 16. and 15. The eleventh, is the minor Semitone, of a Sesquivicefima quarta Proportion, between 25. and 24. The twelfth, the Diesis minor, of a su­pertripartiens centesimas vigesimas quintas Proportion between 128. and 125. The thirteenth, a Comma which is the difference between the Semitone majus, and minus, of a Sesqui [...]ctogesima Proportion, be­tween 81. and 80. The fourteenth, a Schisma which is the half of a Comma, or half of the Dif­ference between the Semitone majus and minus. The fifteenth, is the fifth with a tertia major, or greater Seventh, which is of a Superseptipartiens octavas Pro­portion, as between 15. and 8. The sixteenth, is the lesser Seventh, or quinta cum tertia minore, which is a Superquadripartiens quintas Proportion, between 9. and 5. The seventeenth, are Intervalls not just, which are either deficient or redundant, chiefly by the lesser Semitone, or Comma, or both together: as the Semioctave deficient and abounding Fifth: the minute and superfluous fourth which is named a Tri­tone, and such like. 3. Intervalls compounded of simple Diastems may be infinite. But it is proper to Musick to bound that Infinity of gross Sounds. (which is such only potentially.) Notwithstanding let us take notice of certain compounded Intervalls. First, such as are once compounded, as a Disdiapason, double Octave, or Fifteenth, which is of a quadru­pla Proportion, between 4. and 1. Also a Diapa­son [Page 19] with a Diapente, an Octave, with a Fifth, or Twelfth, of a triple Proportion, between 3. and 1. Also a Diapason with a Diatessaron, an Octave with a Fourth, or Eleventh, of a dupla superbipartiens tertias Proportion, between 8. and 3. Al [...]o others are twice compounded, as a Trisdiapason, Triple Octave, or two and twentieth of an Octupla Propor­tion, between 8. and 1. &c. Thirdly, others are thrice compounded, as a Tetradiapason, quadrupla Octave, or nine and twentieth of a sedecupla Pro­portion, between 16. and 1. Others are four times compounded, and so ad infinitum. 4. An Octave is the most simple, perfect, and prime musical Inter­vall. 5. An Octave divided be gets all other simple Diastems. Therefore from the Division of the 0ctave, the Harmonies of every Genus do flow. For every Octave being divided two wayes, beget­teth two Moods of it self. 6. An Octave is first di­vided into a fifth and fourth, of which it doth consist: and that either by harmonical or arithmetical Divi­sion. That is called the harmonical Medium of an Octave, when the fifth is beneath the fourth: and that the arithmetical, when the fourth is beneath the fifth. Let this be the Example of Harmonical Di­vision.

But I suppose the Author meaneth thus: [...]

[Page 20]Division Arithmetical is thus: [...]

Therfore in the harmonical Division of an Octave the fifth remaining immoveable, the fourth is pla­ced above the fifth: in the arithmetical Division, the fifth remaining immoveable, the fourth is put beneath the fifth. 7. If a Fifth be taken from an Eighth, there remaineth a Fourth, and so on the contrary. 8. A Fifth is divided into a Ditone, and Semiditone. 9. A Ditone is compounded of the greater and lesser Tone 10. The Tonus major is disp [...]sed into the Semitone majus and minus. 11. The D [...]tone is more then the Semiditone by the Semitone minus. 12. A Fourth exceedeth a Ditone by the major Semitone. 13. A Fifth is more then a fourth by the greater Tone. 14. The lesser Tone is excceded by the greater by a Com­ma. 15. The greater Semitone exceedeth the lesser by [...]. 16. A Sixth is made of a Fourth and a Th [...]rd, the greater of the greater, and lesser of the lesser, or the greater of a fifth and lesser Tone, and the lesser of the Semitone major. 17. The se­venth major, is made of a Fifth and greater Third, the minor, of the minor. 18. The greater Tone doth contain almost ten Comma's, the lesser almost nine; the greater Semitone almost five, and the lesser a most four. 19. A fifth doth contain two greater T [...]nes, one lesser, and the Semitone majus: A fourth [Page 21] one greater and lesser Tone, and the Semitone majus. Therefore an Octave hath in it self six Tones three major, and three minor, with the les­ser D [...]esis: to wit, five Tones, three greater, and two lesser, with two major Semitones, and so it doth comprehend more then fifty Comma's. 20. Com­pounded Intervalls do imitate the nature of their simple. A Disdiapason ariseth from two Octaves, an Octave with a Fifth comprehendeth eight Tones, five ma­jor, three minor, and three greater Semitones. A Trisdiapason is divided into three Octaves, and so of the rest. These Propositions are demonstrated by propositions arithmetical of proportions added, sub­stracted, coupled, &c. v. gr. An Octave is of a dupla proportion, a Fifth of a Sesquialtera, a Fourth of a Sesquitertia. Therefore an Octave doth consist of a Fifth and a Fourth. This whole matter is demonstrated in a Monochord: How these things may be vulgarly propounded, you may see hereaf­ter in the last Chapter and last Rule.

7. The Scale of Musick is explained in these Theorems.

1. The Series of Intension and Remission: or of Ascension from a grave Sound into an Acute, and of the Descension from an acute into a grave, is called the Scale of Musick. 2. The Scale of Musick doth vary both according to ancient and modern Musicians. For the Scale of the most ancient Musicians, was on­ly [Page 22] of one Diapason for radical Simplicity. The Scale of the Pythagorians was of a Disdiapason, for the keeping of Mediocrity. And now it is of a Tris, and Tetra-Diapason, for the grateful variety of vo­cal and Instrumental Musick. The Scale also is ei­ther Simple: and that either old as the enharmonic, chromatic, and diatonic; or new as the Syntonic: or mixed, which is compounded of simple [Intervalls] Of these the enharmonic and chromatic, in respect of their Difficulty and imperfection are not used in Solitary Musick. 3. The Syntonian Scale is of all others the most harmonical, to which the Diaton Scale may aptly be mixed: as it may be seen in a Clavichord, and wind Instrument, i. e. an Organ; where the white Keyes do proceed in the Syntonian Scale; which is somewhat moderated by the Diaton. The Syntonian Scale proceedeth by the great Tone, the lesser Tone, and the greater Semitone which ariseth from the minor Tone: the diatonic or diaton proceedeth by two Tones and a Semitone. To these the enharmonic Scale is added, proceeding by two Dieses, the greater and lesser, and an immediate Ditone in his Tetrachords. Also the chromatic proceedeth by two Semitones, the greater and the lesser, and an immediate Semi­ditone. So the black Keyes proceed with the white in the chromatic: from whence they are called fict in the Syntonian. Hence also ariseth the Scale irre­gular or flat, which differeth not from the regular or dural, but by accidental Transposition, or by the fourth above, or by the fifth beneath. And this is the Disposition of the old diatonic Scale.

  • [Page 23]1. The greater Tone. 9.8.
  • 2. The greater Tone. 9.8.
  • 3. The lesser Semitone from the greater Tone 256.243
  • 4. The greater Tone. 9.8.
  • 5. The greater Tone. 9.8.
  • 6. The greater Tone. 9.8.
  • 7. The lesser Semitone. 256.243.
  • 8. The greater Tone. 9.8. and so on through the Octaves below and above.

But the Disposition of the new and perfect Syntonian Scale is as followeth;

  • 1. The greater Tone. 9.8.
  • 2. The lesser Tone. 10.9.
  • 3. The greater Semitone. 16.15.
  • 4. The greater Tone. 9.8.
  • 5. The lesser Tone. 10.9.
  • 6. The greater Tone. 9.8.
  • 7. The greater Semitone. 16.15.
  • 8. The greater Tone. 9.8. And so on through the Octaves above and below. Compare these things with the antecedent Rule, and following Chapters.

CHAP. V. Of the Signs of a Musical Sound.

PRECEPTS.

THE Signs of a Musical Sound do follow.

And those are of a Sound either broad, long, or thick.

The signes of a long Sound do note the duration thereof: and they are either principal or lesse principal.

The principal Signes are a Note and a Pause.

A Note is a signe of a present and posi­tive sound: and containeth Touch, and that either whole or not whole.

It containeth the whole Touch either eight times as a Large, or four times as a Long, or twice as a Breve, or once as a Semibreve.

The rest do contain not the whole, but [Page 25] part of a Touch, and that either the half part as a Minim, or the fourth part as a Crotchet, or the eigth part as a Quaver, or the sixteenth part as a Semiquaver.

A Pause is the Index of a privitive or absent Sound, that is of silence: and it answereth either to a Large, or Long, or Breve, &c.

Signes lesse principal are a semicircle with a Center, Custos, or the like.

Signes of a broad sound, are a prick of Augmentation, breathing, and Syn­cope: of which, Syncope, is a certain loosing of the Touch; Notes, or Pauses; breathing answereth a Semi Minim.

The Signes of a Crasse Sound are parallel Lines, whereof the place and name do occur.

The place is a Musical System, and that greater or lesser.

The greater System for the most part doth consist of ten Lines: and serveth for the Composing of a Song, called other­wise a conjoyned System.

The lesser System doth consist of five Lines, and serveth chiefly to a Song pricked out. This is otherwise called a simple System.

[Page 26]The Name is aswell a Letter as a Uoice, or as others will, a Musical Syllable.

A Letter is as a Key by which the Song is opened, therefore called Clavis. Such letters are seven. A. B. C. D. E. F. G.

The musical Uoices or Syllables are six, ut, re, mi, fa, sol, la.

These are found in a Musical Scale either continued or discontinued.

There, there is no need of Mutation: but here otherwise.

RULES.

1. The most certain and ready Signs of Sounds are Cyphers of Numbers.

Because a Sound can neither by any Man be writ­ten in Paper, nor kept in his Mind, neither only nor alwayes; therefore it standeth in need of certain Signs, by which the Quantity and Quality thereof may be represented. For because in the Numbers and Proportions of these, all the Dimensions of Sound have their assigned Essence; the most sure and ready Signs are Cyphers of Numbers placed accor­ding [Page 27] to their Longitude, Latitude, and Profundity. For according to Longitude. 1.2.3.4.8. ½ 1/3 ¼ may note the stay of one Touch, two, three, or four, &c. According to Latitude in like manner; and according to Crassitude the g [...]eater Numbers may signifie the grave Sound; and the lesser Numbers, the acute Sound. But it behoveth here to retain vul­gar Signs, because they are most used.

