The headword is accusative singular of di/esis (delta 955).
[1] = Hesychius delta1656, Synagoge delta264.
[2] = Photius delta547 (including the initial gloss), with the exception that in place of the Suda's h( pro\ mousikh=s w)|dh=s ki/nhsis ('the movement before a musical ode'), Photius' text reads h( prw/th kata\ mousikh=s w)|dh=s ki/nhsis ('the first movement into a musical ode')
[3] = Damascius fr. 199 Zintzen (127 Asmus); cf. Photius, Bibliotheca 344b.19-22.
[4] cf. Boethius, De institutione musica 1.21 diesis est semitonii dimidium [...] Enarmonium vero quod est [...] cantatur in omnibus tetrachordis per diesin et diesin et ditonum. See also, very generally Hesychius delta1657 di/esis para\ toi=s mousikoi=s kalei=tai me/ros ti to/nou. According to Pap. 13 Hibeh (ed. Grenfell-Hunt I, p. 14, lines 15-17), among the three main genres of ancient music (diatonic, chromatic, enharmonic) the enharmonic one was peculiar to tragic Athenian drama.
[5] Many ancient sources emphasize the difficulty of singing in the enharmonic genre: e.g. Aristoxenus held the diatonic one to be earliest, because it was the most proper to human voices. The enharmonic is defined as the most elegant one, but also the hardest; the audience got used to hearing this kind of harmony only with some trouble. (A similar assessment occurs in Aristides Quintilianus 1.9.19 M. = 16,10-18 W.)