Modes

Frequent it is among Practitioners to treat of these Modes, and what they are, all well know; therefore would it be superfluous here to insist thereon: wee shall observe only, that they have their originall from hence, that an Eighth is not divided into equall Degrees, for one while a Tone, another while a Semitone…

Or thus [68]:

{ Third minor defective  { G ad b. 480, 405.
{ by a Schism           { F ad D. 384, 324.
A { Fifth defective by one { G ad D. 480, 324.
  { Schism              { D ad G. 324, 240.
{ Fourth increased by   { b ad G. 405, 240.
{ one Schism            { D ad F. 324, 192.
{ Sixth major increased { 
{ by a Schism           { 

But so great are these Numbers, that such intervals cannot be tollerated of themselves; but, as we have formerly noted, because the interval of a Schisme is so small, as it can hardly bee discerned by the ears, therefore doe they borrow sweetenesse of those Consonances, to which they are neareſt. Nor doe the Terms of Consonances to consist in indivisibili, as that if one of them be a little changed, all the sweetenesse of the Consonance must instantly be lost: and this can only be the reason, why Dissonances of this Second Genus may be, in a voice successive of the same part, admitted in place of Consonances, from which they are divided.

In the Third Genus are contained, a Tritone, and a Fifth false; for in this, a Semitone majus is accounted for a Tone major; but in a Tritone, the Contrary: and they are explicated by these numbers [69]:

Tritone ³²/₄₅.   Fifth false ⁴⁵/₆₄

Or

Or thus [70]:

{ Tritone  { F ad D. 540, 384.
A {         { b ad E. 405, 288.
{ Fifth false { F ad F. 384, 270.
{             { E ad b. 288, 202. vel 576, 405.

Which Numbers are also too great to explicate any intervall which may not be ingrate to the ears; nor have they any Consonances very near, from which they may borrow sweetenesse, as the Precedent ones have. Hence comes it, that these last Dissonances ought to be avoided in relation; at least, when slow and soft Musick is made, and not diminute: for in very diminute Musick and such as is sung swiftly, the hearing is too much imployed to take notice of the defects of such Dissonances: which defect is much more evident from hence, that they are near to a Fifth, with which the Hearing therefore compares them, and, from the conspicuous sweetenesse of this, doth the more clearly discern the imperfection of those.

Here we shall end our explication of all the Affections of a Sound; having first only taken notice, in order to the probation of what we formerly said, that all the Variety of sounds, as to Grave and Acute, doth arise in Musick only from these Numbers 2, 3, and 5. we say that all numbers, by which all well Degrees, as Dissonances are explicated, are compoſed of those three, and by them, division being made, may at length be resolved even to an unity.

CHAP.