204edo

Revision as of 12:02, 13 April 2024 by FloraC (talk | contribs) (Cleanup)
← 203edo 204edo 205edo →
Prime factorization 22 × 3 × 17
Step size 5.88235 ¢ 
Fifth 119\204 (700 ¢) (→ 7\12)
Semitones (A1:m2) 17:17 (100 ¢ : 100 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

204edo is the first merger of 12edo and 17edo. Using the patent val, it tempers out 531441/524288 (Pythagorean comma) and [30 6 -17 in the 5-limit; 1728/1715, 3136/3125 and 14348907/14049280 in the 7-limit; 441/440, 1944/1925, 5632/5625, and 35937/35840 in the 11-limit. It supports the 7-limit semisept temperament, and the alternative 204e val can support the 11-limit semisept. It supports intercom temperament.

Odd harmonics

Approximation of odd harmonics in 204edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.96 +1.92 +1.76 +1.97 +1.62 +0.65 -0.03 +0.93 +2.49 -0.19 +1.14
Relative (%) -33.2 +32.7 +30.0 +33.5 +27.6 +11.0 -0.6 +15.8 +42.3 -3.3 +19.3
Steps
(reduced)
323
(119)
474
(66)
573
(165)
647
(35)
706
(94)
755
(143)
797
(185)
834
(18)
867
(51)
896
(80)
923
(107)