1063edo: 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 41: | Line 50: | ||
| 0.0937 | | 0.0937 | ||
| 8.30 | | 8.30 | ||
|} | |||
=== 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 57: | Line 73: | ||
| 6/5 | | 6/5 | ||
| [[Counterhanson]] | | [[Counterhanson]] | ||
|} | |||
<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
| ← 1062edo | 1063edo | 1064edo → |
Theory
1063et tempers out 2401/2400 in the 7-limit; 95703125/95664294, 26214400/26198073, 78675968/78594219, 1953125/1951488, 1879453125/1879048192, 3294225/3294172, 43923/43904, 102487/102400 and 781258401/781250000 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.209 | -0.237 | -0.246 | -0.424 | +0.488 | +0.030 | +0.511 | +0.512 | -0.038 | -0.351 |
| Relative (%) | +0.0 | +18.5 | -21.0 | -21.8 | -37.6 | +43.3 | +2.7 | +45.3 | +45.4 | -3.4 | -31.1 | |
| Steps (reduced) |
1063 (0) |
1685 (622) |
2468 (342) |
2984 (858) |
3677 (488) |
3934 (745) |
4345 (93) |
4516 (264) |
4809 (557) |
5164 (912) |
5266 (1014) | |
Subsets and supersets
1063edo is the 179th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1685 -1063⟩ | [⟨1063 1685]] | -0.0658 | 0.0658 | 5.83 |
| 2.3.5 | [-20 -24 25⟩, [77 -31 -12⟩ | [⟨1063 1685 2468]] | -0.0099 | 0.0956 | 8.47 |
| 2.3.5.7 | 2401/2400, 3500000000/3486784401, 3367254360064/3363025078125 | [⟨1063 1685 2468 2984]] | +0.0144 | 0.0930 | 8.24 |
| 2.3.5.7.11 | 2401/2400, 19712/19683, 43923/43904, 1953125/1951488 | [⟨1063 1685 2468 2984 3677]] | +0.0361 | 0.0937 | 8.30 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 229\1063 | 258.514 | [-32 13 5⟩ | Lafa |
| 1 | 280\1063 | 316.087 | 6/5 | Counterhanson |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct