150edo: Difference between revisions

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== 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 ~~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.

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== Regular temperament properties ==

=== Rank-2 temperaments ===

{{rank-2 ~~begin}}~~

{| class="wikitable center-all left-5"

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

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Temperaments

|-

| 1

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|-

| 10

| ~~31\150 (~~1\150)

| 1\150

| ~~248.00 (~~8.00)

| 8.00

| ~~15/13 (176~~/~~175)~~

| 225/224

| [[Decoid]] (150e)

~~{{rank~~-~~2 end}~~}

|-

~~{{orf}}~~

| 30

| 1\150

| 8.00

| 225/224

| [[Triacontoid]]

|}

<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|150}}
+{{ED intro}}
 == 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 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.
@@ Line 15: / Line 15: @@
 == Regular temperament properties ==
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| 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
@@ Line 30: / Line 37: @@
 |-
 | 10
-| 31\150<br />(1\150)
+| 1\150
-| 248.00<br />(8.00)
+| 8.00
-| 15/13<br />(176/175)
+| 225/224
 | [[Decoid]] (150e)
-{{rank-2 end}}
+|-
-{{orf}}
+| 30
+| 1\150
+| 8.00
+| 225/224
+| [[Triacontoid]]
+|}
+<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]