22L 1s: Difference between revisions

Line 9:

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 '''quartismoid''', since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6.

==~~Relation to equal divisions~~==

==Tuning ranges==

=== ~~13edf~~ ===

=== 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.

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

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

~~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.~~

~~==== 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.

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 ====

==== 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 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 =~~==

== 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.

== Modes ==

Eliora proposes naming the brightest mode Alpharabian, after the fact that 33/32 is called Al-Farabi quarter-tone, and the rest after Tarot Major Arcana adjectivals based on how many generators down there is.

{| class="wikitable"

|+

!Mode

!Name

|-

|<nowiki>22|0</nowiki>

|Alpharabian

|-

|<nowiki>21|1</nowiki>

|Magical

|-

|<nowiki>20|2</nowiki>

|High Priestess's

|-

|<nowiki>19|3</nowiki>

|Empress's

|-

|...

|-

|<nowiki>2|20</nowiki>

|Judgemental

|-

|<nowiki>1|21</nowiki>

|Worldwide

|-

|<nowiki>0|22</nowiki>

|Foolish

|}

== Scale tree ==

@@ Line 9: / Line 9: @@
 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 '''quartismoid''', since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6.
-==Relation to equal divisions==
+==Tuning ranges==
-=== 13edf ===
+=== 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.
-==== Mavila fifth and 91edo ====
+=== Diatonic fifth (hard of supersoft) ===
-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.
-==== 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.
+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 ====
+==== 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 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 ===
+== 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.
+== Modes ==
+Eliora proposes naming the brightest mode Alpharabian, after the fact that 33/32 is called Al-Farabi quarter-tone, and the rest after Tarot Major Arcana adjectivals based on how many generators down there is.
+{| class="wikitable"
+|+
+!Mode
+!Name
+|-
+|<nowiki>22|0</nowiki>
+|Alpharabian
+|-
+|<nowiki>21|1</nowiki>
+|Magical
+|-
+|<nowiki>20|2</nowiki>
+|High Priestess's
+|-
+|<nowiki>19|3</nowiki>
+|Empress's
+|-
+|...
+|...
+|-
+|<nowiki>2|20</nowiki>
+|Judgemental
+|-
+|<nowiki>1|21</nowiki>
+|Worldwide
+|-
+|<nowiki>0|22</nowiki>
+|Foolish
+|}
 == Scale tree ==