( 7°;)

To Rectifie this, there is another Division thought möre convenient;which is Ptolcmey s Diatonum Intensum ( of the Diatonicis Kind, more Intenseor Acute than that other.) Which instead of two Füll Tones for fa,fil, ia,astigns ( what we now call ) a Greatcr and a Lejser Tone ; ( which by themore Nice Muficians of this and the last Age, scems to be more embraced;)Ailigning to fa, sol , that of 9 to 8, ( which they call the Greatcr Tone ; )and to sei, la, that of 10 to 9, ( which they call the Lejser Tone:) Andthcreforc to fa, /a, ( the Ditone or Greatcr Third ) that of 5 to 4. ( Foj

^ x — l . ) And conlequcntly to mi, fa, ( which is remaining

of the Fourth ) that of 1 si to 1 e. For — ) — ( —. That is; if out of

' a 3 ii

that of 4 to z, we talte thatof 5 to 4, there remains that oft si to 1 y.

Many other ways there are ( with which I (hall not trouble you at pre-ient ) of dividing the Fourth or Dia-tcjscron, or the Proportion of 4 to 3, in-to three parts, anfwering to what ( in a loosor way of Expression ) we call

an Half-Notc, and tm wholc Notes. But this of 15 x ‘a - x —

15 8 9

that which is now received as the most proper.

To which thcreforc I shall apply my Dilcourfe , Where ~ is

4

3 1

is-

(what we

call) the Hemitone, or Half-Notc,

in mi,fa\ ~g~ that of the Greater Tone, in

fa, sol, and — the Lejser Tone , in sol, la.

Only with this 'Addition ; That each of thole Tones, is {upon Occasionby Fiats and Sharps ( as we now speak ) divided into two Hemi-toncs, or Half-Notes : Which answers to what by the Grcckj was callcd Muta-io quoad Modos( tha Changc of Mood ; ) and what is now done by rcmoving mi to anether

Key. Namcly ^ ^ x

17

^ j IO 2£ 20

5 9 18

x -

* 18

Thus by the help ot Fiats and Sharps (dividing each xohole Not.e , be itthe Greater or Lejser, into two Half Notes, or what we call so, ) the wholeOElave is divided intoTwelve Parts or Intervall (contained between ThirteenPipes) which are commonly called Hemi-toncs or Half Notes, not that eacliis precilely Half a Note, but sonte what near it, and so called. And I lay,by Fiats and Sharps ; For fometime the one sometinte the other, is ufed. Asfor Instance, a Flat in D, or a Sharp , in C, do either of them destote aMidling Sound ( though- not precifely in the Midst ) between C and l>;Sharper than C, and Flat ter than D.

Aceor-

J