133edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''133edo''' is the [[EDO|equal division of the octave]] into 133 parts of 9.0226 cents each. It tempers out 393216/390625 (Würschmidt comma) and 131072000/129140163 (rodan comma) in the 5-limit.
{{EDO intro}}


Using the patent val, it supports [[superenneadecal]], it tempers out 245/243, 1029/1024 and 395136/390625 in the 7-limit; 385/384, 441/440, 896/891 and 43923/43750 in the 11-limit; 196/195, 325/324, 352/351, 364/363 and 3146/3125 in the 13-limit.
The equal temperament [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and 131072000/129140163 (rodan comma) in the 5-limit.  


Using the 133d val, it supports [[enneadecal]], it tempers 1728/1715, 4000/3969 and 4375/4374.
Using the [[patent val]], it tempers out [[245/243]], [[1029/1024]] and 395136/390625 in the 7-limit; [[385/384]], [[441/440]], [[896/891]] and 43923/43750 in the 11-limit; [[196/195]], [[325/324]], [[352/351]], [[364/363]] and 3146/3125 in the 13-limit. It [[support]]s [[rodan]] and [[superenneadecal]].  


Using the 133d val, it tempers out [[1728/1715]], [[4000/3969]] and [[4375/4374]]. It supports [[enneadecal]].
=== Odd harmonics ===
{{Harmonics in equal|133}}
{{Harmonics in equal|133}}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Revision as of 16:15, 27 May 2024

← 132edo 133edo 134edo →
Prime factorization 7 × 19
Step size 9.02256 ¢ 
Fifth 78\133 (703.759 ¢)
Semitones (A1:m2) 14:9 (126.3 ¢ : 81.2 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

The equal temperament tempers out 393216/390625 (würschmidt comma) and 131072000/129140163 (rodan comma) in the 5-limit.

Using the patent val, it tempers out 245/243, 1029/1024 and 395136/390625 in the 7-limit; 385/384, 441/440, 896/891 and 43923/43750 in the 11-limit; 196/195, 325/324, 352/351, 364/363 and 3146/3125 in the 13-limit. It supports rodan and superenneadecal.

Using the 133d val, it tempers out 1728/1715, 4000/3969 and 4375/4374. It supports enneadecal.

Odd harmonics

Approximation of prime harmonics in 133edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +1.80 +1.66 -3.41 -0.94 -1.43 +3.32 +0.23 +3.30 -1.01 +0.83
Relative (%) +0.0 +20.0 +18.4 -37.8 -10.4 -15.8 +36.7 +2.6 +36.6 -11.1 +9.2
Steps
(reduced)
133
(0)
211
(78)
309
(43)
373
(107)
460
(61)
492
(93)
544
(12)
565
(33)
602
(70)
646
(114)
659
(127)