1944edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1944}} | {{EDO intro|1944}} | ||
== Theory == | == 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]] | 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. 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 [[ | 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 === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|1944}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods<br>per 8ve | ! Periods<br>per 8ve | ||
!Generator | ! Generator* | ||
!Cents<br> | ! Cents* | ||
! Associated<br>Ratio | |||
!Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|313\1944 | | 313\1944 | ||
|193.210 | | 193.210 | ||
|262144/234375 | | 262144/234375 | ||
|[[Luna]] (5-limit) | | [[Luna]] (5-limit) | ||
|- | |- | ||
|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]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
Revision as of 14:04, 15 October 2023
| ← 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. 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). 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
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