204edo: Difference between revisions
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204edo is the first merger of [[12edo]] and [[17edo]]. Using the [[patent val]], it [[tempering out|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo| 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 [[support]]s the 7-limit [[semisept]] temperament, and the alternative 204e val can support the 11-limit semisept. It supports [[Substitute harmonic#Intercom|intercom]] temperament. | 204edo is the first merger of [[12edo]] and [[17edo]]. Using the [[patent val]], it [[tempering out|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo| 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 [[support]]s the 7-limit [[semisept]] temperament, and the alternative 204e val can support the 11-limit semisept. It supports [[Substitute harmonic#Intercom|intercom]] temperament. | ||
Latest revision as of 22:40, 20 February 2025
| ← 203edo | 204edo | 205edo → |
204 equal divisions of the octave (abbreviated 204edo or 204ed2), also called 204-tone equal temperament (204tet) or 204 equal temperament (204et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 204 equal parts of about 5.88 ¢ each. Each step represents a frequency ratio of 21/204, or the 204th root of 2.
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.