1944edo: Difference between revisions
Jump to navigation
Jump to search
Created page with "{{Infobox ET}} == Regular temperament properties == {| class="wikitable center-all left-5" !Periods per 8ve !Generator (reduced) !Cents (reduced) !Associated ratio !Temperame..." |
No edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1944}} | |||
== 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, {{monzo|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 [[wikipedia:Jamala|artist]] who performed a [[wikipedia:1944 (song)|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 === | |||
{{harmonics in equal|1944}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods | ||
per 8ve | per 8ve | ||
!Generator | !Generator<br>(reduced) | ||
(reduced) | !Cents<br>(reduced) | ||
!Cents | |||
(reduced) | |||
!Associated ratio | !Associated ratio | ||
!Temperaments | !Temperaments | ||
|- | |- | ||
|72 | |72 | ||
|892\1944 | |892\1944<br>(1\2016) | ||
(1\2016) | |550.617<br>(0.617) | ||
|550.617 | |73205/53248<br>(?) | ||
(0.617) | |||
|73205/53248 | |||
(?) | |||
|[[Jamala]] | |[[Jamala]] | ||
|} | |} | ||
Revision as of 22:47, 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 |
|---|---|---|---|---|
| 72 | 892\1944 (1\2016) |
550.617 (0.617) |
73205/53248 (?) |
Jamala |