150edo: Difference between revisions

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== 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.

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 ===

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=== 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]]

|-

| 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]] 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.
+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 ===
@@ Line 14: / Line 16: @@
 === 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 31: / Line 34: @@
 | 232.00
 | 8/7
-| [[Mothra]] (150be)
+| [[Quadrawell]]
+|-
+| 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