2. The Doctrine of Notes is contained in these Rules.

1. Notes are either simple or compounded. And those are either whole or broken. These are called bound. Simple Notes are placed without any joyn­ing of either: Compounded, contrarily. Whole Notes are measured by whole Times; broken Notes, by parts of Time. Whole Sounds consist either of one Time, as a Semibreve: or of more, and those ei­ther of two, as a Breve: four, as a Long: or eight, as a Large. The broken Notes do contain either the second part of a Time, as a Minim: or the fourth, as a Crotchet: or the eighth, as a Quaver: or the Sixteenth, as a Semiquaver. According to the following Scheme.

[Page 28]

Names.Figure.Value.
Large.𝆶 Excessus.8.
Long.𝆷 Excessus.4.
Breve.𝆸 Excessus.2.
Semibreve.𝆹 Medium.1.
Minim.톹텥 톹텥 Defectus.½
Crotchet.톺텥 톺텥 Defectus.¼
Quaver.톼텮 톼텮 Defectus.
Semiquaver.톼텯 톼텯 Defectus.1/16

Although more Notes of Longitude may be given, as well greater or lesser, potentially infinite: yet the [...]e notwithstanding do suffice, which were inven­ted by Musicians of former Ages. 2. Notes are varied according to the Augmentation or Diminu­tion of their value, or according to both together. Either all or some are augmented by the half part; and truely, all are augmented either by the Opposition of a Semicircle. 𝇋. 𝇍. and a Prick, of which this is the Rule: A Prick put after Notes doth add the half part of the time above their proper value, as

12.6.3.3/2¾
𝆶.𝆷.𝆸.𝆹.톹텥.

[Page 29] Thus a Prick after a 𝆸. is a Monotone, or 𝆹. after a Semibreve is a Minim, or 톹텥. Some Notes are on­ly augmented by prefixing a Circle 𝇈. as a Large, Long, Breve. Notes are diminished by a Trochaic Touch in a certain proportion, either Tripla or Sesquialtera. Where the Signs are either Number or Colour: as 3/1 is tripla, 3/2 is sesquialtera. Notes are partly augmented and partly diminished, chiefly by the ligation and obliquation of a Breve, which is done for the extending of one Syllable. And a Long also with a Breve is counted for a Semibreve; and also in like manner a Breve with a Breve. But this kind of ligation and obliquation is now wholly omitted, as not necessary in the least.

3. Pauses measuring Silence do answer to those musical Notes whereof they are Privations.

For a Pause (which is noted by a little Line) doth answer either to a Large, or Long, or Breve, or other Note: as in the Type. [...]8. 4. 2. 1. ½ ¼

[Page 30]A double Breathing doth answer to a Quaver: a Triple to a Semiquaver. Hitherto do pertain the Neuma, Custos, and the like. As [...]Neuma. Custos.

4. Signs of a broad Sound are by Ar­tists expressed less carefully.

The Sign of a broad Sound ought to shew the Lati­tude of it according to the asperous, harsh, clear, full, soft, flat, and small Spirit thereof, as the nature of the Text requireth. But Musicians do less weigh the Latitude of a Sound, and do leave it to the Text, and to the things themselves that are to be sung, and are content with few Signs, chiefly using breathing and Syncopation. Breathing doth answer to the Crotchet: Syncope or Syncopation is a certain Luxation, that is, a fraction, and Contraction of Touch, Notes, and Pauses. e. gr. [...]

5. The Sign of a Crass Sound is a cros­sed Line, as they call it.

The Sign signifying Crassitude of gravity and a­cutenesse [Page 31] measurable by proportionable Numbers, is a perpendicular Line, which a right line doth cut; thus, +. The [...]e Lines are called Seats of crass Sounds or Musical Intervalls. Also a Musical System which is twofold, the greater and the lesser. In both there are perpendicular and parallel Lines; indeed in the greater there are [...] ten parallel Lines, in the lesser alwayes five. The greater serveth for the composing of a Song; where the perpendi­cular Lines are cut by the distance of one or two Touches: But the lesser doth serve for Melody, which is to be extracted and noted.

Let this be the Type of the greater System. [...]

Let this be the Type of the lesser System. [...]

Both these Systems are put in a Chart, or Melo­poetick Abacus, or Compositary as they call it. The first is convenient to a young Beginner: the latter, [Page 32] for a longer Practitioner: but others would rather draw more simple Systems in an Abacus; Thus, [...]

6. Of Letters and Voices Musical, as they call them, these are the The­orems.

1. The radical Letters are seven, in this order, a. b. c. d. e. f. g. which do moderate Sounds in the Diato [...]ic Scale of a Diapason. These are usually called Keyes, because that by them a [...]ong is, as it were, opened. They were invented by Guido Are­tine; at this time they are insufficient. 2. Letters or Keyes are either capital, minute, or geminate. Capital are they which are written with Capital, that is with great Letters. Thus Γ. A. B. C. D. E. F. G. of which Γ. A. B. C. are called grave, because they emit a grave Sound in respect of the rest: the rest, as D. E. F. G. are called finals, because every Song regularly doth end in these Keyes. We have only [Page 33] Γ from the School of the Greeks. The minute Keys are in number seven, so called because they are written with little Letters. Of these a. b. c. d. are called asfinal, because in these Keyes the transposed Song doth end: oth [...]rwise call [...]d acute, because they do emit a more acute Sound. The other are called Su­peracute because they are put above the acute, as e.f.g. The geminate Keyes are commonly five in n [...]mber. aa bb. cc. dd. ee. So called because they are written with double Letters. Otherwise called excelling; because in their Sound they transcend all others. But because the number of Keys is not sufficient; there­fore latter Musicians under the great Latin Letters have put seven German Letters: and the double Letters they do fully recite, and more-over they add unto them triplicated Letters. Thus

  • 1. A B C D E F G.
  • 2. A B C D E F G.
  • 3. a b c d e f g.
  • 4. aa bb cc dd ee ff gg.
  • 5. aaa bbb ccc ddd eee fff ggg.

3. Keyes are signed, or understood, or not signed. The signed Keyes are three which are distant one from another by a Fifth, and they are g. c. f. thus [...]

[Page 34]These in the conjoyned System are thus put, and are distant from one another by a Diapente. [...]

In a simple System they are variously placed by reason of the Profundity and Altitude of a Song; As, [...]

But Keyes not signed are known by the signed.

4. Out of these seven Keyes there is a double b. viz. flat and sharp. These two Letters in the signing are distant by the lesser half Note. So that the regular or dural Scale beginneth in C. and the irregular or flat Scale in F. b dural is thus marked ♯ and is cal­led b. quadrate.

5. Besides b. molle, as they call it, there is need of Cancells ♯. and cis, dis, fis, gis: which are cal­led fict Letters by instrumental Musicians. But Da­vid Mostar [...] so accommodateth the Musical Keyes to [...]even n [...]w Vo [...]ces. Four Keyes in the whole are [Page 35] here to be held. The first is C. in which he will al­wayes have bo sung. The second is G. five Tones be­low and four above G, he alwayes singeth bo. The third is F. and four above, and five Tones be­low F. bo. is alwayes sung. Also five Notes above B. molle, and four under B. molle, bo. is alwayes to be sung. 6. Musical Voices are one way rehearsed by the Ancients, and another way by later Musicians. The ancient Musicians did constitute these six ut, re, mi, fa, sol, la. To these six Voices some do add the seventh Si, lest there should be need of some Muta­tion. Concerning this thing Erycius Puteanus in his Musathena doth so for the most part play the Philo­sopher. Guido Aretine (lived under Henry the third Emperour) for his Skill in Musick among the prime of his Age, and delighted with the perfection of the Senary Number, introduced these six Sylla­bic Notes, ut, re, mi, fa, sol, la. which he borrow­ed and translated out of the Hymne.

Ut queant laxis Resonare fibris,
MIra gestorum FAmuli tuorum,
SOLve pollutum LAbij reatum.
Sancte Johannes.

These six Notes so invented, do shew their use every where among Musicians, but very slow and difficult. For what impediment is there of Muta­tions, confusion of Keyes, substitution of Voices? You may see most (whether with Indignation or no) to have spent a good part of their Age upon this Art, [Page 36] and yet to have profited very little, though perfect many years before in the Lection thereof. But the D [...]fficulty doth hinder, and make it a remora to most. Which some do thus take away by joyning si. to the [...]e six received Not [...]s. For which Note you may put Bi. out of the [...]aid Hymne. ‘Solve polluti la BI. i. reatum.’

