(Gk.: ‘separation’).
A term applied to various intervals from the time of Pythagoras.
According to Pythagorean theory, transmitted by Boethius (iii, 5, 8) from Philolaus (ed. Diels, Fragmente der Vorsokratiker, 44 A 26), it was a diatonic semitone equal to the amount that the 4th is in excess of the ditone or major 3rd. Later the term ‘limma’ was substituted to refer to the same interval.
According to Aristoxenus, the diesis was any interval smaller than a semitone. His theory provided for tetrachords that might include a ‘hemitone’, equal to half of a whole tone; a ‘very small chromatic diesis’, equal to a third of a whole tone; or a ‘very small enharmonic diesis’, equal to a quarter of a whole tone (Aristoxenus 21, ed. Meibom, p.46; see also Cleonides, ed. Jan, pp.190ff; Adrastus as quoted by Theon, ed. Hiller, p.55).
According to Marchetto da Padova, the diesis was equal to a fifth of a whole tone. If a melodic whole tone is divided chromatically by the insertion of a leading note (for instance, C–CX–D) the first interval is, according to Marchetto, a ‘chroma’, and the second a ‘diesis’. Later 14th- and 15th-century theorists (e.g. Nicolaus de Capua, ed. A. de la Fage, p.32) associated the sign X with the term diesis, so that in Romance languages the modern Sharp sign came to be called by that name (It. diesis; Fr. dièse).
Many
Renaissance and Baroque theorists used the term for intervals of about a
quarter-tone which were too small to be used melodically even though they were
available on keyboard instruments tuned to some form of mean-tone temperament
with split black keys for G
and A
and for D and E. According to the corresponding arithmetic of just
intonation, the difference between four pure minor 3rds and an octave, known as
the ‘greater diesis’, has the ratio 648:625, i.e. (6:5)4:(2:1), and
amounts to 62.6 cents; and the difference between an octave and three pure
major 3rds, known as the ‘lesser diesis’, has the ratio 128:125, i.e.
(2:1):(5:4)3, and amounts to 41.1 cents.
LUKAS RICHTER