Chromatic genus
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The chromatic genus is a genus of divisions of the tetrachord characterized by an upper interval of a minor third. The remainder of the tetrachord (the pyknon) is divided into two adjacent semitones (hence this genus is the origin of the modern term, chromatic).
Note that the scale generated by the chromatic genus is unrelated to the modern chromatic scale. The modern well-tempered chromatic scale has 12 pitches to the octave, and consists only of semitones. In contrast, the ancient Greek chromatic scale had seven tones to the octave (assuming alternating conjunct and disjunct tetrachords), and had undivided minor thirds as well as semitones.
The scale generated from the chromatic genus is composed of two chromatic tetrachords:
- D-Eb-E-G A-Bb-B-D
Modern chromatic scale:
- D Eb E F F# G Ab A Bb B C C# D Eb E ...
[edit] Tunings of the chromatic
Thrasyllus of Mendes gave the traditional Pythagorean tuning of the chromatic genus:
hypate parhypate lichanos mese 4/3 81/64 32/27 1/1 | 256/243 | 2187/2048 | 32/27 | -498 -408 -294 0 cents
Archytas replaced the 81/64 with the simpler and more consonant 9/7, which he used in all three of his genera:
hypate parhypate lichanos mese 4/3 9/7 32/27 1/1 | 28/27 | 243/224 | 32/27 | -498 -435 -294 0 cents
Didymus's chromatic has only 5-limit intervals, with the smallest possible numerators and denominators. Also note that the successive intervals are all superparticular numbers:
hypate parhypate lichanos mese 4/3 5/4 6/5 1/1 | 16/15 | 25/24 | 6/5 | -498 -386 -316 0 cents
[edit] Byzantine Music
In Byzantine music the chromatic genus is the genus on which the 2nd mode and 2nd plagal mode are based. The "extra" mode nenano is also based on this genus.