This therefore shall be the order of Notes, ut, re, mi, fa, sol, la▪ bi, for th [...]s Heptade these following Rea [...]ons are brought. 1. Whereas Notes are the Index's of Vo [...]ces, and as certain Signs, it is of ne­cessity that there should be as many Notes as Voices. But there are seven distinct voices stablished in that half verse septem discrimina vocum. Therefore there are seven Notes. For by voices are understood those sev [...]n Sounds, which are distinguished by certain In­tervalls. Those Intervalls or Diastems are called Tones. Therefore a Sound, and Tone or Intervall do differ. A Sound is the Voice it self, which be­ing formed by the Mouth, is brought by the Air to the Ears. A Tone is a Space circumscribed by two Sounds: or, the distance of a grave and acute Sound: So that Tones are tho [...]e Intervals, which are placed between the first and secon [...] [...]ound, the second and third, the third and fourth, the fourth and fifth, the fifth and sixth, the sixth and seventh. But this Hep [...]ade of Voices, Ptolomy in his eleventh Book concern [...]ng Musick doth confirm; saying, that by nature Voices can be made neither more nor fewer then seven. 2. The Aegyptians and Grecians have ap­proved [Page 37] the seven Voyces by the number of seven Vowells. For the Egyptians as Demetrius Phalereus doth testifie, did commend their Gods by the modu­lated enunciation of seven vowels. And Plutarch doth accommodate the Greeks seven Vowels to so many Voices of Musick. 3. The Lyre, Cithren, and certain other musical Instruments which are strung with strings, were anciently of seven strings, without doubt, by reason of the seven Voices. The Chords of the Lyre were of old in this order, and by these Names, Hypate, Parhypate, Hyperme­se, Mese, Paramese, Paranete, Ne [...]e. The first is called Hypate, not only for the acutenesse of the Voice, but for a certain excellency and virtue. For Hypatos as it were Hypertatos, doth signifie a de­gree of Eminency and Dignity. Nete, as Neate, that is, the last or ultimate. Neither have the Chords been only by these Names, but also the Sounds themselves, nigh this manner. Hypate hath to him­self Bi. and soundeth acutely: Parhypate, la, and doth lullaby: Hypermese, sol, and doth sound sweetly: Mese, fa, and doth sound temperately: Paramese, mi, and doth delight pleasantly: Para­nete, re, and doth grate tremulously: Nete, ut, and doth, as it were low hoarfly. Furthermore the Ancients did attribute the seven Planets to so many Chords of the Lyre, in this Order. To Saturn, Hypate: to Jupiter, Parhypate: to Mars, Hypermese: to Sol, Mese: to Venus, Paramese: to Mercury, Paranete: and to Luna, Nete. In which Compa­ration the acutenesse and gravity of the Chords and Planets do respond exactly. Although others invert [Page 38] the order, and attribute to Saturn Nete, and to Lu­na Hypate. Which Comparation although it may consist: Yet notwithstanding the first is more allow­ed: because Saturn doth proceed in a mundane mo­tion most quickly, Luna most slowly. Look Cicero in his Dream. From the Chords to the Notes we transfer this Comparation, and ascribe to Luna, vt; to Mercury, re; to Venus, mi; to sol, fa; to Jupiter, la; to Saturn, bi. For surely as the Planet's do run round the Week, or the Septenary Circle of dayes in their Term or gliding Course, and each of them by a certain diurnal vicissitude of Government do's obtain the primacy: So these seven Notes do complete the universal harmonical Lection, divided by Musicians into seven Types. These Types are certain and appointed Progressions of Notes, distinguished by iudicial Letters. 4. These seven Voices do render all Musick very facile, aswell in the Theory as in the Practise, thus. All Musick is accomplished by Voices. The Voices being known, Notes are adhibited: To the Notes Characters of Letters; as appeareth by this Diagram.

In a Flat Song.
BetweenAandBalsomiandfaHemiton [...]
BCfasolTone
CDsollaTone
DElabiTone
EFbivtHemitone
FGvtreTone

[Page 39]

In a sharp Song.
BetweenAandBalsolaandbiTone
BCbivtHemitone
CDvtreTone
DEremiTone
EFmifaHemitone
FGfasolTone

Therefore in a Flat Song, A hath mi conjoyned with it, B fa, C sol, D la, E bi, F vt, G re. In a sharp Song, A hath la ascribed to it, B bi, C vt, D re, E mi, F fa, G sol. Which difference the variated Disposition of the Hemitones hath begotten. More­over of these Letters only four are expressed, B, C, F, G. Nor yet those together or conjoynedly, but one or two in the beginning of Lines. The other Letters not noted, you may know by these four. If you ascend from the Index Letter, number the first se­ven according to the Order of the Alphabet, but if you go further, then iterate the same: but if you descend, proceed by a retrograde Order, from the Line to the Intervall, and from the Intervall to the Line. Then you may rightly find out the Letters; by the Letters, the Notes; by the Notes, the Voices; which is the Summe of Musick. Therefore see that you be most exactly skilled in the ascending and des­cending Order of the Notes: and that the Tones and Semitones being observed, you may rise and fall with your Voice. After that, a Song being proposed, you [Page 40] may pass from the Sign and Letter noted, to the Note answering it: from hence, omitting the [...]et­ters, to the other Notes. And this tr [...]el [...] is ea­sie in a flat Song, when B. is marked in the begin­ing of the Lines, there it sheweth that [...]a is [...]o be sung. But in a sharp Song the difference is of these three Letters, C. F. G. of which by that you may know Sol, by that fa, lastly b [...] this Sol Ther [...]fore every where con [...]ult the Signed Letter, find out the Note, and call it by its proper Vo [...]ce, and so pro­ceed from thence by ascending and d [...]scen [...]ing: but if in Singing a Note do occur, which hath a peculiar Letter prefixed, the Tone is to be changed, and the Note of the Letter sung. Therefore if you have rightly accommodated the seven Notes, you may mixe any Concent, or read any Melody that you would, whether it be the simple Aeolian, or the various Asian, or the querulous Lydian, or the re­ligious Phrygian, or Warlike Dorian. But you will say that Songs are not concluded in those Seven Voi­ces, but rise higher. The Answer is ready; As in numbers when we rise from the Monade to the De­nary, the first is the chief of numbers, and by ite­rating and compounding them we proceed in infini­tum. So in these Voices after every seventh Sound, it returneth to the first, but more subtile; and after every seventh Note the first: and so also afterward the second of Notes doth agree with the ninth; the third, with the tenth; the fourth, with the eleventh; the fifth, with the twelfth; the sixth, with the thirteenth; the seventh▪ with the fourteenth, &c. Of Sounds there is the same Judgement. From a [Page 41] Musical Instrument, which by way of Eminency is so called, you may take the Experience of your Ears. But in these Notes observe a double order of Intension and Rem [...]ssion. Intension (by the Greeks E­pitasis) is the commotion of the Voice, from the graver place to an acute: Remission (by the Greeks Anesis) from an acuter to a grave. But it is worth the pains, that here some Director or Ruler of the Voice (as Tertullian speaks) go before and lead. Hitherto Puteanus, with whom worketh David Mo­start in his Introduction of Musick, as indeed he proveth the Septenary of Voices. But he doth sub­stitute other Voices in this manner, bo, ce, di, ga, lo, ma, ni. But so that in C of a sharp Song bo is sung. Also in F. of a flat, bo. e. gr. [...] [...]

But let Mostart himself be heard. Who saith thus, It is worth our labour seriously to invent such Musical Voices as exhibite unto us a perfect Octave, [Page 42] so that it be the Consequence of eight Tones or Notes: by which Connexion and Series the perfection of any Melody may be performed, without any Mutation: which indeed is the torture of tender wits. And the Series is this, bo, ce, di, ga, lo, ma, ni. bo Which Abridgement if it should be admitted, those old vulgar Keyes should be abolished, the Letters of those seven Syllables being only retained in every Song, viz. b. c. d. g. l. m. n.

For Example sake. [...]

Therefore Mostart rejecteth the six Voices of the Ancients; becau [...]e they complete not an Octave, and for that Cause require Mutation, which is the tor­ture of the Ingenious: and also the seven Voices of latter Musicians, because they do not respond to the seven Letters or Keyes. But because those Voices of the Ancients be much used in Schools, therefore let us see their use. For 1. Some of those Voices are su­periour, by which a Song descendeth, viz. la, sol, fa, and others are inferiour, by which it as­cendeth, as ut, re, mi. 2. All those Voices are equally distant one from another by a Tone, besides mi and fa which are distant by a Semitone. 3. Of these [Page 43] Voices, vt and fa sound flatly; mi and la sharply; the rest, meanly. But concerning this thing others speaks thus, vt and sol denote Sweetnesse, re and la gravity, mi Lamentation, fa threatnings. Lastly, others consider these Voices thus. Vt and fa are flat Voices by b moll, because they emit a flat and effe­minate Sound: re and la natural, because they af­ford a natural and middle Sound: mi and la b durales, because they make a sharp and manlike Sound. Ac­cording to these Verses;

Vt cum fa mollis vox est; quia Cantica mollit:
Mi cum la dura est, Nam duras efficit odas.
Sol naturalis (quoniam neutras facit) & re.

4. Certain Voices do answer all Keyes. Thus

Alamire
Bfami 
Csolfavt
Dlasolre
Elami 
Ffavt 
Gsolrevt

5. These Voices are circumscribed in certain pa­rallel Lines, so that in a Song we may ascend and descend; and that in a progression either continued, or discontinued. Continued Progression is that which observeth the natural Order of Voices, and is cal­led a natural Song; As, [Page 44] [...]

Discontinued Progression is the Mutation of a Voice, which is considered either in the minor or greater System. Mutation in the lesser System, is made for the Paucity of Voices: and it is either Vocal or mental. That is called explicite, this implicite. And both is diverse in a flat Song, and in a sharp. In a flat Song Mutation is made in d. a. g. whose memo­rial Note is dag. In a sha [...]p Song Mutation is made in d. a. e. Whose Voice of remembrance is dea. In the greater System Mutation is made according to the triple Scale. The first is b dural Scale; which is the Progression of Musical Voices, rising from a. into b. sharply, that is, by the Voice mi. The second is b moll; which is the progression of Musical Voices, rising from a. into b moll, that is the Voice fa. The third is the fict Scale, which in every Key admit­teth a strange Voice. And hence it is called fict Mu­sick: because modulated by feigned Voices. i. e. by such as are sung in any Key, in which essentially they are not contained. As vt in e. re. in f. and so on.

[Page 45]This is the Type of the Triple Scale.

5. Tetrachordeeb      la
dd      lasol
cc      solfa
bb      fami
4. Tetrachord of excellents.aab    lamire
g     solrevt
f     favt 
eb   lami  
3. Tetrachord of Superiors.d   lasolre  
c   solfavt  
bb  fami   
a  lamire   
2. Tetrachord of Finals.G  solrevt   
F  favt    
Eblami     
D solre     
1. Tetrachord of grave Sounds.C favt     
Bbmi      
Abre      
Γ vt      

[Page]And this is the old Diaton Scale. Thus we have con­tracted the new Syntonian Scale of Lippius.

