Chromatic genus
In Ancient Greek music theory, the chromatic genus (Greek: χρωματικό γένος or χρωματική) (also known as chrōma, from the Greek word χρώμα, "colour") is a genus of the tetrachord characterized by an upper interval of a minor third. The two middle notes of the tetrachord were movable (kinoumenoi) while the two outer notes were immovable (hestōtes) (Mathiesen 2001, 6.iii.c). The movable members of the tetrachord (the pyknon) is divided into two adjacent semitones (hence this genus is the origin of the modern term, chromatic).[citation needed]
Note that the scale generated by the chromatic genus is not like the modern chromatic scale. The modern (18th century) well-tempered chromatic scale has 12 pitches to the octave, and consists of semitones of various sizes; the equal temperament common today, on the other hand, also has 12 pitches to the octave, but the semitones are all of the same size. 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 (Dorian) scale generated from the chromatic genus is composed of two chromatic tetrachords:
Play (help·info)Whereas in modern music theory, a chromatic scale is:
- D D♯ E F F♯ G G♯ A A♯ B C C♯ D D♯ E ...
Tunings of the chromatic
Theon of Smyrna gives an incomplete account of Thrasyllus of Mendes' formulation of the Greater Perfect System, from which the diatonic and enharmonic genera can be deduced. For the chromatic genus, however, all that is given is a 32:27 proportion of mese to lichanos. This leaves 9:8 for the pyknon, but there is no information at all about the position of the chromatic parhypate and therefore of the division of the pyknon into two semitones, though it may have been the limma of 256:243, as Boethius does later (Barbera 1977, 306, 309). Someone has referred to this speculative reconstructions as the traditional Pythagorean tuning of the chromatic genus[citation needed]:
hypate parhypate lichanos mese 4/3 81/64 32/27 1/1 | 256/243 | 2187/2048 | 32/27 | -498 -408 -294 0 cents
Archytas used the simpler and more consonant 9/7, which he used in all three of his genera. His chromatic division is (Barbera 2001):
hypate parhypate lichanos mese 4/3 9/7 32/27 1/1 | 28/27 | 243/224 | 32/27 | -498 -435 -294 0 cents
According to Ptolemy's calculations, Didymus's chromatic has only 5-limit intervals, with the smallest possible numerators and denominators (Richter 2001). 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
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.[citation needed]
See also
Sources
- Barbera, C. André. 1977. "Arithmetic and Geometric Divisions of the Tetrachord". Journal of Music Theory 21, no. 2 (Autumn): 294–323.
- Barbera, André. 2001. "Archytas of Tarentum". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Mathiesen, Thomas J. 2001. "Greece, §I: Ancient". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Richter, Lukas. 2001. "Didymus [Didymos ho mousikos]". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.