11L 2s: Difference between revisions

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| Pattern = LLLLLLsLLLLLs
| Pattern = LLLLLLsLLLLLs
}}
}}
The '''11L 2s''' [[MOS scale]] is most notable for being used by [[Ivan Wyschnegradsky]] and having a name "diatonicized chromatic scale". The more concise name for the scale, proposed by Eliora, is '''hendecoid'''.
The '''11L 2s''' [[MOS scale]] is most notable for being used by [[Ivan Wyschnegradsky]] and having a name "diatonicized chromatic scale". The more concise name for the scale, proposed by Eliora, is '''hendecoid'''. Another possible name for this mos in TAMNAMS is '''p-enhar balzano''', being one of four enharmonic scales of [[2L 7s]].


From a regular temperament theory perspective, is notable for correponding to the mega chromatic scale of [[Heinz]] temperament. Its generator of 5\11 to 6\13 hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale - the strong relationship to the number 11 is the reason for the name "hendecoid".
From a regular temperament theory perspective, is notable for correponding to the mega chromatic scale of [[Heinz]] temperament. Its generator of 5\11 to 6\13 hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale - the strong relationship to the number 11 is the reason for the name "hendecoid".
== Modes ==
* 12|0 LLLLLLsLLLLLs
* 11|1 LLLLLsLLLLLLs
* 10|2 LLLLLsLLLLLsL
* 9|3 LLLLsLLLLLLsL
...


== Scale tree ==
== Scale tree ==
{| class="wikitable"
{| class="wikitable center-all"
! colspan="8" | generator
! colspan="6" |Generator
! L
!L
! s
!s
! L/s
!L/s
! gen (cents)
!Comments
! comment
|-
|-
| 5\11
|7\13
|
|
|
|
Line 27: Line 35:
|
|
|
|
|1
|1
|1.000
|
|
|-
| || || || || ||41\76||6||5||1.200
|
|
| 1
|-
| 0
| || || || ||34\63|| ||5||4||1.250
|
|
| 545.455
|-
| || || || || ||61\113||9||7||1.286
|
|
|-
|-
| || || ||27\50|| || ||4||3||1.333
|
|
|-
| || || || || ||74\137||11||8||1.375
|
|
|-
| || || || ||47\87|| ||7||5||1.400
|
|
|-
| || || || || ||67\124||10||7||1.428
|
|
|-
| || ||20\37|| || || ||3||2||1.500
|
|
|-
| || || || || ||73\135||11||7||1.571
|
|
|-
| || || || ||53\98|| ||8||5||1.600
|
|
| 41\90
|-
| 8
| || || || || ||86\159||13||8||1.625
| 1
| 8.000
| 546.667
|
|
|-
|-
|
| || || ||33\61|| || ||5||3||1.667
|
|Freivald / emka is around here
|
|
|
|
| 36\79
|
| 7
| 1
| 7.000
| 546.835
|
|-
|-
|
| || || || || ||79\146||12||7||1.714
|
|
|
|
| 31\68
|
|
| 6
| 1
| 6.000
| 547.059
|
|
|-
|-
|
| || || || ||46\85|| ||7||4||1.750
|
|
|
| 26\57
|
|
|
| 5
| 1
| 5.000
| 547.368
|
|
|-
|-
| || || || || ||71\109||9||5||1.800
|
|
|
|
| 21\46
|
|
|
|
| 4
| 1
| 4.000
| 547.826
| Heinz is around here
|-
|-
|
| ||13\24|| || || || ||2||1||2.000
|
|Basic hendecoid
|
|
| 37\81
|
|
|
| 7
| 2
| 3.500
| 548.148
|
|-
|-
|
| || || || || ||70\107||9||4||2.250
|
| 16\35
|
|
|
|
|
| 3
| 1
| 3.000
| 548.571
|
|
|-
|-
|
| || || || ||45\83|| ||7||3||2.333
|
|
|
| 43\94
|
|
|
| 8
| 3
| 2.667
| 548.936
|
|
|-
|-
|
| || || || || ||77\142||12||5||2.400
|
|
| 27\59
|
|
|
|
| 5
| 2
| 2.500
| 549.153
|
|
|-
|-
|
| || || ||32\59|| || ||5||2||2.500
|
|
|
| 38\83
|
|
|
| 7
| 3
| 2.333
| 549.398
|
|
|-
|-
|
| || || || || ||83\152||13||5||2.600
| 11\24
|
|
|
|
|
|
| 2
| 1
| 2.000
| 550.000
|
|
|-
|-
|
| || || || ||51\94|| ||8||3||2.667
|
|
|
| 39\85
|
|
|
| 7
| 4
| 1.750
| 550.588
|
|
|-
|-
|
| || || || || ||70\129||11||4||2.750
|
|
| 28\61
|
|
|
|
| 5
| 3
| 1.667
| 550.820
|
|
|-
|-
|
| || ||19\35|| || || ||3||1||3.000
|
|
|
| 45\98
|
|
|
| 8
| 5
| 1.600
| 551.020
|
|
|-
|-
|
| || || || || ||63\116||10||3||3.333
|
| 17\37
|
|
|
|
|
| 3
| 2
| 1.500
| 551.351
|
|
|-
|-
|
| || || || ||44\81|| ||7||2||3.500
|
|
|
| 40\87
|
|
|
| 7
| 5
| 1.400
| 551.724
|
|
|-
|-
|
| || || || || ||69\127||11||3||3.667
|
|
| 23\50
|
|
|
|
| 4
| 3
| 1.333
| 552.000
|
|
|-
|-
|
| || || ||25\46|| || ||4||1||4.000
|
|
|
| 29\63
|
|
|
| 5
| 4
| 1.250
| 552.381
|
|
|-
|-
|
| || || || || ||56\103||9||2||4.500
|
|
|
|
| 35\76
|
|
| 6
| 5
| 1.200
| 552.632
|
|
|-
|-
|
| || || || ||31\57|| ||5||1||5.000
|
|
|
|
|
| 41\89
|
| 7
| 6
| 1.167
| 552.809
|
|
|-
|-
|
| || || || || ||37\68||6||1||6.000
|
|
|
|
|
|
| 47\102
| 8
| 7
| 1.125
| 552.941
|
|
|-
|-
| 6\13
|6\11|| || || || || ||1||0||→ inf
|
|
|
|
|
|
|
| 1
| 1
| 1.000
| 553.846
|
|
|}
|}
[[Category:13-tone scales]]
[[Category:13-tone scales]]

