53edo: Difference between revisions

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m Prime harmonics: include accurate 41, stop at 83-limit
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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 ==
Whereas 12edo has a circle of twelve 5ths, 53edo has a spiral of twelve 5ths (since 31\53 is on the 7\12 kite in the scale tree). This shows 53edo in a 12edo-friendly format. Excellent for introducing 53edo to musicians unfamiliar with microtonal music. The two innermost and two outermost intervals on the spiral are duplicates.
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]]