[figure]

[Page 47]In this Table musical Sounds are so contained, that first there is the Simple Vnison. 2. The Tonus mi­nor. 3. The Tonus major. 4. The greater Semi­tone. 5. The Semiditone. 6. The Ditone. 7. The Fourth. 8. The Fifth. 9. The lesser Sixth. 10. The greater Sixth. 11. The lesser Seventh. 12. The greater Seventh. 13. The Octave. And this is the Cyclus or Compass of the Diapason. Con­cerning the Proportions of all these Sounds, look into the former Chap. thus v. gr. To the Octave ascribe 1.2. to the Septima 8.15. and so of others: So that the lesser number be applied to the upper Note in the Scale. The significates of the Letters. B. L. b.l.bb. are a little before called bo.ce.di.ga.lo.ma.ni.

CHAP. VI. Of the Musical DYAS.

PRECEPTS.

HItherto of the simple part of an har­monical Song: the compounded part thereof followeth; whose tracta­tion is called practical or Melopoetical Musick, if the form of the Song be added.

The compounded part of an harmoni­cal [Page 48] Song, is that which ariseth from mu­sical sounds or Monads conjoyned accor­ding to three Dimensions.

And it is either primary or secondary.

The primary is called harmony and consonancy, which doth arise from grave and acute sounds united by such a pro­portion, that it may delight the hearing.

The secondary is dissonancy or Anar­mosty, which ariseth from such a propor­tion of grave and acute Sounds, that it offendeth the hearing.

And this double part is either a musi­cal Dyas, or Tryas, of which the one is perfect, and the other imperfect.

A musical Dyas, is that which ariseth from two sounds: consonant and harmo­nical from Consonants, and dissonant from Dissonants.

And it is more simple, or more com­pounded. That is called radical, this radicated.

The simple Consonant Dyads, are seven, viz. An Octave, Fifth, Fourth, Ditone, Semiditone, greater Sixth, and lesser Sixth: the dissonant Dyads are the other simple Intervalls, as the Tone major and minor, the Semitone greater and lesser, the Seventh [Page 49] greater and lesser; and lastly, all sim [...]le Intervalls not Just, as the Semioctave, Semififth, &c.

The Dyas more compounded is that which ariseth from the simple Dyas: and that again is either consonant or disso­nant: and both compounded either once, twice, thrice, or so forward. In Dyads once compounded the double Octave, also the Octave with a Fifth, the Octave with a Fourth, and Octave with a Ditone do consonate: but the Octave with both tones, with a Semitone, and with an Intervall not just doth dissonate. In Dyads twice compounded the triple Octave, and double Octave, with a Fifth do consonate: but the double Octave with both tones, with the Semitone, and so forwards; doth dissonate.

RULES.

1. There are two Arbiters of congruous and incongruous Proportions.

The first is superior, which doth judge of Propor­tions [Page 50] à priori, to wit, Logos: the other is inferior, which doth exactly judge of Sounds à posteriori, to wit, the Hearing. And there is a necessity that both these Judges should concur, as Ptolomy doth rightly teach: but falsly Pythagoras, who doth think that no­thing here is to be attributed to the hearing; and falsly Aristoxenus, that supposeth nothing here is to be at­tributed to Ration. But the nature of Proportions is demonstrated by the Monochord: for that in it all Musical Diastems are contained.

2. The Simple Vnison is the Radix of all Consonancy and Dissonancy.

Vulgarly they imagine that the Unison doth both consonate and dissonate. But they erre; for the Unison doth equisonate only, because it hath the pro­portion of Equality, and is the principal of every Interval. e. gr. [...]

Rightly therefore the simple Vnison is made the Radix of Consonancy and Dissonancy.

3. The Simple Consonant Dyads are in number Seven, and may be called Simple Concordancies.

Vulgarly they thus rehear [...]e the Simple Concordan­cies. There are twelve Concordancies, the 1.3.5.6.8.10.12.13.15.17.19.20. And these are divided two waves. First, there are Simple, re­plicated or triplicated. The Simple Concordances are the 1.3.5.6. which are also called primary. The Replicated are such as are equisonant to the former, conceived by a double Dimension, as the 8.10.12.13. Otherwise called Secondary. For in Sound the Octave doth associate with the Vnison, the tenth with the third, the twelfth with the fifth, and the thir­teenth with the sixth. The triplicated Consonants are the 15.17.19.20. otherwi [...]e called tertiaries. Of these the 15. is coequated in Sound with the Octave and the first: the seventeenth with the tenth and third, and the nineteenth with the twelfth and fifth, and the twentieth doth equisonate with the thirteenth and sixth, According to this Type.

1.3.5.6.
8.10.12.13.
15.17.19.20.

Lastly, There are Concordances perfect, or im­perfect. The Perfect are those which can stand by themselves, that is, begin and terminate a Song: as [Page 52] the 1.5.8. The imperfect are those which may con­cur in Counterpoint, as the 3.6.10. The Discordan­ces are nine, viz. the 2.4.7.9.11.14.16.18.21. Others also do number the perfect Concordances thus, the 1.3.5.8. because they respond to the Pythogori­cal Quaternary. But it behoveth them to play the Phi­losophers of Concordances more acurately. There are seven Concordances or simple Consonances. Of which the Octave is the first, which is of a dupla propor­tion between 2. and 1. In his Terms the most sim­ple Conveniency is diverse, as is between the whole and the half. The Fifth doth obtain the second place; then followeth the fourth; then the Ditone or third in a sharp Song; then the Semiditonus, which is the third in a flat Song; in the last place save one is the Sexta major in a sharp Song; and in the last place, the Sexta minor in a flat Song. And this is the Or­der of Perfection. For although every Simple Con­sonancy is perfect in his degree; yet notwithstanding in respect of another, it is either more perfect or imperfect; yet so as the first and most perfect is the Octave, that compounded Unison; the most imper­f [...]ct and last, is the lesser Sixth; the intermediate are measurably as the most perfect or most imperfect are nearer. Here Musicians do wonder, why the Septinary begetteth no Consonancy, when as it num­bereth all simple Consonances. And this is the Scheme of those seven simple Consonances. [...]

[Page 53]Of these the first three are perfect, the four lat­ter are imperfect. And indeed principally the Octave, in respect of his excellent perfection doth equisonate and unisonate after the Vnison an [...] [...]imple Equison. After it the Fifth for its perfection doth consonate by his most grateful, firm, and masculine Sound. After it the Ditone or greater Third by his sweet Im­perfection doth concent but more cheerfully, strong­ly, and lively. Then the Semiditone or lesser Third also by his sweet Imperfection doth concent more softly, remisly, and heavily. Then the greater Sixth by his Imperfection doth circumsonate as it were more high and pleasantly. Last of all the les­ser Sixth doth also so circumsonate but more slowly, flatly, and weakly. These four latter Consonances were not used by the Ancients in their Diatone Scale: but now they are used most chiefly, naturally, and artificially in the Syntonian Scale. And this is the Order of Perfection in the seven simple Consonances. The Order of the Crassitude of Sound, or of In­tension and Remission is this, which is firmly con­trary to the first. After the simple Unison is the Se­miditone, then the Ditone, then the Fourth, Fifth, Sixth minor, Sixth major, and Octave. From these it is an easie thing to Judge of Simple Dissonances, to wit, because they are all Tones placed without the Septinary of Consonances; as the greater and lesser Tone; the greater and lesser Semitone; the greater and lesser Seventh, and lastly Intervalls not just de­ficient. For in these are disagreeing Proportions, whose extreme Sounds do but ill agree, and there­fore if they be put together, they offend the Ears.

4. Compounded Dyads do imitate the nature of Simple.

This is true both of compounded Concordances and Discordances, according to that elegant Axiom of Musicians. Of Octaves there is the same and like Judgement. And that for the essential Simili­tude of dupla, quadrupla, octupla, and sedecupla Proportion, as 16.8.4.2.1. Also of compoun­ded Dyads the Order of perfection and Crassitude, is like unto the Order of their simple Dyads. Other­wise although the Composition of perfect Concordan­ces might proceed in infinitum: yet notwithstanding because they are not the same Terms of Sound and Hearing (which thing therefore obtaineth in the rest of the Senses) it is necessary that we be mindful of Mediocrity, lest we create trouble to the Eare, by any Sound too great or too acute.

5. It behoveth us alwayes to have in our Eye the Radixes of Simple Dy­ads.

As it is very compendious, to observe simple only and radical Dyads both consonant and dissonant, and then by those to judge of compounded Dyads: so also it is very compendious to consider the Roots of those simple Dyads, according to this Type.

[Page 55]

Bo.ni.ma.lo.ga.di.ce.
90.96.108.120.135.144.160.
1.2.4.8.  3.6. 5. 

See before in the Syntonic Table. Here, between the Consonances of the Octave and fourth, the Radix is the Fifth: of both Sixes, both Thirds. There­fore the Octave and fourth may be reduced to the Fifth; and the sixth to the third. The Root of simple Dissonant Dyads is the second, to which both Sevenths may be reduced.

CHAP. VII. Of the Musical TRIAS.

PRECEPTS.

THE Musical Trias is that which doth arise from three sounds and as many Dyads: otherwise called the unitri­sonous Radix.

And it is either consonant or dissonant.

The consonant Trias is that in which a third and a fifth doth concur, yet so as [Page 56] that it ariseth from two thirds.

The dissonant Tryas is that which ari­seth from seconds.

RULES.

1. The Harmonical Tryas is the Root of all the Harmony that can be in­vented,

And may be called the unitrisonous Radix: be­cause it doth consist of three Monads or Sounds, and as many Dyads: all of them in that whole Tryas, and every one most sweetly concenting one with a­nother, because they are joyned together in a certain Order by just Proportions. Those Sounds or Mo­nads being three in number, and as many Dyads, ma­king this Trias, are these. First, the two Ex­tremes are distant one from another by a Diapente, which is of a Sesquialtera Proportion. Then there is one middle, which by his softer sweetnesse doth joyn those two Extremes, concenting together by a perfect and masculine Sound, and is distant from one of them by a Ditone, and from the other by a Semi­ditone. There is the Proportion of a Sesquiquarta, here of a Sesquiquinta. e. gr. [Page 57] [...]

Here 4. and 5. then 4. and 6. then lastly 5. and 6. do conspire. This unitrisonous Radix is the Rule and Measure of all Consonances, and is alwayes in one manner. Yet this only is the difference, that in a flat Song it is more imperfect and soft, but in a sharp Song, more natural, perfect, nobler, and sweet. The first hath the Ditone above the Semidi­tone, the latter hath the Ditone beneath the Semidi­tone. Moreover this Radix is either increased or diffused. The increased, is that which hath the Octave for his Companion, to excite the more va­rious and fuller Harmony. The diffused is that, who [...]e radical parts or voices are not so near unto one ano­ther, because dispersed into various Octaves. For the nearer the Voices are one to another, the more ex­cellent is the Symphony. The best Disposition of all look above Chap. 5. Rule 6. where I do write of signed Keyes.

2. The Musical Trias doth arise both from Arithmetical and Geometrical Proportion.

Proportion is threefold: First arithmetical, which [Page 58] is, when the numbers are distant one from another by an equal Difference, and that either continued; as 1.2.3.4. or dis-joyned, as 3.6.8.11. The [...]e the Difference is an unity, here a ternary. Secondly, Geometrical; which is, when there is the same Ra­tion of more Terms compared with one another: and it is either continued, as 4.8.16. or dis-joyn­ed, as 2.4.8.16. Thirdly, musical or harmoni­cal Proportion, ariseth from arithmetical and geo­metrical: and it is no other, then a Symmetry of Concents, which is discerned in the most perfect mu­sical Triade; which Lippius therefore calleth the chiefest, sweetest, and plainest Compendium of Me­lopoetical Musick. But let us pursue these things further. Musical or Harmonical Proportion is the Symetry or Equality of Concents which doth arise from Proportion arithmetical and geometrical; so that three Terms being put, even as the greatest is to the least, so is the Differ [...]nce of the middle, and the greatest to the Difference of the middle and least. As 3.4.6. Here, as Six are the Duplum to three: so two (which is the Difference between 4. and 6.) are the Duplum to the Unity, which is the Difference between 3. and 4. Such is the pro­portion in the unitrisonus Radix. 1.3.5. Also be­tween 6.8.12. For three Terms musically propor­tional are found from three arithmetically propor­tional, if the first arithmetically proportional be multiplied into the second and third, and the second into the third. So from these three arithmetically proportional 2.4.6. are found these three musically proportional. 8.12.24. But that numbers are mu­sically [Page 59] proportional, is hence manifest, if in them those three Proportions are found, on which all Musick doth depend: to wit, Dupla, or Diapa­son, which doth constitute an Octave: Sesquialtera, or Diapente, which doth constitute a Fifth: and Sesquitertia, or Diatessaron, which doth constitute a Fourth. So in these Numbers 6.4.3. between 6. and 3. is dupla: between 6. and 4. sesquialtera: be­tween 4. and 3. sesquitertia. I say, three to four, are in the sesquitertian Ration, as the Diatessaron System: four to six are in the Sesquialtera Ration, as the Diapente: three to six are in the dupla Ration, as the Diapason System. And of these the rest a [...]e com­pounded, viz. the Disdiapason, &c. This also is of force in Organical Musick. For if two Strings e­qually thick and stretched differ in Longitude by a Sesquialtera Ration, benig struck, they will equally Sound the Harmony of a Diapente: if they differ in Longitude by a Sesquitertiae Ration, a Diatessaron: if by a dupla, a Diapason, which vulgarly they call an Octave, as a Diapente a fifth, and a Diatessaron a Fourth. The same is in Hollownesse, or in Whistles. From this Operation alwayes except the unitrisonous Radix, because it is the foundation of o­ther musical proportions.

CHAP. VIII. Of the Forme of an Harmonical Song.

PRECEPTS.

THus much concerning the matter of an harmonical Song: now of the Forme thereof, which is the artificial disposition of Musical Monads, Dyads, and Tryads, according to the Text, and this is called Melodie.

Melodie is simple, or compounded. That is called Monodie, this Symphony.

Simple Melodie is that which is content with one onely Series of musical voices: as is discerned in Choral Musick, called Unicinium.

Compounded Melodie is that which doth conjoyne more simple Melodies be­tween themselves: and is usually called Counterpoint; as is discerned in figural [Page 61] Musick. To which appertaine Songs of two, three, and four voices, &c.

Counterpoint is either simple or colour­ed.

Simple Counterpoint is that which hath least of Artifice: and may be called pure Composition, whose Rules or Or­naments are the Sounds of Longitude, Latitude, or Crassitude.

Counterpoint coloured is that which hath more of Art: and may be called a­dorned Composition, whose Rules or Or­naments do respect the Longitude, Lati­tude, and Crassitude of a Sound.

RULES.

1. A Musical Text doth give as it were a Soul to an Harmonical Song, as to the Image thereof.

Wherefore seeing the Image is such as is the Ar­chetype, the practical Musician or Composer as they call him, is to take care that he understand aright the nature of his Text, in respect of things and words. For an Harmonical Song ought to be accommodated both to things and words. The things may be all di­vine [Page 62] and humane matters, but chiefly practical, which concern the active felicity of man; the mean to ac­quire which, is virtue moderating the Affections, which do depend upon things or objects either great, or low, or mean: and those again either pleasant or delightful, or unpleasant and sorrowful, or mode­rate. Words may be either of prose or verse, yet so as that they be like unto things practical, even, and congruous. So that he ought to know the nature of all Letters, (of which in my Rhetoricks.) Moreover, an harmonical Song will rightly express the Text, if the Musician give heed to the trine Di­mension of Sound, viz. Longitude, Latitude, and Crassitude. For things grave are rightly expressed by long and profound Sounds: light things by short and acute Sounds: Masculine things by sharp Sounds: soft things by flat [...]ounds: pleasant things by lively and quick Sounds: Sad things by languid and slow Sounds: and mean things by mean Sounds; as we see it falleth out in Poesy.

2. More Simple Melody, which is cal­led Monadie, is first to be compo­sed.

A young Composer should first compose the most simple Melodies, which arise not from Musical Dy­ads and Tryads, but from Monads, or a simple Disposition of musical Voices. e. gr. Let this be the Subject, Laudate Dominum, which may be sung with this Melodie. [Page 63] [...]

Or after the new manner, which Lippius hath, which dependeth upon the Syntonick Table, in the 5 Chapter before mentioned.

288.320.288.270.270.288.
Lauda [...]edominum.
2.1 1/2½½½2.

Here the Numbers placed above the Text do shew the Notes of the Syntonic Table: and the numbers underneath do expresse the measure of the Touch. Therefore such will be the Series according to this new Mode. [...]

3. Compounded Melodie doth respect ei­ther two, three, or four Simple Me­lodies, cardinal and radical.

Of these the Composition and Connexion of four [Page 64] Melodies is most perfect. For as a body mixed of four Elements, is a temperament of four humours: So every harmonical Polyphony doth arise from four sim­ple Melodies. Of these two are extreme, the Bass which is the gravest; and the Discantus which is the acutest: and two are intermediate; the one is nearer to the Bass, which is the Tenor; and the other is nearer to the Discantus, which is the Altus, accor­ding to the Disposition of the four Elements, Earth, Water, Air, and Fire. Of which, two are extreme, and as many Median, as is noted in our Physicks. And this is the Musical Tetras, in which the Melody of the Bass is fundamental▪ whence its name is from Basis a foundation: or Bassus profound: the Melo­die of the Tenor and Discantus (whose vicissitude is very elegant) is principal or regal. Lastly the Me­lodie of the Altus is explemental. This Tetras, or Song of four voices, doth comprehend both musi­cal Monads, Dyads, and Tryads, aswell Simple as Compounded, and is the Radix of all perfect Mu­sical Composition. This therefore is the Order in Musicks. The Musical Monade is the Radix of one Melodie, or Song of one Voice: the Dya [...] of two: the Trias of three: and the Tetras of four: More­over this Composition is called Counterpoint, be­cause point is put against point.

4. Pure Composition, or Simple Coun­terpoint; hath this Artifice.

1. Pure Composition doth make the four Melo­dies, [Page 65] more simple, plain, and easie: yet so that it keepeth the trine Dimension of Sound. 2. This is the Rule of the Longitude of a Sound. Every one of the four radical Melodies doth so proceed by his Monads, that Notes of more simple value may be added, the Touch being every where equal. 3. The Rules of Latitude is this. 1. All the members of all the Melodies do make a Consonancy; which doth depend upon that unitrosonous harmonical Radix, of which mention is made in the foregoing Chapter. And because the parts and productions of that Triade are various, the Consonancys may be mingled among themselves, yet so as that the peculiar Ration of the perfecter of them be kept: for in every Genus that which is most perfect is the measure of the rest. 2. All melodies should be compared with them­selves most diligently. viz. The Bass with the Tenor, the Tenor with the Altus, the Altus with the Dis­cantus, the Bass with the Altus, the Tenor with the Discantus, lastly, the Bass with the Discantus. Or more briefly, the Tenor with the Bass, the A [...]tus with the Tenor and Bass, the Discantus with the Al­tus, Tenor, and Bass. For so every one compared with another will make six times an excellent Song of two Parts: So that every part of the Me­lody will be adorned with some harmonical Dyade. And also in those Dyades, varietie is to be used, yet so that the perfecter do rule. 3. Consonant Dyades by ascending and descending together may all mutu­ally antecede and follow one another, if they be of divers species: but if of the same, as the three per­fect Consonancies with the simple unison, they may [Page 66] not, but the other imperfect Dyads may. But more briefly, two simple Unisons may not be put toge­ther ascending or descending: nor two Octaves, nor two Fifths, nor two Fourths. 4. Those Dyads which are nearer in Crassitude, will better precede and succeed, then those which are more remote. To which purpose is that saying of Musicians, By how much nearer Voices are to one another, by so much they make the better Symphony. 5. Monads should be applied so in all Melodies, that every one should ele­gantly walk in his own Region, and commonly of one Octave, or Diapason. 6. Let the Bass always take the lower part or foundation of the harmonical Triade in the place of the gravest: but the Tenor in the place of the graver, the Altus of the acuter, and the Discantus of acutest Monads: So let them take all three parts of the harmonical Triade, viz. The lowest or first, the middle and last. But in aug­mentation and multiplication the first of the Triade is chiefly to be repeated, the last more rarely, the middle seldomest. 7. [...]et Melodies associate by gradual, not by skipping motion. For if every Melodie do proceed rather by degrees, then flie vi­olently by greater Intervalls and Leaps, it will be more grateful to the Ears; yet the Bass is allowed to move by Leaps. 8. Let the Bass be first composed. Because it is the foundation of the Triads. Here­to belongeth th [...]s Rule. Better is that harmonical Triade who [...]e Basis is lowest, then those whose Ba­sis is in an hi [...]her place. But now let us see an Ex­ample. Let the Text be Laudate Dominum. And this you may thus express in a pure Song. Go to the [Page 67] Syntonian Table, and from thence pick out Conso­nancies after this manner.

