22L 1s: Difference between revisions
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| Pattern = LLL...22x...LLLs | | Pattern = LLL...22x...LLLs | ||
| Other names = quartismoid | |||
}} | }} | ||
{{MOS intro}} | |||
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. | |||
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 | 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 == | |||
{{TAMNAMS use}} | |||
=== Intervals === | |||
{{MOS intervals}} | |||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
== Scale tree == | == Scale tree == | ||
{ | {{MOS tuning spectrum}} | ||
== See also == | |||
==See also== | |||
* [[33/32]] | * [[33/32]] | ||
* [[33/32 equal step tuning]] | * [[33/32 equal step tuning]] | ||