[18] So in the Euclidean Sectio Canonis the propositions which deal with the 'movable' notes, viz. Paranêtê and Lichanos (Theor. xvii) and Parhypatê and Tritê (Theor. xviii), begin by postulating the Mesê (estô gar mesê ho B k.t.l.).
[19] The term hêgemôn or 'leading note' of the tetrachord Mesôn, here applied to the Mesê, is found in the same sense in Plutarch, De Mus. c. 11, where ho peri ton hêgemona keimenos tonos] means the disjunctive tone. Similarly Ptolemy (Harm. i. 16) speaks of the tones in a diatonic scale as being en tois hêgoumenois topois, the semitones en tois hepomenois (sc. of the tetrachord): and again of the ratio 5:4 (the major Third) as the 'leading' one of an Enharmonic tetrachord (ton epitetarton hos estin hêgoumenos tou enarmoniou genous).
[20] The investigation occupies a considerable space in his Harmonics, viz. pp. 27-29 Meib. (from the words peri de synecheias kai tou hexês), and again pp. 58-72 Meib.
[21] This point is one which Aristoxenus is fond of insisting upon: cp. p. 10, 16 ou pros tên katapyknôsin blepontas hôsper hoi harmonikoi: p. 38, 3 hoti de estin hê katapyknôsis ekmelês kai panta tropon achrêstos phaneron: p. 53, 3 kata tên tou melous physin zêtêteon to hexês kai ouch hôs hoi eis tên katapyknôsin blepontes eiôthasin apodidonai to hexês.
The statement that the ancient diagrams gave a series of twenty-eight successive dieses or quarter-tones has not been explained. The number of quarter-tones in an octave is only twenty-four. Possibly it is a mere error of transcription (κη for κδ). If not, we may perhaps connect it with the seven intervals of the ordinary octave scale, and the simple method by which the enharmonic intervals were expressed in the instrumental notation. It has been explained that raising a note a quarter of a tone was shown by turning it through a quarter of a circle. Thus, our c being denoted by
, c* was
, and c♯ was
