21L 1s: Difference between revisions

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| Collapsed = 1

| Pattern = LLL...21x...LLLs

| Other names = tricesimoprimal quartertonic

| Other names = escapist,<br> tricesimoprimal quartertonic

}}

~~21L 1s is~~ the ~~scale that~~ is ~~most commonly produced~~ by ~~stacking~~ the ~~interval of~~ [[32/31]] or [[31/30]].

[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum; [[User:Lériendil|Lériendil]] proposes '''noletic''' for similar reasons, as 9 generators reach a diatonic [[4/3]], supporting the scale [[9ed4/3]] known also as "noleta".

A name '''tricesimoprimal quartertonic''~~' is proposed~~ for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/~~960 - the~~ tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.

[[User:Moremajorthanmajor|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960—the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.

==Tuning ranges==

== Tuning ranges ==

The scale's approach to standard harmony can be considered based on the mode.

=== Diatonic fifth and 65edo (Ultrasoft and supersoft) ===

=== Brighter modes ===

==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ====

Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth.

If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth.

=== Fifth-sixth (hard of supersoft) ===

==== Fifth-sixth (hard of supersoft) ====

From 1\21 to 3\65, 13 steps amount to a fifth-sixth.

If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora.

=== Darker modes ===

If instead the small step is stacked down, this enables the scale to approximate the standard 4:5:6 and 10:12:15 triads, as the [[escapade]] temperament does.

The escapade temperament reaches 4/3 in 9 gensteps, meaning that modes from Hermit (12|9) onward support a perfect fifth from the tonic. This also enables the modes from Hermit through Temperance (7|14) to support the major triad, 4:5:6, and from Devil (6|15) onward to support the minor triad, 10:12:15. The 700 cent fifth is supported in [[108edo]], stacking steps of 5\108 downward.

== Relation to other equal divisions ==

2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.

== Scale properties ==

=== Intervals ===

=== Generator chain ===

=== Modes ===

== Proposed mode names ===

The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them.

{| class="wikitable"

|-

! Mode

! Name

|-

| 21{{pipe}}0

| Foolish

|-

| 20{{pipe}}1

| Magical

|-

| 19{{pipe}}2

| High Priestess's

|-

| 18{{pipe}}3

| Empress's

|-

| …

|-

| 3{{pipe}}19

| Lunar

|-

| 2{{pipe}}19

| Solar

|-

| 1{{pipe}}20

| Judgemental

|-

| 0{{pipe}}21

| Worldwide

|}

== Intervals ==

== Scale tree ==

== See also ==

* [[32/31]]

* [[31/30]]

* [[Escapade]]

@@ Line 6: / Line 6: @@
 | Collapsed = 1
 | Pattern = LLL...21x...LLLs
-| Other names = tricesimoprimal quartertonic
+| Other names = escapist,<br> tricesimoprimal quartertonic
 }}
-L 1s is the scale that is most commonly produced by stacking the interval of [[32/31]] or [[31/30]].
+{{MOS intro}}
+[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum; [[User:Lériendil|Lériendil]] proposes '''noletic''' for similar reasons, as 9 generators reach a diatonic [[4/3]], supporting the scale [[9ed4/3]] known also as "noleta".
-A name '''tricesimoprimal quartertonic''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960 - the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.
+[[User:Moremajorthanmajor|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960—the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.
-==Tuning ranges==
+== Tuning ranges ==
+The scale's approach to standard harmony can be considered based on the mode.
-=== Diatonic fifth and 65edo (Ultrasoft and supersoft) ===
+=== Brighter modes ===
+==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ====
 Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth.
 If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth.
-=== Fifth-sixth (hard of supersoft) ===
+==== Fifth-sixth (hard of supersoft) ====
 From 1\21 to 3\65, 13 steps amount to a fifth-sixth.
 If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora.
+=== Darker modes ===
+If instead the small step is stacked down, this enables the scale to approximate the standard 4:5:6 and 10:12:15 triads, as the [[escapade]] temperament does.
+The escapade temperament reaches 4/3 in 9 gensteps, meaning that modes from Hermit (12|9) onward support a perfect fifth from the tonic. This also enables the modes from Hermit through Temperance (7|14) to support the major triad, 4:5:6, and from Devil (6|15) onward to support the minor triad, 10:12:15. The 700 cent fifth is supported in [[108edo]], stacking steps of 5\108 downward.
 == Relation to other equal divisions ==
 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.
+== Scale properties ==
+{{TAMNAMS use}}
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
+== Proposed mode names ===
+The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them.
+{| class="wikitable"
+|-
+! Mode
+! Name
+|-
+| 21{{pipe}}0
+| Foolish
+|-
+| 20{{pipe}}1
+| Magical
+|-
+| 19{{pipe}}2
+| High Priestess's
+|-
+| 18{{pipe}}3
+| Empress's
+|-
+| …
+| …
+|-
+| 3{{pipe}}19
+| Lunar
+|-
+| 2{{pipe}}19
+| Solar
+|-
+| 1{{pipe}}20
+| Judgemental
+|-
+| 0{{pipe}}21
+| Worldwide
+|}
+== Intervals ==
+{{MOS intervals}}
+== Scale tree ==
+{{MOS tuning spectrum}}
+== See also ==
+* [[32/31]]
+* [[31/30]]
+* [[Escapade]]