961edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
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| 0.1008 | | 0.1008 | ||
| 8.01 | | 8.01 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 62: | Line 48: | ||
| 4/3 | | 4/3 | ||
| [[Pontiac]] | | [[Pontiac]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Scales == | == Scales == | ||
Revision as of 02:13, 16 November 2024
| ← 960edo | 961edo | 962edo → |
Theory
961edo has a reasonable 7-limit interpretation. The equal temperament tempers out the schisma in the 5-limit; 4375/4374, 65625/65536, and 14348907/14336000 in the 7-limit, supporting pontiac, the 395 & 566 temperament.
In the 11-limit, the 961e val ⟨961 1523 2231 2698 3324] scores the best, which tempers out 102487/102400 and 234375/234256. It prompts us to consider the 961de val ⟨961 1523 2231 2697 3324], which tempers out 3025/3024 and 184877/184320. The patent val ⟨961 1523 2231 2698 3325] tempers out 4000/3993 and 46656/46585.
It works much better as a 2.3.5.7.13.17 subgroup temperament, in which case it tempers out 10985/10976, 1275/1274, 2025/2023 and 4914/4913.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.186 | -0.466 | +0.165 | -0.372 | +0.607 | -0.153 | +0.597 | -0.065 | -0.323 | -0.021 | -0.179 |
| Relative (%) | -14.9 | -37.3 | +13.2 | -29.8 | +48.6 | -12.3 | +47.8 | -5.2 | -25.8 | -1.7 | -14.3 | |
| Steps (reduced) |
1523 (562) |
2231 (309) |
2698 (776) |
3046 (163) |
3325 (442) |
3556 (673) |
3755 (872) |
3928 (84) |
4082 (238) |
4221 (377) |
4347 (503) | |
Subsets and supersets
Since 961 factors into 312, 961edo has 31edo as its subset edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-1523 961⟩ | [⟨961 1523]] | 0.0587 | 0.0587 | 4.70 |- | 2.3.5 | 32805/32768, [-22 -137 103⟩ | [⟨961 1523 2231]] | 0.1060 | 0.0823 | 6.59 |- | 2.3.5.7 | 4375/4374, 32805/32768, [15 9 14 -22⟩ | [⟨961 1523 2231 2698]] | 0.0648 | 0.1008 | 8.01 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 399\961 | 498.231 | 4/3 | Pontiac Template:Rank-2 end Template:Orf