1944edo
| ← 1943edo | 1944edo | 1945edo → |
1944 equal divisions of the octave (abbreviated 1944edo or 1944ed2), also called 1944-tone equal temperament (1944tet) or 1944 equal temperament (1944et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1944 equal parts of about 0.617 ¢ each. Each step represents a frequency ratio of 21/1944, or the 1944th root of 2.
Theory
1944edo is consistent in the 5-odd-limit to which it provides good approximation, and a near-perfect 15/8, but it is only consistent that far since harmonic 7 is about halfway between its steps. In the 5-limit, it tempers out the luna comma, [38 -2 -15⟩. In the 1944d val in the 7-limit, it is a landscape system tempering out 250047/250000, and as a consequence it tunes the 24th-octave chromium temperament, providing a tuning close to POTE tuning.
In higher limits, 1944edo is a tuning for the jamala temperament in the 2.5.11.13.19.41.47 subgroup, for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.103 | +0.106 | -0.307 | -0.206 | -0.083 | +0.213 | +0.003 | -0.017 | +0.018 | +0.207 | +0.121 |
| Relative (%) | -16.7 | +17.2 | -49.8 | -33.4 | -13.5 | +34.5 | +0.5 | -2.8 | +2.9 | +33.5 | +19.6 | |
| Steps (reduced) |
3081 (1137) |
4514 (626) |
5457 (1569) |
6162 (330) |
6725 (893) |
7194 (1362) |
7595 (1763) |
7946 (170) |
8258 (482) |
8539 (763) |
8794 (1018) | |
Subsets and supersets
Since 1944 factors into 23 × 35, 1944edo has subset edos 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 313\1944 | 193.210 | 262144/234375 | Luna (5-limit) |
| 24 | 944\1944 (53\1944) |
582.716 (32.716) |
7/5 (?) |
Chromium (1944d) |
| 72 | 892\1944 (1\1944) |
550.617 (0.617) |
73205/53248 (?) |
Jamala |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct