1407edo: Difference between revisions
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! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
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! Temperaments | ! Temperaments | ||
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<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[Category:Akjayland]] | [[Category:Akjayland]] | ||
Revision as of 13:25, 16 November 2024
| ← 1406edo | 1407edo | 1408edo → |
Theory
1407edo is excellent in the 7-limit, in which it supports the 441 & 966 akjayland temperament with period 21. Just like 441edo, it tempers out the akjaysma and the landscape comma. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.
It tunes the pure bastille temperament in the 1407eff val and the marvelous bastille temperament in the patent val in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.036 | +0.040 | +0.044 | -0.358 | +0.411 | -0.051 | +0.142 | +0.297 | -0.153 | +0.380 |
| Relative (%) | +0.0 | -4.2 | +4.7 | +5.2 | -42.0 | +48.1 | -6.0 | +16.6 | +34.8 | -17.9 | +44.6 | |
| Steps (reduced) |
1407 (0) |
2230 (823) |
3267 (453) |
3950 (1136) |
4867 (646) |
5207 (986) |
5751 (123) |
5977 (349) |
6365 (737) |
6835 (1207) |
6971 (1343) | |
Subsets and supersets
Since 1407 factors into 3 × 7 × 67, 1407edo has subset edos 3, 7, 21, 67, 201, and 469.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 814\1407 | 694.243 | [381 0 -159 -4⟩ | Bastille (2.5.7) / pure bastille (1407eff) / marvelous bastille (1407) |
| 3 | 292\1407 | 249.040 | 1536/1331 | Tribilo |
| 7 | 10\1407 | 8.529 | 1029/1024 | Nitrogen |
| 21 | 686\1407 (16\1407) |
585.074 (13.646) |
91875/65536 (126/125) |
Akjayland |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct