Manchester Memoirs, Vol. xlviii. (1904), No. 13. 



XIII. Mean Tones, Equal Tempered Tones, and the 

 Harmonic Tetrachords of Claudius Ptolemy. 



By R. C. Phillips. 



(Communicated by C. W. Sutton, M.A.J 



Received March 2nd. Read March 2gth, igo^.. 



The harmonic, or enharmonic systems of music of 

 the ancient Greeks are considered by many writers to 

 belong to an order of melody long extinct ; though there 

 is abundant evidence to show that the present scale of the 

 Arabs is a direct survival of that of classical times. This, 

 the modern Damascus scale, as explained by the learned 

 Michail Meshaq'ah, is intended to consist of twenty-four 

 equal quarter-tones in the octave ; and his arithmetical 

 and geometrical constructions show how a canon, or 

 monochord string can be thus divided with considerable 

 accuracy. 



The equal division of the octave is referred to by 

 Aristides Quintilianus, as being probably the most 

 " consonant," (that is, suitable) could it be attained ; and 

 this writer of the first or second century, A.D., describes 

 melodic progressions on the then enharmonic scale of 

 precisely the same nature as those new found in modern 

 Arabic music. He mentions that the Pythagoreans 

 divided the octave into twenty-four " dieses," but these 

 were certainly not all equal ; they constitute, however, 

 the first attempt to divide the octave into twenty-four 

 approximately equal intervals. 



The system of Aristoxenus is often cited as a solution 



May 2nd, igo^. 



