Consonancies

I observe:

1. 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.

2. 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. 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].

Heer we are required to note, that from the first Division doth arise only one Consonance: from the second, two: from the third, three: as this Table demonstrateth [10].

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.