11L 2s

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↖ 10L 1s ↑11L 1s 12L 1s ↗
← 10L 2s11L 2s 12L 2s →
↙ 10L 3s ↓11L 3s 12L 3s ↘
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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
Descends from 2L 7s (balzano)
Required step ratio range 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¢)

11L 2s, also called hendecoid or Wyschnegradsky's diatonicized chromatic scale, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 2 small steps, repeating every octave. 11L 2s is a grandchild scale of 2L 7s, expanding it by 4 tones. Generators that produce this scale range from 646.2¢ to 654.5¢, or from 545.5¢ to 553.8¢. This scale is most notable for being used by Ivan Wyschnegradsky, bearing the name diatonicized chromatic scale. Eliora has proposed the name hendecoid for its strong relationship to the number 11, as it's an 11+-limit scale and has generators that are close to 11/8. Frostburn has proposed the name p-enhar balzano, as a grandchild scale 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. If just 11/8 is used as generator, the step ratio is around 1.509.

Modes

Modes of 11L 2s
UDP Rotational order Step pattern
12 | 0 1 LLLLLLsLLLLLs
11 | 1 8 LLLLLsLLLLLLs
10 | 2 2 LLLLLsLLLLLsL
9 | 3 9 LLLLsLLLLLLsL
8 | 4 3 LLLLsLLLLLsLL
7 | 5 10 LLLsLLLLLLsLL
6 | 6 4 LLLsLLLLLsLLL
5 | 7 11 LLsLLLLLLsLLL
4 | 8 5 LLsLLLLLsLLLL
3 | 9 12 LsLLLLLLsLLLL
2 | 10 6 LsLLLLLsLLLLL
1 | 11 13 sLLLLLLsLLLLL
0 | 12 7 sLLLLLsLLLLLL

Scale tree

Scale Tree and Tuning Spectrum of 11L 2s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
7\13 646.154 553.846 1:1 1.000 Equalized 11L 2s
41\76 647.368 552.632 6:5 1.200
34\63 647.619 552.381 5:4 1.250
61\113 647.788 552.212 9:7 1.286
27\50 648.000 552.000 4:3 1.333 Supersoft 11L 2s
74\137 648.175 551.825 11:8 1.375
47\87 648.276 551.724 7:5 1.400 Emka
67\124 648.387 551.613 10:7 1.429
20\37 648.649 551.351 3:2 1.500 Soft 11L 2s
73\135 648.889 551.111 11:7 1.571
53\98 648.980 551.020 8:5 1.600 Freivald
86\159 649.057 550.943 13:8 1.625
33\61 649.180 550.820 5:3 1.667 Semisoft 11L 2s
79\146 649.315 550.685 12:7 1.714
46\85 649.412 550.588 7:4 1.750
59\109 649.541 550.459 9:5 1.800
13\24 650.000 550.000 2:1 2.000 Basic 11L 2s
Scales with tunings softer than this are proper
58\107 650.467 549.533 9:4 2.250
45\83 650.602 549.398 7:3 2.333
77\142 650.704 549.296 12:5 2.400
32\59 650.847 549.153 5:2 2.500 Semihard 11L 2s
83\153 650.980 549.020 13:5 2.600
51\94 651.064 548.936 8:3 2.667
70\129 651.163 548.837 11:4 2.750
19\35 651.429 548.571 3:1 3.000 Hard 11L 2s
63\116 651.724 548.276 10:3 3.333
44\81 651.852 548.148 7:2 3.500
69\127 651.969 548.031 11:3 3.667
25\46 652.174 547.826 4:1 4.000 Superhard 11L 2s
Heinz
56\103 652.427 547.573 9:2 4.500
31\57 652.632 547.368 5:1 5.000
37\68 652.941 547.059 6:1 6.000
6\11 654.545 545.455 1:0 → ∞ Collapsed 11L 2s