1944edo: Difference between revisions
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 29: | Line 31: | ||
|- | |- | ||
| 24 | | 24 | ||
| 944\1944<br>(53\1944) | | 944\1944<br />(53\1944) | ||
| 582.716<br>(32.716) | | 582.716<br />(32.716) | ||
| 7/5<br>(?) | | 7/5<br />(?) | ||
| [[Chromium]] (1944d) | | [[Chromium]] (1944d) | ||
|- | |- | ||
| 72 | | 72 | ||
| 892\1944<br>(1\1944) | | 892\1944<br />(1\1944) | ||
| 550.617<br>(0.617) | | 550.617<br />(0.617) | ||
| 73205/53248<br>(?) | | 73205/53248<br />(?) | ||
| [[Jamala]] | | [[Jamala]] | ||
|} | |} | ||
{{orf}} | |||
Revision as of 00:52, 16 November 2024
| ← 1943edo | 1944edo | 1945edo → |
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 |