22L 1s: Difference between revisions

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=== 13edf ===

From 1\22 to 4\91, 13 steps amount to a diatonic fifth. Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth. In 91edo, the fifth produced by 13 steps is the same as 4 steps of 7 edo, and thus is the boundary between mavila and diatonic.

~~Further breaking down the categories, when the step ratio is greater than~~ 4~~.472~~, ~~then~~ 13 ~~generators~~ amount to a ~~superpyth~~ fifth ~~and~~ the ~~tuning approaches~~ [[~~22edo~~]].

==== Mavila fifth and 91edo ====

Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth. In [[91edo]], the fifth produced by 13 steps of the quartismoid scale is the same as 4 steps of [[7edo]], and thus is the exact boundary between mavila and diatonic.

In 156edo, the fifth becomes the [[12edo]] 700-cent fifth.

==== Diatonic fifth ====

From 1\22 to 4\91, 13 steps amount to a diatonic fifth.

If the pure 33/32 is used as a generator, the resulting fifth is 692.54826 cents, which puts it in the category around flattone.

==== 700-cent, just, and superpyth fifths ====

In 156edo, the fifth becomes the [[12edo]] 700-cent fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a convergent denominator to the approximation of log2(3/2).

When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].

=== 6ed6/5 ===

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| || || ||5\112|| || ||5||2||2.500

|13 steps adding to 1/4 comma meantone fifth

|13 steps adding to 1/4 comma meantone fifth is around here

is around here

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| || || || || ||13\291||13||5||2.600

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|13 steps adding to a 700 cent fifth is here

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@@ Line 12: / Line 12: @@
 === 13edf ===
-From 1\22 to 4\91, 13 steps amount to a diatonic fifth. Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth. In 91edo, the fifth produced by 13 steps is the same as 4 steps of 7 edo, and thus is the boundary between mavila and diatonic.
-Further breaking down the categories, when the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].
+==== Mavila fifth and 91edo ====
+Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth. In [[91edo]], the fifth produced by 13 steps of the quartismoid scale is the same as 4 steps of [[7edo]], and thus is the exact boundary between mavila and diatonic.
-In 156edo, the fifth becomes the [[12edo]] 700-cent fifth.
+==== Diatonic fifth ====
+From 1\22 to 4\91, 13 steps amount to a diatonic fifth.
+If the pure 33/32 is used as a generator, the resulting fifth is 692.54826 cents, which puts it in the category around flattone.
+==== 700-cent, just, and superpyth fifths ====
+In 156edo, the fifth becomes the [[12edo]] 700-cent fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a convergent denominator to the approximation of log2(3/2).
+When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].
 === 6ed6/5 ===
@@ Line 98: / Line 106: @@
 |-
 | || || ||5\112|| || ||5||2||2.500
-|13 steps adding to 1/4 comma meantone fifth
+|13 steps adding to 1/4 comma meantone fifth is around here
-is around here
 |-
 | || || || || ||13\291||13||5||2.600
@@ Line 117: / Line 124: @@
 |-
 | || || || ||7\156|| ||7||2||3.500
-|
+|13 steps adding to a 700 cent fifth is here
 |-
 | || || || || ||11\245||11||3||3.667