Neutral temperaments: Difference between revisions
From Xenharmonic Reference
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Revision as of 23:51, 27 February 2026
Dichotic is an exotemperament that can be defined to temper out 25/24, the dicot comma, 45/44, and 64/63. As a result it also tempers out 55/54.
Interval chart
This interval chart uses Partch's 11-limit tonality diamond and maps it onto 7edo and 10edo. This also gives an idea of what intervals are possible in dichotic temperament. Intervals in bold are in the 7-note MOS (symmetric mode) and intervals in italics are in the 10-note MOS (both near-symmetric modes). Note that the interval that can be mapped to 11/8 and 10/7 and the interval mapped to 7/5 and 16/11 cannot coexist in the same 10-note MOS.
| 0\7 | 1\7 | 2\7 | 3\7 | 4\7 | 5\7 | 6\7 | 7\7 | |
|---|---|---|---|---|---|---|---|---|
| 0\10 | 1/1 | |||||||
| 1\10 | 12/11, 10/9 | |||||||
| 2\10 | 11/10, 9/8, 8/7 | 7/6 | ||||||
| 3\10 | 6/5, 11/9, 5/4 | 14/11 | ||||||
| 4\10 | 9/7 | 4/3 | ||||||
| 5\10 | 11/8, 10/7 | 7/5, 16/11 | ||||||
| 6\10 | 3/2 | 14/9 | ||||||
| 7\10 | 11/7 | 8/5, 18/11, 5/3 | ||||||
| 8\10 | 12/7 | 7/4, 16/9, 20/11 | ||||||
| 9\10 | 9/5, 11/6 | |||||||
| 10\10 | 2/1 |
Theory
Dichotic is generated by a neutral 3rd, or one half of a perfect fifth. A notation system based on dichotic temperament is still in the works.
