1944edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods<br>per 8ve | ||
per 8ve | |||
!Generator<br>(reduced) | !Generator<br>(reduced) | ||
!Cents<br>(reduced) | !Cents<br>(reduced) | ||
!Associated ratio | !Associated ratio | ||
!Temperaments | !Temperaments | ||
|- | |||
|1 | |||
|313\1944 | |||
|193.210 | |||
|262144/234375 | |||
|[[Luna]] (5-limit) | |||
|- | |||
|24 | |||
|944\1944<br>(53\1944) | |||
|582.716<br>(32.716) | |||
|7/5<br>(?) | |||
|[[Chromium]] (1944d) | |||
|- | |- | ||
|72 | |72 | ||
|892\1944<br>(1\ | |892\1944<br>(1\1944) | ||
|550.617<br>(0.617) | |550.617<br>(0.617) | ||
|73205/53248<br>(?) | |73205/53248<br>(?) | ||
|[[Jamala]] | |[[Jamala]] | ||
|} | |} | ||
Revision as of 22:53, 10 July 2023
| ← 1943edo | 1944edo | 1945edo → |
Theory
1944edo is consistent in the 5-limit to which it provides good approximation, and a near-perfect 15/8, but it is only consistent that far. In the 5-limit, it does temper 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.
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) and which is named after an artist who performed a song about the same year as the edo number. 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) | |
Regular temperament properties
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
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 |