22L 1s: Difference between revisions

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 | Pattern = LLL...22x...LLLs
 }}
-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.
+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.
+From 1\22 to 4\91, 13 steps amount to a diatonic fifth. Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth.
 == Scale tree ==
 {| class="wikitable center-all"
 ! colspan="6" rowspan="2" |Generator
-! colspan="2" |Cents
 ! rowspan="2" |L
 ! rowspan="2" |s
 ! rowspan="2" |L/s
+!Comments
 |-
-!Chroma-positive
-!Chroma-negative
 |-
-|1\23|| || || || || || || ||1||1||1.000
+|1\23|| || || || || ||1||1||1.000
+|
 |-
-| || || || || ||6\137|| || ||6||5||1.200
+| || || || || ||6\137||6||5||1.200
+|
 |-
-| || || || ||5\114|| || || ||5||4||1.250
+| || || || ||5\114|| ||5||4||1.250
+|
 |-
-| || || || || ||9\205|| || ||9||7||1.286
+| || || || || ||9\205||9||7||1.286
+|
 |-
-| || || ||4\91|| || || || ||4||3||1.333
+| || || ||4\91|| || ||4||3||1.333
+|13 steps adding to lower bound of diatonic fifths (684.17c) is here
 |-
-| || || || || ||11\250|| || ||11||8||1.375
+| || || || || ||11\250||11||8||1.375
+|
 |-
-| || || || ||7\159|| || || ||7||5||1.400
+| || || || ||7\159|| ||7||5||1.400
+|
 |-
-| || || || || ||10\227|| || ||10||7||1.428
+| || || || || ||10\227||10||7||1.428
+|
 |-
-| || ||3\68|| || || || || ||3||2||1.500
+| || ||3\68|| || || ||3||2||1.500
+|[[23edo and octave stretching|Stretched 23edo]] is in this range
 |-
-| || || || || ||11\249|| || ||11||7||1.571
+| || || || || ||11\249||11||7||1.571
+|
 |-
-| || || || ||8\181|| || || ||8||5||1.600
+| || || || ||8\181|| ||8||5||1.600
+|
 |-
-| || || || || ||13\294|| || ||13||8||1.625
+| || || || || ||13\294||13||8||1.625
+|
 |-
-| || || ||5\113|| || || || ||5||3||1.667
+| || || ||5\113|| || ||5||3||1.667
+|
 |-
-| || || || || ||12\271|| || ||12||7||1.714
+| || || || || ||12\271||12||7||1.714
+|
 |-
-| || || || ||7\158|| || || ||7||4||1.750
+| || || || ||7\158|| ||7||4||1.750
+|
 |-
-| || || || || ||9\203|| || ||9||5||1.800
+| || || || || ||9\203||9||5||1.800
+|
 |-
-| ||2\45|| || || || || || ||2||1||2.000
+| ||2\45|| || || || ||2||1||2.000
+|Basic quartismoid
 |-
-| || || || || ||9\202|| || ||9||4||2.250
+| || || || || ||9\202||9||4||2.250
+|
 |-
-| || || || ||7\157|| || || ||7||3||2.333
+| || || || ||7\157|| ||7||3||2.333
+|
 |-
-| || || || || ||12\269|| || ||12||5||2.400
+| || || || || ||12\269||12||5||2.400
+|
 |-
-| || || ||5\112|| || || || ||5||2||2.500
+| || || ||5\112|| || ||5||2||2.500
+|13 steps adding to 1/4 comma meantone fifth
+is around here
 |-
-| || || || || ||13\291|| || ||13||5||2.600
+| || || || || ||13\291||13||5||2.600
+|
 |-
-| || || || ||8\179|| || || ||8||3||2.667
+| || || || ||8\179|| ||8||3||2.667
+|
 |-
-| || || || || ||11\246|| || ||11||4||2.750
+| || || || || ||11\246||11||4||2.750
+|
 |-
-| || ||3\67|| || || || || ||3||1||3.000
+| || ||3\67|| || || ||3||1||3.000
+|
 |-
-| || || || || ||10\223|| || ||10||3||3.333
+| || || || || ||10\223||10||3||3.333
+|
 |-
-| || || || ||7\156|| || || ||7||2||3.500
+| || || || ||7\156|| ||7||2||3.500
+|
 |-
-| || || || || ||11\245|| || ||11||3||3.667
+| || || || || ||11\245||11||3||3.667
+|
 |-
-| || || ||4\89|| || || || ||4||1||4.000
+| || || ||4\89|| || ||4||1||4.000
+|
 |-
-| || || || || ||9\200|| || ||9||2||4.500
+| || || || || ||9\200||9||2||4.500
+|13 steps adding to 3/2 perfect fifth is around here
 |-
-| || || || ||5\111|| || || ||5||1||5.000
+| || || || ||5\111|| ||5||1||5.000
+|
 |-
-| || || || || ||6\133|| || ||6||1||6.000
+| || || || || ||6\133||6||1||6.000
+|
 |-
-|1\22|| || || || || || || ||1||0||→ inf
+|1\22|| || || || || ||1||0||→ inf
+|
 |}
 ==See also==
 * [[33/32]]
 * [[33/32 equal step tuning]]