 2.1 1/2½½½2.
Discantus.180192180180180180.
 Altus.240240240216216240.
 Tenor.288320288270270288.
 Bassus.360480360540540720.
 Laudatedominum.

These Consonancies you may thus transfer into the great System. [...]Lau╌da╌te — do╌mi╌num.

Or if you had rather you may thus write the seve­ral * Touches in several Cells.

* Touch is that which Musicians call Tactus, or the stroke of the hand by which Time is measured. Or it is the successive Motion of the hand, direct­ing by equal measure the Quantity of all Notes and Pauses in a Song, according to the variety of Signes and Proportions. The parts thereof are Elevation and Depression; or the Fall and Rise of the hand. [Page 68] [...] Be╌ne dic╌a╌ni╌ma╌me╌a — Je╌ho╌vae.

In the latter Example you may observe the Tenor to have the same Voice with the Bass in the first Cell: and in the Sixth and Seventh, two Minums put for one Semibreve.

V. Adorned Composition, or Coloured Counterpoint, is contained in these Rules.

1. Adorned Composition doth constitute a Song [...]armonical more broken, florid, and coloured, there­ [...]ore more difficult and effectual. Therefore this doth as it were garnish these three Dimensions of a Song with various Gems and flowers: so that pure Composition may rightly be compared to Grammer, which teach [...]th to [...]peak purely: and adorned Com­position to Rhetorick, which teacheth to speak Ele­gantl [...]. 2. Artificial Licenses are used in adorned Compos [...]tion. For as there are allowed Poetical [Page 69] Licenses, which do beautifie Art, and not destroy it: so also there are Melopoetical Licenses, by which the pure and simple Dimensions of a Song are beau­tified. 3. These are the Orn [...]ments of Longitude. 1. An harmonical Song is adorned with the varie­tie of a Spondaic, and trochaic Touch: and of un­equal Notes, especially Syncopated. So the Bass doth move more slowly, and the other Melo­dies with coloured celeritie; which is that in Mu­sick, as flourishing is in Writing. 2. An harmo­nical Song according to the Nature of the Text, is distinguished by Rests and Closes. For even as Speech is distinguished by Comma's, Colons, and due Periods; so ought an harmonical Song, accor­ding to the nature of the Text, to be distinguished by greater and lesser Rests; also by Closes native, primarie, secondarie, tertiarie, peregrine, more perfect, or more imperfect. A perfect Close doth consist of three Voices; the antepenult, penult, and last: by which the Close is chiefly known, and which is to arise out of an harmonical Triade. e. g. [...]

The Primarie Close is that whose last is the first; the secondary, the supreme; the tertiarie the middle of the Triade; but of these in the following Chap­ter. 4. The Ornaments of Latitude are these. An harmonical Song should be so expressed by Voice or I [...]strument, or both together; that according to the [Page 70] Condition of the Text, an asperous, sharp, swift, full, gentle, flat, submiss, or small Spirit, &c. should be heard. 5. The Ornaments of Crassitude have these Axioms. 1. Varietie should chiefly rule in an harmonical Song; I say varietie of Dyad's and Triads, more grave, more mean, more acute, simple and compounded, diffused and augmented, more perfect, and more imperfect, natural and fict. Hence is a various Licence: for in the Bass it is lawful to use the last and middle Monade of an Unitrisonous Radix: and Dyads prohibited, may antecede and follow one another; and a Dias and a Trias also anarmonical may be used. All which things are done either covertly or openly. Covert­ly, either by greater Rests, or by Sounds not of­fending by reason of their swiftnesse, or by con­trary made Sounds; or by an excuseing Polyphonie, or by Syncope. Openly for the texts sake, and sin­gular Artifice. v. gr. If the Text command, and as it were compel to manifest some Discord. Ac­cording to that of the Logicians; Contraries pla­ced nigh themselves are the more clearly illustrated. When therefore in Singing some harsh sound is heard, which presently passeth into a sweet harmony, the hearing is therewith more affected, than if there were a current of perpetual Harmony. 2. When the whole harmonical Song is rendred more beauti­ful by the ornament of Celerity and Syncope; then chiefly the Close should be artificial. 3. Polyphony or multiplication of cardinal melodies do very much [...]dorn Singing. e. gr. As if there be two, three, or more Basses, Tenor's, Altus's, Discant's, [Page 71] and those placed in certain Quires, according to the Text and Circumstances. 4. The various man­ner and motion of ascending and descending, is granted to principle Melodies and sometimes out of their Proper Regions; as for the Bass to invade the Confines of the Tenor, or the Tenor of the Altus. 5. The ornament of musical ornaments is that which they call a Fuge. This Ornament at this day is most excellent, difficult, ingenuous, efficacious, and full of Liberty. And this Fuge is nothing else then a more artificial repetition and imitation of cer­tain Parts: to which a more Simple Repetition and Imitation is opposed, which also hath his Commen­dations amongst Musicians. And this is the Exam­ple of a Fuge in the Unison after two Times. [...] [...] Unum est necessarium. [...] [...]

[Page 72]* I suppose that this Example was mistaken or ra­ther mis-placed by the Printer or some other, for I cannot imagine that the Learned Authour would give the Reader Four parts of Simple Counter-point, for an Example of a Fuge in the Unison after two Minims. Of which let this be an Example. [...]

And thus the Composer may continue his Fuge as long as he pleaseth.

6. The Exercise of a Fuge is to begin in an Harmo­nical Tryade onely. For so other forms and species of Fuges may more easily be apprehended. And for Examples you may look amongst those Principal and Heroick practical Musicians, as Orlandus and Marentius. Of which two, the one in his Mot­tets, and the other in his Madrigals, hath brought Me­lopoesie to his highest pitch. There are latter Imita­tors of these principal Melopoets, who notwith­standing ought to have their due praise.

CHAP. IX. Of the Affections of an Harmo­nicall Song.

PRECEPTS.

IN the last place the Affections of a musicall Song do follow, wherewith it is affected and perfected.

And they are either material or formal.

The material Affection of a Song, is that which floweth from the matter thereof. And it is a certain Genus of Modulation.

The formal Affection of a Song, is that which floweth from the Form there­of: and is called a musical Trope or Mood; which is a Rule, according to which we direct the course of a Song. Otherwise called Nomus and Tonus. And it is the same in Musick, as a certain kind of verse is in Poetry.

[Page 74]A musical Mood is either simple or compounded.

The simple is primarie or secondarie. That is called Authentick, and this Pla­gal.

The primarie mood is either legiti­mate or spurious.

The legitimate is either more natural in a sharp Scale, or more soft in a flat Scale. And both is threefold; the Ionick, Lydian, Mixolydian, Dorian, Phrygian, and Aeolian.

The spurious, bastard, [...]or illegitimate Mood is the Hyper-Aeolian, and Hyper-Phrygian.

The secondary or Plagal Mood is also called remisse and submisse: and it is Hypo-Ionic, Hypo-Doric, Hypo-Phrygian, Hypo Lydian, Hypo-Mixolydian, and Hypo-Aeolic.

The compounded or connex Mood, is that which doth arise from simple Moods: when the Authent is joyned with the Pla­gal Mood: whence it is called the Plagio­syntactical-Trope.

RULES.

1. The mixed Genus of Modulation is now for the most part in use.

The Genus of Modulation is certain, according unto which the Song doth proceed in his Melodies in a certain Musical Scale. Therefore as the Scale of Musick is simple, or mixed, and that old or new: (also the old Scale is either Enharmonic, or chromatic, or diatonic: the new, Syntonic) So also the Ge­nus of Modulation is simple, or mix'd, or com­pounded: the simple is old or new: Again the old is enharmonic, chromatic, or dia [...]onic. And is also called Enharmonisme, Chromatisme, and Diato­nisme. The new is Syntonic or Syntonisme. The mixed Genus of Modulation is that which is variously compounded of the Simple. Of the Simple, at this Day, Enharmonisme and Chromatisme (to wit alone:) partly for their Imperfection, partly for their Difficulty are not in use; but the Syntonian-Diatonisme, or Diaton-Syntonisme, yet so, that chromatisme be often mixed, and sometimes also Enharmonisme, if there be need, according to the force and acuracy of the Text.

2. A Musical Mood is the most certain Rule of a Song.

A musical Mood is that, according to which a musical Song is limited, and without it would be too ample and wandring. The Mood therefore doth con­tain Melody with certain Limits, and as it were Bounds of an ha [...]mon [...]cal Trias, in the Compass of an Octave or Diapason; so that wholly it doth con­tinually proceed in a due order, from the beginning, by the middle, to the end, for the artificial expres­sing unto, and imprinting upon the hearers the vir­tue of the Text.

3. The Doctrine of Moods is contained in these Rules.

1. We cannot moderate or modulate any Song, un­lesse we first know the Tone thereof. The Tone is known by the end, according to Rule: in the end it is seen of what Tone it is. The end also of a Song is judged by the musical Mood, which therefore by some is called a Tone, according to this Diversity of Tones, there are also divers Melodies. For as one Tone is in vt, and another in re: So also are the Melodies. Yet here you must remember, that every Tone or [...]ood may not only be known by the end, but also by the beginning, and middle or Division thereof: al [...]o by his skipping. 2. A musical Mood, is an [Page 77] Octave mediated by his neighbouring voice. Other­wise it is defined to be the Species of a Diapason, which is made up of a Diatesseron and Diapente. 3. The Simple Mood is that in which one harmonical Triade only doth rule with his Octave, in respect of the Text and more simple Affection. 4. All the Moods are six, even as there are six voices. vt. re. mi. fa. sol. la. The Ancients had only four Moods, the first, second, third, and fourth: to which now the four final Voices do respond. re. mi. fa. sol. These four Moods the Grecians call Authentic, and the Latines herile or Clamous. For they have, as I may so speak, a greater Authority of ascending then the rest. But the Latines more narrowly considering the ascension and descension of every Tone, have constituted to every Mood a subjugal Mood; and those four they call Plagal; also subjugal, servile, and the like. And these descend more then the first. And hence arise the eight Moods, by which every Song is governed per Arsin & Thesin, by rising or falling. But our Latter Musicians more diligently considering the variety of Tones, have constituted twelve legitimate Tones. viz. six Authent, and as many Plagal. For as there are six Voices. vt. re. mi. fa. sol. la. so also there are six Authent, and as many Plagal, which are vulgarly named by strange Names of Nations: I say, of those Nations who commonly were delighted with them. And to these twelve legimate Tones, two illegitimate were ad­ded. Unto all which, various mixed Moods may be added. 5. An Authent Mood is primary, the Plagal secondary, and this doth not differ from that, [Page 78] but in respect of subjection, when it is called Hypo­tropus, remiss and submiss, because the harmonical Mediation of the Octave, which doth agree with the primary, is changed into the arithmetical, by the in­version of the fourth beneath the fifth with the Tri­ade. 6. Concerning the Excellency and Efficacy of the musical Moods, there are diverse opinions. Casus in politicis lib. 8. chap. 5. saith thus, Musick is va­rious and manifold. One kind is humble and remiss, as the Lydian; another is vehement and more moved, as the Phrygian; another is more moderate and mean which is called the Doric; and a little after, that grave, divine, and oraculous Musick, called the Doric, allureth the mind to the study of Wisdome and true Piety. This, both the heathen of old used in their Synagogues, and Christians now use in their Churches. For in it there is a certain imitation of Celestial Harmony, by which as by a sweet and whol­some Medicine, the Diseases of the mind are cu­red, Vices are dissipated, Cares are lessened: and th [...] Dew of Divine Grace is leisurely, and by little and little distilled. And in the end of the Chapter, he saith, that the Doric Musick hath respect unto Virtues, and divine Inspiration; and that it forceth men into Extasie of mind, and oblivion of the world; so that it driveth away evil Spirits, which he proveth by the Example of Saul. Lippius in his musical Sy­nopsis, saith thus: the most natural and chief of all the Moods in these times, is the Ionic, with his secun­dary the Hypo Ionic. (against which many ancient and modern Musicians do speak.) But let us look up­on the nature of the Moods in Specie. 7. The na­ture [Page 79] of the Authent Moods is this. The Authent Mood hath his final Key in the Diapente below, and is divided harmonically. And that is called harmo­nical Division, where the Octave hath the Fifth be­neath the Fourth, thus; First the Ionic doth occur, which is by Lucian called Glaphyrus. i. e. pleasant: and by Apuleius wanton. And now it is much used. It runneth between C. and c. is divided in G. and en­deth in c. In a flat Song it runneth between F. and f. and is divided in C. and endeth in f. It is most agreeable to Iambic's and Trochaic's. Then the Dorian Mood runneth between D. and d. and is di­vided in a. ending in d. but raised, or in a flat Song, hath his course between g. and gg. and is divided in d. and endeth in gg. By Lucian it is called grave, and by Apuleius warlike. It is most fit to sing to he­roick Verse: for it hath wonderful Gravity with A­lacrity. The Phrygian Mood hath his course between E. and e. and is divided in mi which is in b. ending in e. In a flat Song it runneth between a. and aa. and is divided in e. and endeth in a a. Lu­cian calleth it Entheus, Apuleius religious. For it hath the severe Insultation of an angry man, whence it is called Scolius. It is impetuous, accommodated to warlike Affairs. It is also Iambic and tragic; di­stracting and ravishing the mind, putting it as it were out of it self, as Aristotle saith, 8. pol. c. 5. and Plato 3. de Instit. The Lydian Mood doth take his course between F. and f. is divided in c. and endeth in f. in a flat Song it runneth between b. and bb. and is divided in f. and endeth in bb. It is harsh, threat­ning, and merry. As Plato 3. dial. de rep. who [Page 80] condemneth the Lydian and Ionic Harmony as sottish. This Mood is sharp, and according to Apuleius, threatning: and to Lucian Bacchicus. q. raging. The Mixolydian Mood runneth between g. and gg. and is divided in d. and endeth in gg. In a flat Song it runneth between c. and cc. and is divided in gg. And endeth in cc. It moveth the Affections, and ren­dreth them sorrowful and contracted; because it is mingled with the Dorick gravity. Lastly, the Ae­olian Mood runneth between a. and aa. and is divided in e. and endeth in aa. being raised up, it runneth between d. and dd. and is divided in aa. and endeth in dd. It is mild and very sweet, being sung to Lyrick Verses. 8. The nature of the Plagal Moods is this. This Mood is called Plagal, as if we should say ob­lique or inver [...]ed; which hath its final Key in the low­est part of the fifth, but above the fourth: and is divided arithmetically. That Division is by Mu­sicians called arithmetical, Where the Octave hath the fourth beneath the fifth; which is the more un­pleasant. This Mood borroweth his name from the Authent, Hypo being prefixed thereunto. First the Hy­poionic Mood runneth between Γ. and g. and divideth and endeth in C. being raised up, it runneth between C. and c. it is divided in F. In this Mood, the Mo­lity of the Ionic Mood is rectified. The Hypodorian Mood runneth between A. and a. is divided and en­deth in D. being raised up between D. and d. is divided and endeth in g. It hath a harsh kind of Gravity, and flattereth not. The Hypophrigian Mood runneth between B sharp, and b sharp, is divi­ded and ended in E. being raised up, it runneth be­tween [Page 81] E. and e. is divided and ended in a. This Mood is humble, and inclineth to weeping, as making a sorrowful Complaining and pitiful Lamentation. The Hypolydian Mood runneth between C. and c. is divided and ended in F. being raised up it runneth be­tween F. and f. is divided and ended in b flat. It expresseth a kind of sorrowful Continency, and is called the pious, and as it were puling Mood; and stirreth up tears. The Hypomixolydian Mood run­neth between D. and d. is divided and ended in g. being raised, it runneth between G. and g. is divi­ded and ended in c. In it there is a certain natural jollity. The Hypo Aeolian Mood runneth between E. and e. is divided and ended in a. being raised up, it runneth between a. and aa. and is divided in d. 9. This is the nature of the illegitimate Moods. An illegitimate or bastard Mood, is that, which can­not aptly be divided into the fifth and fourth: but into the Tritone and Semidiapente. And it is eithe [...] the Hyper Aeolian Mood, or the Hyperphrygian. The Hyper Aeolian Mood is the illegitimate of the Authent; which runneth between b. and bb. having below a Semidiapente, and above a Tritone. The Hyperphrygian is the Bastard of the Plagal Mood, which runneth between F. and f. having a Tritone below, and a Semidiapente above. 10. Every sim­ple Mood, out of his own proper harmonical Triade, doth give to every harmonical Song, peculiar Orna­ments. To wit, Fuges and Closes proper, prima­ry, secundary, and tertiary. Unto which, strange Closes from a strange Triad may be added; if they be well taken. The primary Fuge, and also the [Page 82] Close is from the first of his proper [...]riaede: the Se­condary from the highest: and the [...]ertiat from the middle. 11. Every Mood in respect of his Effect and Affection, doth follow his Radix. i. e. his Mo­nads, Dyads, and Trias of which he doth consist. Hence it is (saith Lippius) that one Mo [...]d is very cheerful and lively; as the Ionic very much, the Ly­dian devoutly; the M [...]xolydian moderately; ano­ther flat, soft, sorrowful, and grave, as the Doric meanly; the Aeolian lesse; and the Phrygian ex­ceedingl [...]. 12. A compounded Mood doth proceed from simple Moods, and from it a Song is called mix­ed. A Mood is compounded of Moods neer unto him, as the Ionic and Hyper-Ionic which is often seen: or of Moods wholly diverse, as the Ionic and Doric; which is lesse used. This mixture depen­deth more or lesse upon the affected Text. 13. The Mood in instrumental Musick, by the Media­tion of Chromatisme, is transposed either to the fourth above; or, which is the same, to the fifth beneath. Hence, from a regular or sharp Mood, an irregu­lar Mood is made, which is called mollis. It is transposed also to the second, third, or other In­terval: So that one Mood is changed into the nature of another; as the Lydian, into the Ionic: the Hypolydian into the Hypo-Ionic. 14. Alwayes the two proximate Moods (the Authent with his Plagal) have the same fifth, and the same fourth. Thus, [Page]

1 & 2.Quartam.re sol.
Quintam.re la.
3 & 4.Quartam.mi la.
Quintam.mi mi.
5 & 6.Quartam.vt fa.
Quintam.fa fa.
7 & 8.Quartam.re sol.
Quintam.vt sol.
9 & 10.Quartam.re sol.
Quintam.re la.
11 & 12.Quartam.vt fa.
Quintam.vt sol.

