1407edo: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
table |
||
| Line 10: | Line 10: | ||
1407's divisors are {{EDOs|1, 3, 7, 21, 67, 201, 469}}. | 1407's divisors are {{EDOs|1, 3, 7, 21, 67, 201, 469}}. | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 814\1407 | |||
| 694.243 | |||
| {{Monzo|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 | |||
| 215\441<br>(5\441) | |||
| 585.03<br>(13.61) | |||
| 91875/65536<br>(126/125) | |||
| [[Akjayland]] | |||
|} | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
[[Category:Akjayland]] | [[Category:Akjayland]] | ||
Revision as of 13:42, 26 March 2023
| ← 1406edo | 1407edo | 1408edo → |
Theory
| 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) | |
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.
1407's divisors are 1, 3, 7, 21, 67, 201, 469.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
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 | 215\441 (5\441) |
585.03 (13.61) |
91875/65536 (126/125) |
Akjayland |