22L 1s: Difference between revisions

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| Pattern = LLL...22x...LLLs
| Pattern = LLL...22x...LLLs
}}
}}
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.
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.
 
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 ==
== Scale tree ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" rowspan="2" |Generator
! colspan="6" rowspan="2" |Generator
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |s
! rowspan="2" |L/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==
==See also==
* [[33/32]]
* [[33/32]]
* [[33/32 equal step tuning]]
* [[33/32 equal step tuning]]

Revision as of 14:55, 25 September 2022

← 21L 1s 22L 1s 23L 1s →
↙ 21L 2s ↓ 22L 2s 23L 2s ↘ 
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│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\23 to 1\22 (52.2 ¢ to 54.5 ¢)
Dark 21\22 to 22\23 (1145.5 ¢ to 1147.8 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 13:1 to 14:1
Related MOS scales
Parent 1L 21s
Sister 1L 22s
Daughters 23L 22s, 22L 23s
Neutralized 21L 2s
2-Flought 45L 1s, 22L 24s
Equal tunings
Equalized (L:s = 1:1) 1\23 (52.2 ¢)
Supersoft (L:s = 4:3) 4\91 (52.7 ¢)
Soft (L:s = 3:2) 3\68 (52.9 ¢)
Semisoft (L:s = 5:3) 5\113 (53.1 ¢)
Basic (L:s = 2:1) 2\45 (53.3 ¢)
Semihard (L:s = 5:2) 5\112 (53.6 ¢)
Hard (L:s = 3:1) 3\67 (53.7 ¢)
Superhard (L:s = 4:1) 4\89 (53.9 ¢)
Collapsed (L:s = 1:0) 1\22 (54.5 ¢)

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.

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

Generator L s L/s Comments
1\23 1 1 1.000
6\137 6 5 1.200
5\114 5 4 1.250
9\205 9 7 1.286
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
7\159 7 5 1.400
10\227 10 7 1.428
3\68 3 2 1.500 Stretched 23edo is in this range
11\249 11 7 1.571
8\181 8 5 1.600
13\294 13 8 1.625
5\113 5 3 1.667
12\271 12 7 1.714
7\158 7 4 1.750
9\203 9 5 1.800
2\45 2 1 2.000 Basic quartismoid
9\202 9 4 2.250
7\157 7 3 2.333
12\269 12 5 2.400
5\112 5 2 2.500 13 steps adding to 1/4 comma meantone fifth

is around here

13\291 13 5 2.600
8\179 8 3 2.667
11\246 11 4 2.750
3\67 3 1 3.000
10\223 10 3 3.333
7\156 7 2 3.500
11\245 11 3 3.667
4\89 4 1 4.000
9\200 9 2 4.500 13 steps adding to 3/2 perfect fifth is around here
5\111 5 1 5.000
6\133 6 1 6.000
1\22 1 0 → inf

See also

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