204edo: Difference between revisions
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'''204edo''' is the [[EDO|equal division of the octave]] into 204 parts of 5.8824 [[cent]]s each. It is the first merger of [[12edo]] and [[17edo]]. Using the patent val, it tempers out 531441/524288 (pythagorean comma) and 782757789696/762939453125 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 [[Hemimean clan|semisept temperament]], and alternative 204e val can support the 11-limit semisept. | '''204edo''' is the [[EDO|equal division of the octave]] into 204 parts of 5.8824 [[cent]]s each. It is the first merger of [[12edo]] and [[17edo]]. Using the patent val, it tempers out 531441/524288 (pythagorean comma) and 782757789696/762939453125 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 [[Hemimean clan|semisept temperament]], and alternative 204e val can support the 11-limit semisept. | ||
== Harmonics += | |||
{{Harmonics in equal}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 11:01, 24 January 2024
| ← 203edo | 204edo | 205edo → |
204edo is the equal division of the octave into 204 parts of 5.8824 cents each. It is the first merger of 12edo and 17edo. Using the patent val, it tempers out 531441/524288 (pythagorean comma) and 782757789696/762939453125 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 alternative 204e val can support the 11-limit semisept.
= Harmonics +
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -2.0 | +13.7 | +31.2 | +48.7 | -40.5 | -5.0 | +2.5 | -28.3 | -29.6 | -45.0 |
| Relative (%) | +0.0 | -2.0 | +13.7 | +31.2 | +48.7 | -40.5 | -5.0 | +2.5 | -28.3 | -29.6 | -45.0 | |
| Steps (reduced) |
12 (0) |
19 (7) |
28 (4) |
34 (10) |
42 (6) |
44 (8) |
49 (1) |
51 (3) |
54 (6) |
58 (10) |
59 (11) | |