499edo: 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 34: | Line 43: | ||
| 0.1345 | | 0.1345 | ||
| 5.59 | | 5.59 | ||
|} | |||
=== 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 62: | Line 78: | ||
| 2800/2187 | | 2800/2187 | ||
| [[Osiris]] | | [[Osiris]] | ||
|} | |||
<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 13:13, 16 November 2024
| ← 498edo | 499edo | 500edo → |
Theory
499et tempers out 33554432/33480783, 359661568/358722675 and 2401/2400 in the 7-limit; 100663296/100656875, 2097152/2096325, 536870912/535869675, 151263/151250, 104857600/104825259, 131072/130977, 200704/200475, 17537553/17500000, 19712/19683, 1479016/1476225, 3025/3024, 41503/41472, 532400/531441 and 67110351/67108864 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.25 | +0.86 | +0.31 | -0.62 | +1.16 | +0.86 | +0.68 | -0.62 | -0.32 | -0.35 |
| Relative (%) | +0.0 | +10.4 | +35.8 | +13.0 | -25.6 | +48.1 | +35.6 | +28.4 | -25.7 | -13.3 | -14.4 | |
| Steps (reduced) |
499 (0) |
791 (292) |
1159 (161) |
1401 (403) |
1726 (229) |
1847 (350) |
2040 (44) |
2120 (124) |
2257 (261) |
2424 (428) |
2472 (476) | |
Subsets and supersets
499edo is the 95th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [791 -499⟩ | ⟨499 791] | -0.0787 | 0.0787 | 3.27 |
| 2.3.5 | [32 -7 -9⟩, [1 36 -25⟩ | ⟨499 791 1159] | -0.1760 | 0.1519 | 6.32 |
| 2.3.5.7 | 2401/2400, 1959552/1953125, 26873856/26796875 | ⟨499 791 1159 1401] | -0.1598 | 0.1345 | 5.59 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 23\499 | 55.311 | 16875/16384 | Escapade |
| 1 | 126\499 | 303.006 | 25/21 | Quinmite |
| 1 | 146\499 | 351.102 | 49/40 | Newt |
| 1 | 178\499 | 428.056 | 2800/2187 | Osiris |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct