2yO PHILOSOPHICAL TRANSACTIONS. [aNNO 16Q8. 



To rectify this, there is another division thought more convenient ; which is 

 Ptolemy's diatonum intensum, of the diatonic kind, more intense or acute 

 than that other. Whicli, instead of two full tones for fa-sol-la, assigns what 

 is now called a greater and a less tone ; which, by the more nice musicians of 

 this and the last age, seems to be more embraced ; assigning to fa-sol, that of 

 9 to 8, which they call the greater tone, and to sol-la, that of 10 to Q, which 

 they call the lesser tone : and therefore to fa-la, the ditone or greater third, 

 that of 5 to 4. For lo x 4- = '•/ =4- And consequently, to mi-fa, which 

 is remaining of the fourth, that of lO to 15. For i) {. (-la. That is, if out 

 of that of 4 to 3, we take that of 5 to 4, there remains that of 1 6 to 15. 

 There are many other ways of dividing the fourth or diatessaron, or the pro- 

 portion of 4 to 3, into three parts, answering to what, in a looser way of ex- 

 pression, we call a half note, and '2 whole-notes. But this of -f4 X I- X V° = -ri 

 is that which is now received as the most proper. To which therefore I shall 

 apply my discourse. Where -j-f- '^ what we call the hemitone or half-note, in 

 mi-fa; f that of the greater-tone, in fa-sol ; and '-/ the lesser-tone, in sol-la. 

 Only with this addition ; that each of those tones is, upon occasion, by flats 

 and sharps divided into 2 hemitones or half-notes: which answer to what the 

 Greeks called mutatio quoad modos, the change of mood ; and what is now 

 done by removing mi to another key. Namely -f- = -f^- := -fr X t-J- ; and '-J 



g — g \/ 1 9 



"~" 1 8 "^ T^ '^ IB* 



Thus, by the help of flats and sharps, dividing each whole-note, be it the 

 greater or the less, into 2 half-notes, or what we call so, the whole octave is 

 divided into 12 parts or intervals, contained between 13 pipes, which are com- 

 monly called hemitones or half-notes. Not that each is precisely half a note, 

 but somewhat near it, and so called. As for instance, a flat in d, or a sharp 

 in c, do either of them denote a middling sound, though not precisely in the 

 middle, between c and d ; sharper than c, and flatter than d. Accordingly ; 

 supposing mi to stand in b fa b mi, which is accounted its natural seat, the 

 sounds of each pipe are to bear these proportions to each other, viz. 



BCtD*EF4.G*a*b 



mi fa 4 sol * la fa » sol «. la * mi 



