150edo: Difference between revisions

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==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.

== 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 ===

==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"

|+Table of rank-2 temperaments by generator

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| 8/7

| [[Mothra]] (150be)

~~[[Category:Equal divisions of the octave~~|~~###]] ~~

|}

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 {{Infobox ET}}
 {{EDO intro|150}}
-==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.
+== 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}}
-==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"
 |+Table of rank-2 temperaments by generator
@@ Line 25: / Line 32: @@
 | 8/7
 | [[Mothra]] (150be)
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+|}