41edo: Difference between revisions

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== Relationship to ~~12-edo~~ ==

== Relationship to 12edo ==

~~Whereas 12edo has a~~ circle of ~~twelve 5ths, 41edo has~~ a ~~<u>~~spiral~~</u>~~ of ~~twelve 5ths, since~~ 24\41 is on the 7\12 kite in the scale tree. ~~(See Chapter 5.7~~ of ~~[https://www.tallkite.com/AlternativeTunings.html Kite~~'s ~~book~~] ~~for an explanation of kites~~.) This spiral of ~~5th shows 41edo in~~ a ~~12edo-friendly format. Excellent~~ for introducing 41edo to musicians unfamiliar with microtonal music. There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 12edo. The two innermost and two outermost intervals on the spiral are duplicates.

41edo’s [[circle of fifths|circle of 41 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This is possible because 24\41 is on the 7\12 kite in the [[scale tree]]. Stated another way, it is possible because the absolute value of 41edo's [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) is 1.

This "spiral of fifths" can be a useful construct for introducing 41edo 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.

There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 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:41-edo spiral.png|579x579px]]

@@ Line 690: / Line 690: @@
 {{Q-odd-limit intervals|41}}
-== Relationship to 12-edo ==
+== Relationship to 12edo ==
-Whereas 12edo has a circle of twelve 5ths, 41edo has a <u>spiral</u> of twelve 5ths, since 24\41 is on the 7\12 kite in the scale tree. (See Chapter 5.7 of [https://www.tallkite.com/AlternativeTunings.html Kite's book] for an explanation of kites.) This spiral of 5th shows 41edo in a 12edo-friendly format. Excellent for introducing 41edo to musicians unfamiliar with microtonal music. There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 12edo. The two innermost and two outermost intervals on the spiral are duplicates.
+edo’s [[circle of fifths|circle of 41 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This is possible because 24\41 is on the 7\12 kite in the [[scale tree]]. Stated another way, it is possible because the absolute value of 41edo's [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) is 1.
+This "spiral of fifths" can be a useful construct for introducing 41edo 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.
+There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 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:41-edo spiral.png|579x579px]]