22L 1s: Difference between revisions

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| nSmallSteps = 1

| Equalized = 1

| ~~Paucitonic~~ = 1

| Collapsed = 1

| Pattern = LLL...22x...LLLs

| Other names = quartismoid

}}

~~22L 1s is the~~ scale ~~that~~ is ~~most commonly~~ produced by stacking the interval of [[33/32]]. If it ~~had~~ a ~~name~~, ~~it would most probably be alpharabian or quartismoid~~, ~~since five 33~~/~~32s are often~~ equal to 7/6.

==See also==

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.

== Tuning ranges ==

=== Mavila fifth and 91edo (Ultrasoft and supersoft) ===

Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth, which corresponds to the ultrasoft step ratio range. 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.

=== Diatonic fifth (hard of supersoft) ===

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{{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{{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]].

== Relation to other equal divisions ==

6 steps act as a pseudo-6/5, and when they actually act as 6/5 along with 5 steps being equal to 7/6, [[385/384]] is tempered out. If one were to instead tune in favour of 6/5 instead of 7/6, the resulting hardness would be around 1.233. 114edo and 137edo represent this the best.

== Scale properties ==

=== Intervals ===

=== Generator chain ===

=== Modes ===

== Scale tree ==

== See also ==

* [[33/32]]

* [[33/32 equal-step tuning]]

* [[33/32 equal step tuning]]

@@ Line 4: / Line 4: @@
 | nSmallSteps = 1
 | Equalized = 1
-| Paucitonic = 1
+| Collapsed = 1
 | Pattern = LLL...22x...LLLs
+| Other names = quartismoid
 }}
-L 1s is the scale that is most commonly produced by stacking the interval of [[33/32]]. If it had a name, it would most probably be alpharabian or quartismoid, since five 33/32s are often equal to 7/6.
+{{MOS intro}}
-==See also==
+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.
+== Tuning ranges ==
+=== Mavila fifth and 91edo (Ultrasoft and supersoft) ===
+Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth, which corresponds to the ultrasoft step ratio range. 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.
+=== Diatonic fifth (hard of supersoft) ===
+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{{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{{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]].
+== Relation to other equal divisions ==
+steps act as a pseudo-6/5, and when they actually act as 6/5 along with 5 steps being equal to 7/6, [[385/384]] is tempered out. If one were to instead tune in favour of 6/5 instead of 7/6, the resulting hardness would be around 1.233. 114edo and 137edo represent this the best.
+== Scale properties ==
+{{TAMNAMS use}}
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
+== Scale tree ==
+{{MOS tuning spectrum}}
+== See also ==
 * [[33/32]]
-* [[33/32 equal-step tuning]]
+* [[33/32 equal step tuning]]