Revision as of 12:42, 10 April 2023

↖ 10L 1s ↑ 11L 1s 12L 1s ↗
← 10L 2s 11L 2s 12L 2s →
↙ 10L 3s ↓ 11L 3s 12L 3s ↘ 
┌╥╥╥╥╥╥┬╥╥╥╥╥┬┐
│║║║║║║│║║║║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLsLLLLLs
sLLLLLsLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\13 to 6\11 (646.2 ¢ to 654.5 ¢)
Dark 5\11 to 6\13 (545.5 ¢ to 553.8 ¢)
TAMNAMS information
Related to 2L 7s (balzano)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 2L 9s
Sister 2L 11s
Daughters 13L 11s, 11L 13s
Neutralized 9L 4s
2-Flought 24L 2s, 11L 15s
Equal tunings
Equalized (L:s = 1:1) 7\13 (646.2 ¢)
Supersoft (L:s = 4:3) 27\50 (648.0 ¢)
Soft (L:s = 3:2) 20\37 (648.6 ¢)
Semisoft (L:s = 5:3) 33\61 (649.2 ¢)
Basic (L:s = 2:1) 13\24 (650.0 ¢)
Semihard (L:s = 5:2) 32\59 (650.8 ¢)
Hard (L:s = 3:1) 19\35 (651.4 ¢)
Superhard (L:s = 4:1) 25\46 (652.2 ¢)
Collapsed (L:s = 1:0) 6\11 (654.5 ¢)

The 11L 2s MOS scale is most notable for being used by Ivan Wyschnegradsky and having a name "diatonicized chromatic scale". The more concise name for the scale, proposed by Eliora, is hendecoid. Another possible name for this mos in TAMNAMS is p-enhar balzano, being one of four enharmonic scales of 2L 7s.

From a regular temperament theory perspective, is notable for correponding to the mega chromatic scale of Heinz temperament. Its generator of 5\11 to 6\13 hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale - the strong relationship to the number 11 is the reason for the name "hendecoid".

Modes

  • 12|0 LLLLLLsLLLLLs
  • 11|1 LLLLLsLLLLLLs
  • 10|2 LLLLLsLLLLLsL
  • 9|3 LLLLsLLLLLLsL

...

Scale tree

Generator L s L/s Comments
7\13 1 1 1.000
41\76 6 5 1.200
34\63 5 4 1.250
61\113 9 7 1.286
27\50 4 3 1.333
74\137 11 8 1.375
47\87 7 5 1.400
67\124 10 7 1.428
20\37 3 2 1.500
73\135 11 7 1.571
53\98 8 5 1.600
86\159 13 8 1.625
33\61 5 3 1.667 Freivald / emka is around here
79\146 12 7 1.714
46\85 7 4 1.750
71\109 9 5 1.800
13\24 2 1 2.000 Basic hendecoid
70\107 9 4 2.250
45\83 7 3 2.333
77\142 12 5 2.400
32\59 5 2 2.500
83\152 13 5 2.600
51\94 8 3 2.667
70\129 11 4 2.750
19\35 3 1 3.000
63\116 10 3 3.333
44\81 7 2 3.500
69\127 11 3 3.667
25\46 4 1 4.000
56\103 9 2 4.500
31\57 5 1 5.000
37\68 6 1 6.000
6\11 1 0 → inf
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