41edo: Difference between revisions

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== Approximation to JI ==

=== ~~15-odd-limit interval~~ mappings ===

=== Interval mappings ===

~~The following table shows how [[15~~-odd-limit intervals~~]] are represented in 41edo. Prime harmonics are in '''bold'''.~~ As 41edo is consistent in the 15-odd-limit, the results by direct approximation and patent val mapping are the same.

{{Q-odd-limit intervals|41|note=As 41edo is consistent in the 15-odd-limit, the results by direct approximation and patent val mapping are the same. }}

~~{{15-odd-limit|41~~}}

== Relationship to 12-edo ==

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.

@@ Line 681: / Line 681: @@
 == Approximation to JI ==
-=== 15-odd-limit interval mappings ===
+=== Interval mappings ===
-The following table shows how [[15-odd-limit intervals]] are represented in 41edo. Prime harmonics are in '''bold'''. As 41edo is consistent in the 15-odd-limit, the results by direct approximation and patent val mapping are the same.
+{{Q-odd-limit intervals|41|note=As 41edo is consistent in the 15-odd-limit, the results by direct approximation and patent val mapping are the same. }}
-{{15-odd-limit|41}}
 == Relationship to 12-edo ==
 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.