150edo: Difference between revisions

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~~'''~~150edo~~'''~~ is ~~the [[~~equal ~~division of the octave]] into 150 equal steps exactly 8 cents each. This means eleven such steps are 88 cents, relating 150edo~~ to the [[88cET|88cET]] nonoctave tuning. 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|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.

==Regular temperament properties==

===Rank-2 temperaments===

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

|+Table of rank-2 temperaments by generator

! Periods<br>per 8ve

! Generator<br>(Reduced)

! Cents<br>(Reduced)

! Associated<br>Ratio

! Temperaments

|-

| 1

| 11\150

| 88.00

| 21/20

| [[Octacot]] (150e) / [[october]] (150)

|-

| 1

| 29\150

| 232.00

| 8/7

| [[Mothra]] (150be)

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

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 {{Infobox ET}}
-'''150edo''' is the [[equal division of the octave]] into 150 equal steps exactly 8 cents each. This means eleven such steps are 88 cents, relating 150edo to the [[88cET|88cET]] nonoctave tuning. 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.
+{{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.
+==Regular temperament properties==
+===Rank-2 temperaments===
+{| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+! Periods<br>per 8ve
+! Generator<br>(Reduced)
+! Cents<br>(Reduced)
+! Associated<br>Ratio
+! Temperaments
+|-
+| 1
+| 11\150
+| 88.00
+| 21/20
+| [[Octacot]] (150e) / [[october]] (150)
+|-
+| 1
+| 29\150
+| 232.00
+| 8/7
+| [[Mothra]] (150be)
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->