Hemipyth: Difference between revisions
List edo mappings up to 13b. |
Complete edo table up to 24. |
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Many temperaments naturally produce intervals that split ~3/2, ~2 or ~4/3 exactly in half and can thus be interpreted as neutral thirds, semioctaves or semifourths within the temperament. | Many temperaments naturally produce intervals that split ~3/2, ~2 or ~4/3 exactly in half and can thus be interpreted as neutral thirds, semioctaves or semifourths within the temperament. | ||
== Equal temperaments == | |||
An important property of edos > 1 is that they must by necessity include at least one of the notable hemipyth intervals: | An important property of edos > 1 is that they must by necessity include at least one of the notable hemipyth intervals: | ||
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| 13b || no || no || yes | | 13b || no || no || yes | ||
|- | |||
| 14 || yes || yes || yes | |||
|- | |||
| 15 || no || no || yes | |||
|- | |||
| 16 || yes || no || no | |||
|- | |||
| 17 || no || yes || no | |||
|- | |||
| 18 || yes || no || no | |||
|- | |||
| 18b || yes || yes || yes | |||
|- | |||
| 19 || no || yes || no | |||
|- | |||
| 20* || yes || yes || yes | |||
|- | |||
| 20b || yes || no || no | |||
|- | |||
| 21 || no || yes || no | |||
|- | |||
| 22 || yes || no || no | |||
|- | |||
| 23 || no || no || yes | |||
|- | |||
| 24 || yes || yes || yes | |||
|} | |} | ||
<nowiki>*</nowiki>) Above the patent val of 20edo results in the same tuning as the patent val of 10edo, so it adds nothing new. | |||
Note how in hemipyth the patent val of 24edo is not tuned the same as 12edo's patent val. In fact 24edo is arguably the smallest edo where all of the important hemipyth intervals are tuned reasonably accurately. | |||