21L 1s: Difference between revisions

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proposed the name escapist
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| Collapsed = 1
| Collapsed = 1
| Pattern = LLL...21x...LLLs
| Pattern = LLL...21x...LLLs
| Other names = escapist, 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]].  
{{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".


[[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: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.  


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


==Tuning ranges==
=== Brighter modes ===
 
==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ====
=== 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.   
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.   
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.   
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.   
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 ==
== 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.  
2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.  


==Modes==
== 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.
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"
{| class="wikitable"
|+
!Mode
!Name
|-
|-
|<nowiki>21|0</nowiki>
! Mode
|Foolish
! Name
|-
| 21{{pipe}}0
| Foolish
|-
|-
|<nowiki>20|1</nowiki>
| 20{{pipe}}1
|Magical
| Magical
|-
|-
|<nowiki>19|2</nowiki>
| 19{{pipe}}2
|High Priestess's
| High Priestess's
|-
|-
|<nowiki>18|3</nowiki>
| 18{{pipe}}3
|Empress's
| Empress's
|-
|-
|...
|
|...
|
|-
|-
|<nowiki>3|19</nowiki>
| 3{{pipe}}19
|Lunar
| Lunar
|-
|-
|<nowiki>2|19</nowiki>
| 2{{pipe}}19
|Solar
| Solar
|-
|-
|<nowiki>1|20</nowiki>
| 1{{pipe}}20
|Judgemental
| Judgemental
|-
|-
|<nowiki>0|21</nowiki>
| 0{{pipe}}21
|Worldwide
| Worldwide
|}
|}


==Scale tree==
== Intervals ==
{| class="wikitable center-all"
{{MOS intervals}}
! colspan="6" |Generator
 
!L
== Scale tree ==
!s
{{MOS tuning spectrum}}
!L/s
 
!Comments
== See also ==
|-
* [[32/31]]
|1\22
* [[31/30]]
|
* [[Escapade]]
|
|
|
|
|1
|1
|1.000
|
|-
| || || || || ||6\131||6||5||1.200
|
|-
| || || || ||5\109|| ||5||4||1.250
|
|-
| || || || || ||9\196||9||7||1.286
|
|-
| || || ||4\87|| || ||4||3||1.333
|
|-
| || || || || ||11\239||11||8||1.375
|
|-
| || || || ||7\152|| ||7||5||1.400
|
|-
| || || || || ||10\217||10||7||1.428
|
|-
| || ||3\65|| || || ||3||2||1.500
|13 steps adding to upper bound of diatonic fifths (720¢) is here
|-
| || || || || ||11\238||11||7||1.571
|
|-
| || || || ||8\173|| ||8||5||1.600
|
|-
| || || || || ||13\281||13||8||1.625
|
|-
| || || ||5\108|| || ||5||3||1.667
|
|-
| || || || || ||12\259||12||7||1.714
|
|-
| || || || ||7\151|| ||7||4||1.750
|
|-
| || || || || ||9\194||9||5||1.800
|
|-
| ||2\43|| || || || ||2||1||2.000
|Basic tricesimoprimal quartertonic
|-
| || || || || ||9\193||9||4||2.250
|
|-
| || || || ||7\150|| ||7||3||2.333
|
|-
| || || || || ||12\257||12||5||2.400
|
|-
| || || ||5\107|| || ||5||2||2.500
|
|-
| || || || || ||13\278||13||5||2.600
|
|-
| || || || ||8\171|| ||8||3||2.667
|
|-
| || || || || ||11\235||11||4||2.750
|
|-
| || ||3\64|| || || ||3||1||3.000
|
|-
| || || || || ||10\213||10||3||3.333
|
|-
| || || || ||7\149|| ||7||2||3.500
|
|-
| || || || || ||11\234||11||3||3.667
|
|-
| || || ||4\85|| || ||4||1||4.000
|
|-
| || || || || ||9\191||9||2||4.500
|
|-
| || || || ||5\106|| ||5||1||5.000
|
|-
| || || || || ||6\127||6||1||6.000
|
|-
|1\21|| || || || || ||1||0||→ inf
|
|}
==See also==
*[[32/31]]
*[[31/30]]