270 PHILOSOPHICAL TRANSACTIONS. [aNNO 1746. 



The following is an octave only of the ascending and descending scales of the 

 diatonic genus of the ancients, with the names of their several sounds, as also 

 the corresponding modem letters. 



Ascending. Descending. 



A Proslambanomenos g 



t • 



T T 



B hypate hypaton y 



144 -HI 



c parhypate hypaton e 



* 



lychanos hypaton 



hypate meson 

 parhypate meson 



£. *. 



a V 



i 



lychanos meson 



a mese g 



- Where it appears that the same Greek names seiTC for the sounds in the as- 

 cending and descending scales. 



In the octave here given, 4 sounds, viz. the proslambanomenos, hypate hypaton, 

 hypate meson, and mese, were called stabiles, from their remaining fixed through- 

 out all the genera and species. The other 4 sounds being the parhypate hypaton, 

 lychanos hypaton, parhypate meson, and the lychanos meson, were called mobiles, 

 because they varied according to the different species and varieties of music. 



By genus and species was understood a division of the diatessaron, containing 4 

 sounds, into 3 intervals. The Greeks constituted 3 genera, known by the names 

 of enharmonic, chromatic, and diatonic. The chromatic was subdivided into 3 

 species, and the diatonic into 2. The 3 chromatic species were the chromaticum 

 molle, the sesquialterum, and the toniaeum. The 2 diatonic species were the 

 diatonicum molle, and the intensum ; so that they had 6 species in all. Some 

 of these are in use among the moderns, but others are as yet unknown in theory 

 or practice. 



The diatonicum intensum was composed of 2 tones, and a semitone : but, to 

 speak exactly, it consists of a semitone major, a tone minor, and a tone major. 

 This is in daily practice ; and we find it accurately defined by Didymus, in 

 Ptolemy's Harmonics published by Dr. Wallis. The next species is the diatonicum 

 molle, as yet undiscovered by any modern author. Its component intei-vals are, 

 the semitone major, an interval composed of 2 semitones minor, and the comple- 

 ment of these 2 to the 4th, being an interval equal to a tone major, and an en- 

 harmonic diesis. The 3d species is the chromaticum toniaeum. Its component 



