150edo: Difference between revisions

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{{Infobox ET}}
{{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 -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Revision as of 13:28, 19 February 2023

← 149edo 150edo 151edo →
Prime factorization 2 × 3 × 52
Step size 8 ¢ 
Fifth 88\150 (704 ¢) (→ 44\75)
Semitones (A1:m2) 16:10 (128 ¢ : 80 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO 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 134-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 Tetracot family, for which 88 cents provides a generator.

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 11\150 88.00 21/20 Octacot (150e) / october (150)
1 29\150 232.00 8/7 Mothra (150be)
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