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 ==

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 ===

==Regular temperament properties==

===Rank-2 temperaments===

=== Subsets and supersets ===

Since 150 factors into 2 × 3 × 52, 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

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

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| 232.00

| 8/7

| [[~~Mothra~~]] (~~150be~~)

| [[Quadrawell]]

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

|-

| 10

| 31\150 (1\150)

| 248.00 (8.00)

| 15/13 (176/175)

| [[Decoid]] (150e)

|}

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|150}}
+{{ED intro}}
-==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 ==
+edo 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}}
-==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
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 24: / Line 34: @@
 | 232.00
 | 8/7
-| [[Mothra]] (150be)
+| [[Quadrawell]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+|-
+| 10
+| 31\150<br />(1\150)
+| 248.00<br />(8.00)
+| 15/13<br />(176/175)
+| [[Decoid]] (150e)
+|}
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct