22L 1s: Difference between revisions

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}}

This scale is produced by stacking the interval of [[33/32]] (around ~~53¢~~).

This scale is produced by stacking the interval of [[33/32]] (around 53{{c}}).

The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] ~~- five~~ 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.

The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]]—five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.

== Tuning ranges ==

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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.

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

==== 700-cent, just, and superpyth fifths (step ratio 7:2 and harder) ====

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 semiconvergent denominator to the approximation of log2(3/2).

In 156edo, the fifth becomes the [[12edo]] 700{{c}} fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a semiconvergent 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]].

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~~== Scale tree ==~~

== See also ==

~~{{Scale tree}}~~

==See also==

* [[33/32]]

* [[33/32 equal step tuning]]

@@ Line 9: / Line 9: @@
 }}
 {{MOS intro}}
-This scale is produced by stacking the interval of [[33/32]] (around 53¢).
+This scale is produced by stacking the interval of [[33/32]] (around 53{{c}}).
-The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.
+The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]]—five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.
 == Tuning ranges ==
@@ Line 20: / Line 20: @@
 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.
+If the pure 33/32 is used as a generator, the resulting fifth is 692.54826{{c}}, which puts it in the category around flattone.
 ==== 700-cent, just, and superpyth fifths (step ratio 7:2 and harder) ====
-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 semiconvergent denominator to the approximation of log2(3/2).
+In 156edo, the fifth becomes the [[12edo]] 700{{c}} fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a semiconvergent 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]].
@@ Line 39: / Line 39: @@
 {{MOS tuning spectrum}}
-== Scale tree ==
+== See also ==
-{{Scale tree}}
-==See also==
 * [[33/32]]
 * [[33/32 equal step tuning]]