150edo: Difference between revisions
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==Theory== | ==Theory== | ||
Every 11th step of 150edo is equal to the [[88cET|88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo|75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for [[Tetracot_family#Octacot|Tetracot family]], for which 88 cents provides a generator. | Every 11th step of 150edo is equal to the [[88cET|88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo|75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for [[Tetracot_family#Octacot|Tetracot family]], for which 88 cents provides a generator. | ||
{{Harmonics in equal|150|columns=10}} | |||
==Regular temperament properties== | ==Regular temperament properties== | ||
===Rank-2 temperaments=== | ===Rank-2 temperaments=== | ||
Revision as of 05:12, 2 August 2023
| ← 149edo | 150edo | 151edo → |
Theory
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 tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is contorted in the 5-limit, tempering out the same commas as 75edo, including 20000/19683 and 2109375/2097152. It provides a good tuning for Tetracot family, for which 88 cents provides a generator.
| 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) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 11\150 | 88.00 | 21/20 | Octacot (150e) / october (150) |
| 1 | 29\150 | 232.00 | 8/7 | Mothra (150be) |