Table of Contents
I observe:
- A Unison is not a Consonance because therein is no Difference of Sounds, as to Acute and Grave.
But that it bears the same relation to Consonances, that Unity doth to Numbers.
- Of 2 Terms, required in Consonances, that which is the more Grave, is far the more Potent, and doth in a manner contain the other Term in it selfe: as is manifest in the Nerves of a Lute, of which when any one is percuffed, those strings, which are an Eighth, or Fifth more acute [8], tremble and resound of their own accord; but those which are more Grave do not, at least do not appear to the sence so to do; the Reason whereof is thus demonstrated.
That is, is Four or Seven Notes higher: For the Fifth is the Fourth from the First, and the Eight is the Seventh, &c. The knowledge of which Notes, together with all other Consonances, and Musical Intervalls (some few excepted, not now in use,) may be, without difficulty, obtained by inspection on the first Figure following.
[Diagram top left] Exces. 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 Inclus. 1 2 3 4 5 6 7 8
[Diagram bottom left] Inclus. 8 7 6 1 2 3 4 Exces. 1 2 3
Whereof the Space from the Bridge to the Nuts, is understood to be divided into 540, or 10000 equall parts: the Number of which parts (accounting from the Bridge) to each equall division of the foure Chords, or Strings, numbred at the Bridge 1, 2, 3, 4; is to be found on the Right hand. The first (B o) presents you all the Intervalls under an Eight, and their proportions, names, and differences by parallel entrance towards the Right hand, and is thus to be read: viz., Bo [542, or 10000], is to B 1 [5184, or 9600], as 25, to 24, as an Unison, to its Acute Semitone minus: Bo [540, or 10000], B 2 [50625, or 9375] :: 16, 15 :: Unison, Sem major; B 2 [270, or 5000], B 20 [28125, or 5208] :: 24, 25 :: Unison, Sem minor; B 21 [270, or 5000], B 19 [288, or 5·333] :: 15, 16 :: Unison, Sem major: The Habitues, or Proportion of B 1, to B 2, or of B 2, to B 1; or the difference of a Semitone minus, and major, or of a Seventh major, and Semi-Eight, is a Diesis minor, &c. Hence it appeareth that B o, if struck, when stop’d at 1, doth found a Semitone minus more acute, than if it doth, if struck, when unstop’d or open: and that a Semitone minor (as 01) is of the 25, and is subtracted from it, and 24 of the 25, and is added to it. And the like (mutatis mutandis) in all the Rest. The Second Cord (V F) is divided according to the Third (1 F) according to ♮, that is, from F to F as in the Scale, P. 41. And the Fourth (W A), as the like instruments are usually fitted. Thus having all the Intervalls under an Eight, those above are easily known: for they are all compounded either of one, or more Eights only, as the Fifteenth, Two & twentieth, Nine and twentieth, &c. or else of one, or more Eights, and some one of these. And (therefore) as B o was divided, to make the first few Notes after, above the Unison, so is B 21 understood to be divided, to make the seven next after, or above the Diapason, &c. ad infinitum.
Yet
One sound bears the same respect to another sound, that one string bears to another string: but in every string that is greater, all the other strings, that are lesse, are comprehended; though every string that is longer, doth not comprehend all the others, that are shorter: and therfore also in every Graver Sound, all others more Acute are comprehended; but not, on the contrary, in every Acuter Sound are the more Grave comprehended: whence it is evident, that the more Acute Termis to be found by the Division of the more Grave. Which Division that it ought to be Arithmeticall, i. e. into equall parts, is consequent from what was before observed in the sixth Præconsiderable.
[Diagram of a line A to B with points D,C,E marked at specific intervals: 0 at A, 2 at D, 3 at C, 4 at E, and 6 at B.]
Let, therfore, AB bee the more Grave Term, in which if I would find the Acuter Term of all the first Consonances, I must divide it by the first of all Numbers, viz. by 2, as is done in C; and then AC,AB, are distant each from other, the first of all the Consonances, which is called an Eighth and Diapason. Further, would I have other Consonances, which immediately follow the first; I must divide AB into three equall parts; and then I shall have not only one Acute Term, but two, viz. AD, and AE, from which there will arise two Consonances of the same kind, viz. a Twelfth, and a Fifth. Again, I can subdivide the line AB into 4, or 5, or 6 parts, but no further; because such is the imbecillity of the Ears, as that they cannot distinguish, without so much labour as must drown the pleasure, any more Differences of Sounds [9].
From the first Division arises only 1 Consonance.
From the second, two.
From the third, three, as this Table demonstrateth [10].
[10] But more clearly this fig. following, where the Space A B is actually and distinctly divided into 2, 3, 4, 5, 6, 8, 9, 10, equal parts.
| Eight | 8 | ||||
| Fifth | 1/3 | 3/8 | |||
| Fourth | Fifth | Eight | |||
| Eight | Fifteenth | 8 | |||
| Third ma. Fourth | Fifth | Eight | |||
| A | Sixth major | 8 | B | ||
| Tenth major | |||||
| Seventeenth major | |||||
| Third mi. Sixth ma. Fourth | Fifth | Eight | |||
| Fifth | 8 | ||||
| Eight | Twelfth | ||||
| Ninteenth | |||||
| 2 | 3 | 4 | 5 | 6 | 8 |
| Third major | Fourth | Fifth | Sixth major | Eight | Ninth major |
First Figure. Ratio Interval Name Ratio Interval Name Ratio Interval Name Ratio Interval Name Ratio Interval Name 1/2 Eighth 1/3 Twelfth 2/3 Fifth 1/4 Fifteenth 2/4 Eighth 3/4 Fourth 1/5 Seventeenth Major 2/5 Tenth Major 3/5 Sixth Major 4/5 Ditone 1/6 Nineteenth 2/6 Twelfth 3/6 Eighth 4/6 Fifth 5/6 Third Minor
Here wee have not set downe all Consonances that are; in regard, that, to our more facile Invention of the rest, requisite it is that we first treat Of MUSIc.
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