53edo: Difference between revisions
m →Prime harmonics: include accurate 41, stop at 83-limit |
→Relationship to 12edo: Rewrote based on new info on Kite’s user page, to be less misleading, less controversial, and show off the use cases better |
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== Relationship to 12edo == | == Relationship to 12edo == | ||
53edo's [[circle of fifths|circle of 53 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This is possible because 31\53 is on the 7\12 kite in the [[scale tree]]. Stated another way, it is possible because the absolute value of 53edo's [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) is 1. | |||
This "spiral of fifths" can be a useful construct for introducing 53edo to musicians unfamiliar with microtonal music. It may help composers and musicians to make visual sense of the notation, and to understand what size of a jump is likely to land them where compared to 12edo. | |||
The two innermost and two outermost intervals on the spiral are duplicates, reflecting the fact that it is a repeating circle at heart and the spiral shape is only a helpful illusion. | |||
[[File:53-edo spiral.png|588x588px]] | [[File:53-edo spiral.png|588x588px]] | ||