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| == 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. |
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| == Modes ==
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| 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.
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| {| class="wikitable"
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| |+
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| !Mode
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| !Name
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| |-
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| |<nowiki>22|0</nowiki>
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| |Alpharabian
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| |-
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| |<nowiki>21|1</nowiki>
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| |Magical
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| |-
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| |<nowiki>20|2</nowiki>
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| |High Priestess's
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| |-
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| |<nowiki>19|3</nowiki>
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| |Empress's
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| |-
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| |...
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| |...
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| |-
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| |<nowiki>2|20</nowiki>
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| |Judgemental
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| |-
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| |<nowiki>1|21</nowiki>
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| |Worldwide
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| |-
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| |<nowiki>0|22</nowiki>
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| |Foolish
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| |}
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| | |
| == Scale tree ==
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| {| class="wikitable center-all"
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| ! colspan="6" |Generator
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| !L
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| !s
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| !L/s
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| !Comments
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| |-
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| |1\23
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| |1
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| |1
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| |1.000
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| |-
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| | || || || || ||6\137||6||5||1.200
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| |-
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| | || || || ||5\114|| ||5||4||1.250
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| |-
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| | || || || || ||9\205||9||7||1.286
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| |-
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| | || || ||4\91|| || ||4||3||1.333
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| |13 steps adding to lower bound of diatonic fifths (685.71c) is here
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| |-
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| | || || || || ||11\250||11||8||1.375
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| |-
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| | || || || ||7\159|| ||7||5||1.400
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| |-
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| | || || || || ||10\227||10||7||1.428
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| |-
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| | || ||3\68|| || || ||3||2||1.500
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| |[[23edo and octave stretching|Stretched 23edo]] is in this range
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| |-
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| | || || || || ||11\249||11||7||1.571
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| |-
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| | || || || ||8\181|| ||8||5||1.600
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| |-
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| | || || || || ||13\294||13||8||1.625
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| |-
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| | || || ||5\113|| || ||5||3||1.667
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| |-
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| | || || || || ||12\271||12||7||1.714
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| |-
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| | || || || ||7\158|| ||7||4||1.750
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| |-
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| | || || || || ||9\203||9||5||1.800
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| |
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| |-
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| | ||2\45|| || || || ||2||1||2.000
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| |Basic quartismoid
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| |-
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| | || || || || ||9\202||9||4||2.250
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| |-
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| | || || || ||7\157|| ||7||3||2.333
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| |-
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| | || || || || ||12\269||12||5||2.400
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| |-
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| | || || ||5\112|| || ||5||2||2.500
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| |13 steps adding to 1/4 comma meantone fifth is around here
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| |-
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| | || || || || ||13\291||13||5||2.600
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| |-
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| | || || || ||8\179|| ||8||3||2.667
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| |-
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| | || || || || ||11\246||11||4||2.750
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| |-
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| | || ||3\67|| || || ||3||1||3.000
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| |-
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| | || || || || ||10\223||10||3||3.333
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| |-
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| | || || || ||7\156|| ||7||2||3.500
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| |13 steps adding to a 700 cent fifth is here
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| |-
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| | || || || || ||11\245||11||3||3.667
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| |-
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| | || || ||4\89|| || ||4||1||4.000
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| |-
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| | || || || || ||9\200||9||2||4.500
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| |13 steps adding to 3/2 perfect fifth is around here
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| |-
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| | || || || ||5\111|| ||5||1||5.000
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| |-
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| | || || || || ||6\133||6||1||6.000
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| |-
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| |1\22|| || || || || ||1||0||→ inf
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| |}
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| ==See also==
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| * [[33/32]]
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| * [[33/32 equal step tuning]]
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21L 1s is the scale that is most commonly produced by stacking the interval of 32/31 or 31/30.
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.
Tuning ranges
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)
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.
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.
