VOL. XLIV.l PHILOSOPHICAL TRANSACTIONS. 26^ 



must have been composed of tones major, and limmas. Hence the 7 intervals 

 of one octave would be thus expressed in numbers, f , -|4|-, -f-, -§-, -|44> tj -!• 

 Some modern authors have from this inferred the imperfection of the Greek 

 music. They allege that we here find the ditonus, or an interval equal to 2 tones 

 major, expressed by -f-^, instead of the true 3d major expressed by 4-. As there 

 can be no question of the beauty and elegance of the latter, the former therefore 

 must be out of tune, and out of tune by a whole comma, which is very shock- 

 ing to the ear. In like manner the trihemitone of the ancients falls short of 

 the 3d minor by a comma; which is also the deficiency of their hemitone or 

 limma, from the true semitone major, so essential to good melody. These errors 

 would make their scale appear much out of tune to us ; and indeed it appeared out 

 of tune to them ; since they expressly tell us that the intervals less than the diates- 

 saron or 4th, as also the intervals between the 5th and octave, were dissonant 

 and disagreeable to the ear. Their scale, which has been called by some the 

 scala maxima, was not intended to form the voice to sing accurately, but was 

 designed to represent the system of their modes and tones, and to give the true 

 4ths and 5ths of every key a composer might choose. Now if, instead of tones 

 major and limmas, we take the tones major and minor, with the semitone major, 

 as the moderns contend we should, we shall have a good scale indeed, but a scale 

 adapted only to the concinnous constitutjon of one key ; and whenever we pro- 

 ceed from that into another, we find some 4th or 5 th erroneous by a comma. 

 This the ancients did not admit of. If, to diminish such errors, we introduce a 

 temperature, we shall have nothing in tune but the octave. We see then that 

 the scale of the ancients was not destitute of reason ; and that no good argu- 

 ment against the accuracy of their practice can from thence be formed. 



It was usual among the Greeks to consider a descending, as well as an ascend- 

 ing scale, the former proceeding from acute to grave, precisely by the same in- 

 tervals as the latter did from grave to acute. The first sound in each was the 

 proslambanomenos. The not distinguishing these two scales has led several 

 learned moderns to suppose, that the Greeks, in some centuries, took the pros- 

 lambanomenos to be the lowest note in their system, and in other centuries to 

 be the highest. But the truth is, that the proslambanomenos was the lowest, 

 or highest note, according as they considered the ascending or descending scale. 

 The distinction of these is conducive to the variety and perfection of melody ; 

 but Dr. P. never yet met with above one piece of music, where the composer 

 appeared to have any intelligence of this kind. The composition is about 150, 

 or more, years old, for 4 voices ; and the words are, Vobis datum est noscere 

 mysterium regni Dei, casteris autem in parabolis; ut videntes non videant, et 

 audientes non intelligant. By the choice of the words, the author seems to allude 

 to his having performed something not commonly understood. 



