150edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
=== 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 34: | Line 41: | ||
| 15/13<br />(176/175) | | 15/13<br />(176/175) | ||
| [[Decoid]] (150e) | | [[Decoid]] (150e) | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
Revision as of 13:19, 16 November 2024
| ← 149edo | 150edo | 151edo → |
Theory
150edo is contorted in the 5-limit, tempering out the same commas as 75edo, including 20000/19683 and 2109375/2097152. However, every 11th step of 150edo is equal to the 88cET nonoctave tuning, which is also represented as octacot through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88 cents provides a generator.
The equal temperament tempers out 245/243, 2401/2400, and 4000/3969 in the 7-limit, 385/384, 896/891, and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.04 | -2.31 | -0.83 | -3.91 | +0.68 | -0.53 | -0.27 | -0.96 | -1.51 | +1.22 |
| Relative (%) | +25.6 | -28.9 | -10.3 | -48.9 | +8.5 | -6.6 | -3.4 | -11.9 | -18.9 | +15.2 | |
| Steps (reduced) |
238 (88) |
348 (48) |
421 (121) |
475 (25) |
519 (69) |
555 (105) |
586 (136) |
613 (13) |
637 (37) |
659 (59) | |
Subsets and supersets
Since 150 factors into 2 × 3 × 52, 150edo has subset edos 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 11\150 | 88.00 | 21/20 | Octacot (150e) / october (150) |
| 1 | 29\150 | 232.00 | 8/7 | Quadrawell |
| 10 | 31\150 (1\150) |
248.00 (8.00) |
15/13 (176/175) |
Decoid (150e) |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct