150edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
[[ | == 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{{c}} 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 === | |||
{{Harmonics in equal|150|columns=10}} | |||
=== 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" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 11\150 | |||
| 88.00 | |||
| 21/20 | |||
| [[Octacot]] (150e) / [[october]] (150) | |||
|- | |||
| 1 | |||
| 29\150 | |||
| 232.00 | |||
| 8/7 | |||
| [[Quadrawell]] | |||
|- | |||
| 10 | |||
| 1\150 | |||
| 8.00 | |||
| 225/224 | |||
| [[Decoid]] (150e) | |||
|- | |||
| 30 | |||
| 1\150 | |||
| 8.00 | |||
| 225/224 | |||
| [[Triacontoid]] | |||
|} | |||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||