11L 2s

Revision as of 15:43, 5 February 2023 by Eliora (talk | contribs) (this fact is the most prominent about 11L 2s, why it isn't at the top of the page)

The 11L 2s MOS scale is most notable for being used by Ivan Wyschnegradsky and having a name "diatonicized chromatic scale".

↖ 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 ¢)
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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.

Scale tree

generator L s L/s gen (cents) comment
5\11 1 0 545.455
41\90 8 1 8.000 546.667
36\79 7 1 7.000 546.835
31\68 6 1 6.000 547.059
26\57 5 1 5.000 547.368
21\46 4 1 4.000 547.826 Heinz is around here
37\81 7 2 3.500 548.148
16\35 3 1 3.000 548.571
43\94 8 3 2.667 548.936
27\59 5 2 2.500 549.153
38\83 7 3 2.333 549.398
11\24 2 1 2.000 550.000
39\85 7 4 1.750 550.588
28\61 5 3 1.667 550.820
(5φ+1)/(11φ+2) φ 1 1.618 550.965
45\98 8 5 1.600 551.020
17\37 3 2 1.500 551.351
40\87 7 5 1.400 551.724
23\50 4 3 1.333 552.000
29\63 5 4 1.250 552.381
35\76 6 5 1.200 552.632
41\89 7 6 1.167 552.809
47\102 8 7 1.125 552.941
6\13 1 1 1.000 553.846