31edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
Reword “relationship to 12” section based on what I learned from TallKite’s user page, to hopefully make this section less potentially misleading and controversial, while preserving the heart of what it’s supposed to be about. Also moved the second chart to the notation section because it seems to belong there rather than where it was. |
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* E𝄪 = F{{demisharp2}} | * E𝄪 = F{{demisharp2}} | ||
* F𝄫 = E{{demiflat2}} | * F𝄫 = E{{demiflat2}} | ||
31edo can be notated with a seperate semi/sesqui sharp/flat chain (like [[17edo]]), with its own enharmonic circle of fifths. | |||
[[File:31edo CoF semi and sesqui.png|none|thumb|500x500px]] | |||
=== Sagittal notation === | === Sagittal notation === | ||
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[[File:31edo Sagittal.png|800px]] | [[File:31edo Sagittal.png|800px]] | ||
== Relationship to | == 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. | |||
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. | |||
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:31-edo spiral.png|582x582px]] | [[File:31-edo spiral.png|582x582px]] | ||
== Scales == | == Scales == | ||