Sharpness: Difference between revisions
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The '''sharpness''' of an [[EDO|edo]] is the number of | The '''sharpness''' of an [[EDO|edo]] is the number of edosteps to which it maps the chromatic semitone aka 3-limit augmented unison aka apotome ([[2187/2048]]). In other words, it is the difference between seven of its best approximation of [[3/2]] and four octaves. | ||
For example, [[12edo]] maps the apotome to one step; it has a sharpness of 1, thus it is a sharp-1 edo. On the other hand, [[17edo]] maps the apotome to two steps, so it is a sharp-2 edo. | For example, [[12edo]] maps the apotome to one step; it has a sharpness of 1, thus it is a sharp-1 edo. On the other hand, [[17edo]] maps the apotome to two steps, so it is a sharp-2 edo. | ||
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=== Further generalizations === | |||
The concept of sharpness can be generalized further to '''dodeca-sharpness''', which is the number of edosteps that the pythagorean comma maps to. For example, 17, 29 and 41 are dodeca-sharp-1 edos, while 19, 31 and 43 are dodeca-flat-1 edos. | |||
The concept can be generalized even further to 17fold-sharpness, 19fold-sharpness, etc. | |||
== See also == | == See also == | ||