150edo: Difference between revisions

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==Theory==
==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.
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.
{{Harmonics in equal|150|columns=10}}
==Regular temperament properties==
==Regular temperament properties==
===Rank-2 temperaments===
===Rank-2 temperaments===

Revision as of 05:12, 2 August 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.

Approximation of odd harmonics in 150edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error Absolute (¢) +2.04 -2.31 -0.83 -3.91 +0.68 -0.53 -0.27 -0.96 -1.51 +1.22
Relative (%) +25.6 -28.9 -10.3 -48.9 +8.5 -6.6 -3.4 -11.9 -18.9 +15.2
Steps
(reduced)
238
(88)
348
(48)
421
(121)
475
(25)
519
(69)
555
(105)
586
(136)
613
(13)
637
(37)
659
(59)

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)