373edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 48: | Line 57: | ||
| 0.1327 | | 0.1327 | ||
| 4.12 | | 4.12 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 88: | Line 104: | ||
| 45/32 | | 45/32 | ||
| [[Untriton]] (5-limit) | | [[Untriton]] (5-limit) | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||
Revision as of 12:42, 16 November 2024
| ← 372edo | 373edo | 374edo → |
Theory
373edo is distinctly consistent to the 15-odd-limit. It has a flat tendency, with harmonics 3 through 13 all tuned flat. The equal temperament tempers out [8 14 -13⟩ (parakleisma) and [-51 19 9⟩ (untriton comma) in the 5-limit; 2401/2400 (breedsma), 65625/65536 (horwell comma), and 43046721/42875000 in the 7-limit; 3025/3024, 8019/8000, 24057/24010, and 496125/495616 in the 11-limit; 729/728, 1001/1000, 1716/1715, 4225/4224, and 10648/10647 in the 13-limit, enabling squbemic chords and sinbadmic chords. It supports the hemitert temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.61 | -0.25 | -0.46 | -1.18 | -0.85 | +1.21 | -1.53 | -0.93 | -0.09 | +0.27 |
| Relative (%) | +0.0 | -19.1 | -7.9 | -14.3 | -36.8 | -26.4 | +37.6 | -47.7 | -28.9 | -2.7 | +8.5 | |
| Steps (reduced) |
373 (0) |
591 (218) |
866 (120) |
1047 (301) |
1290 (171) |
1380 (261) |
1525 (33) |
1584 (92) |
1687 (195) |
1812 (320) |
1848 (356) | |
Subsets and supersets
373edo is the 74th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-591 373⟩ | [⟨373 591]] | +0.1939 | 0.1939 | 6.03 |
| 2.3.5 | [8 14 -13⟩, [-51 19 9⟩ | [⟨373 591 866]] | +0.1658 | 0.1632 | 5.07 |
| 2.3.5.7 | 2401/2400, 65625/65536, 43046721/42875000 | [⟨373 591 866 1047]] | +0.1654 | 0.1413 | 4.39 |
| 2.3.5.7.11 | 2401/2400, 3025/3024, 8019/8000, 65625/65536 | [⟨373 591 866 1047 1290]] | +0.2008 | 0.1449 | 4.50 |
| 2.3.5.7.11.13 | 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 | [⟨373 591 866 1047 1290 1380]] | +0.2056 | 0.1327 | 4.12 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 12\373 | 38.61 | 45/44 | Hemitert |
| 1 | 24\373 | 77.21 | 256/245 | Tertiaseptal |
| 1 | 98\373 | 315.28 | 6/5 | Parakleismic (5-limit) |
| 1 | 111\373 | 357.10 | 768/625 | Dodifo (5-limit) |
| 1 | 162\373 | 521.18 | 875/648 | Maviloid |
| 1 | 183\373 | 588.74 | 45/32 | Untriton (5-limit) |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct