A Ditone, a Third Minor, and Sixths.

By the same way will it be conceived, if any say that a sound doth strike the ears with many percussions or verberations, and that by so much the more swiftly, by how much the more acute the sound is; for then, that the sound AB may arrive at the requisite Uniformity with the sound CD, it ought to strike the ears with only five touches or verberations, while CD strikes only once: but the sound Cf will not so soone returne to an Unifonance…

A Third Minor ariseth from a Ditone, as a Fourth from a Fifth [33], and is therefore more imperfect than a Fourth, as a Ditone, is than a Fifth.

A Ditone is, by many degrees, more perfect than a Fourth.

This is manifest from the Premises; to which, nevertheless, we shall add this; that the Perfection of any Consonance is not to be desumed precisely, from the same, while it is Simple; but also from all the Compounds thereof:

The reason whereof is, that it can never be heard alone so jejune and empty, but the resonance of this composed is also heard together with it; since that, in an Unison, the resonance of a more Acute Eighth is contained, we have formerly evicted. Now, that a Ditone, so considered, doth consist of lesser Numbers than a Fourth [31], and is therefore more perfect than a Fourth; is plain from the Second Figure: wherein we, therefore, placed a Ditone before a Fourth, insomuch as we endeavoured, in that Figure, to place all Consonances according to the order of Perfection.

But here we are obliged to explain, why the third Genus of a Ditone is the most perfect, and makes, in the strings of a Lute, a Tremulation perceptible even by the sight; rather than the First, or Second Genus: which we conceive to proceed from hence; that this Third doth consist in a multiplyed Proportion, but the First in a super-particular, the Second in a multiplyed and super-particular, together [32]. And why, from multiplyed proportion, the most perfect Consonances do arise; which we therefore placed in the First order of the First Figure, we thus demonstrate.

Let the Line AB be distant from CD, in the Third Genus of a Ditone, howsoever men shall imagine the sound to be perceived by the Hearing; certain it is that it is more easie to distinguish what is the proportion betweene AB and CD, than betweene CF and CD; because it will first bee knowne directly by the application of the sound AB, to the parts of the sound CD, viz. Ce,ef,fg, &c. nor will there be any residue in the end: which falls not alike in the proportion of the sound Cf, to CD; for if Cf be applied to fh, there will be the residue hD, by the reflection of which we ought to know what is the proportion between Cf & CD, which is more difficult or tedious.

By the same way will it be conceived, if any say that a sound doth strike the ears with many percussions or verberations, and that by so much the more swiftly, by how much the more acute the sound is; for then, that the sound AB may arrive at the requisite Uniformity with the sound CD, it ought to strike the ears with only five touches or verberations, while CD strikes only once: but the sound Cf will not so soone returne to an Unisonance, for that cannot be done but after the second stroke of the found CD, as is described in the superior Demonstration. The same will also be explained, however we conceive the sound to be heard.

A Third Minor ariseth from a Ditone, as a Fourth from a Fifth [33], and is therefore more imperfect than

a Fourth, as a Ditone, is than a Fifth. Nor is it therefore to bee excluded Musick, since it is not onely not useless, but even necessary, in order to the variation of a Fifth. For, since an Eighth is alwayes heard in an Unison, it cannot adfer this variety; nor a Ditone alone, (for there can be no variety unless betwixt Two, at least:) therfore is a Third Minor associated thereto, to the end that such Tunes, wherein Ditones are more frequent, may be distinct from such as have a Third Minor very often iterated in them.

A Sixth Major proceeds from a Ditone, and by the same reason participateth the nature thereof, as a Tenth Major, and Seventeenth [34]: to the understanding of which, we are to look back upon the First Figure, where, in the number Foure, are found a Fifteenth, an Eighth, and a Fourth, which is the First Compound Number, and which, by a Binary, (which representeth an Eighth,) is resolved even into an Unity; whence it comes that all Consonances generated from it, are apt and convenient for Composition, among which since a Fourth is found, (which, for that respect, we formerly called a Monster, or defective Eighth;) thence doth it follow, that the same is not unprofitable in composition, where the same reasons do not recur, which hinder it from being set alone; for then is it perfected by the adjunct, and remains no longer subject to a Fifth.

A Sixth Minor proceeds from a Third Minor, in the same manner as a Sixth Major doth from a Ditone [35], and so borrows the nature and affections of a Third Minor: nor is there any reason to countermand it.

Here the Series of Consonances would Exact from us a Discourse concerning their various Virtues, as to the excitement of Passions:

But a more exact Disquisition of this, may be collected from the Præcedents; and it exceeds the limits of a Compendium. For, so various are they, and upon so light circumstances supported; that, a whole Volume would not suffice to perfect their Theory. This, therefore, shall we only say, that the chiefest Variety doth arise from these four last; whereof a Ditone and Sixth Major are more gratefull, more sprightfull, and exhilarating than a Third and Sixth Minor; as hath been observed by Practicall Musicians, and may be easily deduced from hence, that a Third Minor is generated from a Ditone only by Accident, but a Sixth Major per se, because it is no other but a Ditone Compound.