204edo: Difference between revisions
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|204}} | {{Harmonics in equal|204}} | ||
=== Subsets and supersets === | |||
Since 204 factors into {{factorization|204}}, 204edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 17, 34, 51, 68, and 102 }}. | |||
Revision as of 12:05, 13 April 2024
| ← 203edo | 204edo | 205edo → |
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
| 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) | |
Subsets and supersets
Since 204 factors into 22 × 3 × 17, 204edo has subset edos 2, 3, 4, 6, 12, 17, 34, 51, 68, and 102.