31edo: Difference between revisions

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Undo revision 207283 by VectorGraphics (talk) Inaccurate statement about spiral charts
Tag: Undo
Still attempting to compromise on the spiral thing
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== Relationship to 12edo ==
== Relationship to 12edo ==
31edo’s [[circle of fifths|circle of 31 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This is possible because 18\31 is on the 7\12 kite in the [[scale tree]]. Stated another way, it is possible because the absolute value of 31edo’s [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) is 1.  
31edo’s [[circle of fifths|circle of 31 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. In Kite Giedraitis' theory, this is possible because going up 12 fifths in 31edo yields a difference (the absolute value of the [[Sharpness|dodeca-sharpness]]) of 1 edostep (which also implies that 18\31 is on the 7\12 kite in the [[scale tree]]).  


This "spiral of fifths" can be a useful construct for introducing 31edo 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.
This "spiral of fifths" can be a useful construct for introducing 31edo 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.