But here let us place Schemes to illustrate this thing.

Authent Moods in a sharp Song.

[Page 84]

Authent Moods in a Flat Song.

[Page 85]

Plagal Moods in a Sharp Song.

[Page 86]

Of the Plagal Mood in a Flat Song.

By these Tables it doth appear that the Plagal Mood differeth not from the Anthent but by remis­sion into the fourth: when in the Authent here is an Elevation into the fi [...]th v. g. if in the Ionic Mood it be vt, sol, in the Hypolonic, it will be vt. fa. hence also the Compass of all Moods may easily be found. [Page 87] v. gr. the Compass of the Ionic Mood in a sharp Song, is sol. vt. in a flat Song fa. vt. the Compass of the Dorian Mood in a sharp Song is re. la. in a flat Song re. sol. and so of the rest.

CHAP. X. Of Special Musick.

PRECEPTS.

THus far of the general part of Mu­sick: the special remaineth, concern­ing the various kinds of Musick, which are taken eith [...]r from the matter: or the Character of the matter: or the Orga­nical Cause: or Artifice of Musick.

First, From the Matter, Musick is ei­ther sacred or civil.

Secondly, From the Character, Musick is either great, or mean, or humble.

Thirdly, From the Organical Cause, Musick is vocal, instrumental, or mix­ed. That is made by the voice of man, the next by divers Instruments, and this [Page 88] by the Uoice and Instrument together.

Fourthly, From Artifice, Musick is either Choral or Figural. That doth in his Notes observe an equal measure, and from the Author is called Gregorian: and this is either old or plaine.

This is such whose unequal Notes do vary their measure, and from the Au­thor is called Ambrosian.

Also mensural, and new Musick.

RULES.

1. The asper Artery [or Windpipe] of a man, Vocal by the Tongue, is the Law of all Musical Instruments.

Lively or Vocal Musick as they call it, seeing it is the Cause of Instrumental Musick, without Contro­versie is the noblest of all. And if it be joyned with instrumental Musick, it is an incredible Means of moving the Affections and Sences. Also Vocal Musick is called the Exemplary or paradigmatical Cause of Instrumental Musick: whatsoever they talk of Pythagoras, that he found out Musick by the stri­king of divers Hammers upon an Anvile.

2. A Song which may be sung both by Voice and Instrument, is various.

To this belongeth a Mottet, Madrigal, Intrade, and bound Fuge: and this of one harmonical Triade only, or of more. Also the unisonous Simply, or multisonous, and that through the eight, fifth, third, &c. Also to these may be referred Songs of one, two, three, four, or five Voices, and like­wise Songs of many Voices, or Polyphoniacs: which for their perfection may swell to forty or more Me­lodies. Of these the Song for one Voice is an har­monical Song potentially: the Song for two Voices, is the first harmonical Song, in Act; but more im­perfect: but the Song for three Voices is perfecter: and the Song of four voices most perfect.

3. Musical Instruments may conveni­ently be reduced to these two kinds.

For some are called Pshelaphetus: and others are called Pneumatic: and these are called Crosta's, which only by striking do make a Concent, and by others are called Entata. These are also called Emp­neusta, and they are moved with the Fingers and Wind. Various kinds of Instruments are compre­hended under these. As the Whistle, Pipe, Cornet, Sackbut, Trumpet, Bagpipe, and the like, which are blown. Also the Clavichord, Psaltery, Pan­dore, [Page 90] Cithren, and the like, which are struck with strings: So also the Lute, Harp, Lyre, Tabor, and other Instruments struck with strings. The Cym­bal, great Bell, and others struck with Brass. Also the musical Triangle struck with Iron or Steel. Or the Wooden Craticle (by the Germans called einstrofiedel' item ein holtzerngelachter) struck with Wood. And lastly the great Wind Instrument or Organ which is both blown and struck together. And here it will be necessary to lay down certain Apho­rismes concerning musical Instruments. 1. The Canon, Mother, and Radix of all Instruments, is the Mo­nochord: which is an Instrument most simple, and intire, made of one or more unisonous Chords; and may be divided into how many, or how great parts you please, according to radical numbers by the biparti­tion, tripartition, quadripartition, &c. thereof. And we may observe fully in this Instrument, all the pro­portions of all musical numbers. And this will be the most simple Example of a Monochord, if you shall put one Chord upon a fit pe [...]ce of Wood; into so many parts as you shall divide the Wood, certain Notes being added, so many distinct Sounds there will be, if you apply your finger to the Chord. 2. The Wooden Craticle is next in plainesse unto the Mono­chord. This is made ready without any trouble, if a Wooden stick being very drie, be proportionably divided into many parts; which according to the Order of Proportions, being bound together by links made of a string, do afford harmonical Sounds, if they be struck with a stick, and put to straw bound together. 3. The Lute is the chiefest of all Instru­ments [Page 91] of Musick. For no Invention of ancient or modern Musicians did ever make a more grateful con­cent. 4. In Clavichords and the like Instruments there is the most evident Reason of the Scale of Musick. Those Instruments do consist of certain Tetrachords, which are double, ordinary, and extraordinary. The or­dinary Tetrachords are four. The first is called Hy­paton i. e. of greater and gravest Chords: from B. to E. and this is the Bass. The Second is Meson, i. e. of Means: from E. to a. and this is the Tenor. It is called Meson, because in old time when there were only three Tetrachords, (the Tetrachord Hy­perboloeon not being added) it was in the midst. The third is Diezeugmenon of distinct Chords, which is disjoyned from a. by a Tone, which is from b. to e. and this is the Altus. The fourth is Hyperboloeon i. e. of excellent or most acute Chords: from e. to aa. and this is the Discantus. The extraordinary Tetrachord is Synemmenon. i. e. of connexed Chords; so called because it is joyned with a. and it extendeth from a. to d. There is also a threefold progression of these Tetrachords, viz. diatonic, enharmonic, and chromatic. The diatonic progression is by a Ditonus and lesser Semitone. The enharmonic by a Ditonus and two Dieses, viz, the greater and lesser Diesis. i.e. the half of the lesser Semitone. And the chroma­tic progression is made by the Semiditone, and grea­ter and lesser Semitones. (vide triple Scale chap. 5.) This Doctrine will be clearer, if the Doctrine of Sounds, or musical Intervalls, or Moods (as they vulgarly call them) be rightly propounded. For there are in all Ten Moods according to a known [Page 92] Song. The Moods are three times three, and one, by which every Song is made. sc. The Unison, Semi­tone, Tone, Semiditone, Ditone, Diatessaron, Di­apente, Semitone with a Diapente, Tone with a Dia­pente, Diapason. And whosoever shall diligently consider these Moods, shall easily know the Ration of musical Intervalls, and so of all Harmony. And the Artificial Division of these Moods is this. A Mood, or rather a Sound, is an Intervall or Distance from another, and that is either equal or unlike. An equal Mood is that which is in the same Degree, and is called the unison or Basis. Also an Unison is the conjunction of two or more Notes in the same place. c. gr. if sol be [...]epeated in the same Key, or la, the Mood is unlike, in which there is both Arsis and The­sis. i. e. Elevation and Demission of the Sound. And this is either continued or interrupted. A continued Sound is a Tone or Semitone. A Tone is the skipping of a Voice from a Voice by a perfect Second sounding strongly. Hence it is called a Second. In the pro­gression of six musical Voices, every next is distant from his next by a Tone. e. gr. vt re. except mi fa joyned together; which Connexion is called a Semi­tone, which is the skipping of the Voice into a Voice by an imperfect Second, sounding flatly: as is the Leaping from mi into fa, and again from fa into mi. scil. the next. By the Greeks it is called Hemitone: and by Musicians the lesser Semitone. The inter­rupted Mood is discrete by certain Intervalls. The first is Diaphonus, as the Ditonus and Semiditonus. The Ditonus is a sharp and perfect third: and doth consist of two Tones, as is between vt mi. fa la. o­therwise [Page 93] called the Third. The Semiditonus is the Intervall of the Voice from a Voice by a flat and imperfect Third As between re fa. mi sol. The Second is Paraphonus. As a Diatessaron and a Dia­pente. A Diatessaron is the leaping from a Voice into a Voice by a fourth. As is between vt fa. re sol. and mi la. otherwise called a fourth. The Diapente is the skipping of a Voice from a Voice by a Fifth: called vulgarly Quadrimode and Quinta. As be­tween vt sol. re la. mi mi. fa fa. And again a Fifth is either compounded with a Tone or a Semitone. Hence a Tone with a Diapente is a perfect Sixth, as is between vt from c to la in a. The Semitone with a Diapente is the imperfect Sixth. As between mi from e to fa in c. and contrarily. The Third is An­tiphonus. as the Diapason: which is the Distance of a Voice from a Voice by an Eighth; whence it is called an Octave. And it is made seven wayes i. e. from every Letter to his like; as from A to a. from a to aa. &c. To these Moods or Intervalls there are four prohibited Intervalls opposed by vulgar Musici­ans. 1. A Tritone which containeth three Tones, and is made from fa to mi. 2. A Semidiapente which passeth from mi to fa. containing two Tones and as many Semitones. 3. A Semidiapason, which is an Octave containing three Semitones and four Tones, reaching from mi to fa. 4. A Disdiapason, which is an Intervall by a Fifteenth; within which there is a Limit appointed to the Voice: beyond which it may not wander; and if it wander it is but feigned; For if more Distances then a Diapason occur, they will equisonate with the former Distances in the Octave.

Conclusion.

AND this is the MVSICAL TEMPLE, whose Foundation is Harmony, or Concord: whose Covering is honest Pleasure: whose Wood and Stones are the Harmonical Monads, Dyads, and Tryads. That thou mayest not only enter this Temple, but build thy self; after the diligent reading of this Synopsis which we here present thee with: Consider those melopoetic Classic's and prime Musi­cians, Orlandus and Marentius. But chiefly ex­ercise thy self in the Analysis of many examples; and then from that betake thy self to the musical Synthesis.

FINIS.

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