150edo: Difference between revisions
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Cleanup; +subsets and supersets |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|150}} | {{EDO intro|150}} | ||
==Theory== | |||
Every 11th step of 150edo is equal to the [[ | == 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 13-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 octacot, for which 88 cents provides a generator. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|150|columns=10}} | {{Harmonics in equal|150|columns=10}} | ||
==Regular temperament properties== | |||
===Rank-2 temperaments=== | === Subsets and supersets === | ||
Since 150 factors into 2 × 3 × 5<sup>2</sup>, 150edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75 }}. | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
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| 8/7 | | 8/7 | ||
| [[Mothra]] (150be) | | [[Mothra]] (150be) | ||
|} | |||
Revision as of 06:38, 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 13-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 octacot, for which 88 cents provides a generator.
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 (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) |