1407edo: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
1407edo is excellent in the 7-limit, in which it supports the 441 & 1407 [[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. | 1407edo is excellent in the 7-limit, in which it supports the 441 & 1407 [[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. | 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 === | |||
{{Harmonics in equal|1407}} | |||
1407's divisors are {{EDOs| | === Subsets and supersets === | ||
1407's divisors are {{EDOs| 3, 7, 21, 67, 201, 469 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 15: | Line 18: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
| Line 23: | Line 26: | ||
| 814\1407 | | 814\1407 | ||
| 694.243 | | 694.243 | ||
| {{ | | {{monzo| 381 0 -159 -4 }} | ||
| [[Bastille]] (2.5.7) / [[pure bastille]] (1407eff) / [[marvelous bastille]] (1407) | | [[Bastille]] (2.5.7) / [[pure bastille]] (1407eff) / [[marvelous bastille]] (1407) | ||
|- | |- | ||
| Line 44: | Line 47: | ||
| [[Akjayland]] | | [[Akjayland]] | ||
|} | |} | ||
[[ | <nowiki>*</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 08:06, 17 October 2023
| ← 1406edo | 1407edo | 1408edo → |
Theory
1407edo is excellent in the 7-limit, in which it supports the 441 & 1407 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
1407's divisors are 3, 7, 21, 67, 201, 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