Music Sound

In ancient Greek music theory, a genus is a family of divisions of the tetrachord (four notes spanning a perfect fourth) used to create musical scales. The three genera are distinguished by their characteristic largest intervals, between the upper two notes. The diatonic genus has a characteristic interval of a major second, the chromatic genus has a minor third, and the enharmonic genus has a major third. (Note that this original Greek usage of diatonic ("streched out"), chromatic ("colorful"), and enharmonic ("harmonious") does not generally correspond to the modern definitions of these terms.) The term pyknon ("compression") refers to the remainder of the tetrachord in the chromatic and enharmonic genera, where two adjacent intervals are a semitone or smaller.

In contrast to modern scales, the tetrachord was perceived as descending from its highest pitch (here mese). Thus the pitches are given in terms of their ratios downward from mese, or as negative cents.

Here are the traditional Pythagorean tunings of the diatonic and chromatic tetrachords:

Diatonic
hypate   parhypate                lichanos                   mese
 4/3       81/64                    9/8                      1/1
  | 256/243  |          9/8          |          9/8           |
-498       -408                    -204                       0 cents

Chromatic
hypate   parhypate      lichanos                             mese
 4/3       81/64         32/27                               1/1
  | 256/243  |  2187/2048  |              32/27               |
-498       -408          -294                                 0 cents

Since there is no reasonable Pythagorean tuning of the enharmonic genus, here is a representative tuning due to Archytas:

Enharmonic
hypate parhypate lichanos                                    mese
 4/3     9/7   5/4                                           1/1
  | 28/27 |36/35|                     5/4                     |
-498    -435  -386                                            0 cents

Originally, the lyre had only four strings, so only a single tetrachord was needed. Larger scales are constructed from conjunct or disjunct tetrachords. Conjunct tetrachords share a note, while disjunct tetrachords are separated by a disjunctive tone of 9/8 (a Pythagorean major second). Alternating conjunct and disjunct tetrachords form a scale that repeats in octaves (as in the familiar diatonic scale, created in such a manner from the diatonic genus), but this was not the only arrangement.

The Greeks analzyed genera using various terms, including diatonic, enharmonic, and chromatic, the latter being the color between the two other types of modes which were seen as being black and white. Scales are constructed from conjunct or disjunct tetrachords: the tetrachords of the chromatic genus contained a minor third on top and two semitones at the bottom, the diatonic contained a minor second at top with two major seconds at the bottom, and the enharmonic contained a major third on top with two quarter tones at the bottom, all filling in the perfect fourth (Miller and Lieberman, 1998) of the fixed outer strings. However, the closest term used by the Greeks to our modern usage of chromatic is pyknon or the density ("condensation") of chromatic or enharmonic genera.

Didymos chromatic tetrachord	16:15, 25:24, 6:5
Eratosthenes chromatic tetrachord	20:19, 19:18, 6:5
Ptolemy soft chromatic	28:27, 15:14, 6:5
Ptolemy intense chromatic	22:21, 12:11, 7:6
Archytas enharmonic	28:27, 36:35, 5:4

(ibid)

Further reading

• Chalmers, John H. Jr. Divisions of the Tetrachord. Frog Peak Music, 1993. ISBN 0945996047

Source

• Miller, Leta E. and Lieberman, Frederic (1998). Lou Harrison: Composing a World. Oxford University Press. ISBN 0195110226.

External links

• Encyclopedia of Microtonal Music Theory