11L 2s: Difference between revisions
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{{Infobox MOS | {{MOS intro|Other Names=hendecoid; Wyschnegradsky's diatonicized chromatic scale}}{{Infobox MOS | ||
| Other names =hendecoid, Wyschnegradsky's<br> diatonicized chromatic | | Other names =hendecoid, Wyschnegradsky's<br> diatonicized chromatic | ||
| Periods = 1 | | Periods = 1 | ||
| Line 8: | Line 8: | ||
| Pattern = LLLLLLsLLLLLs | | Pattern = LLLLLLsLLLLLs | ||
}} | }} | ||
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 | 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 == | ||
Revision as of 01:29, 19 February 2024
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 ¢.
| ↖ 10L 1s | ↑ 11L 1s | 12L 1s ↗ |
| ← 10L 2s | 11L 2s | 12L 2s → |
| ↙ 10L 3s | ↓ 11L 3s | 12L 3s ↘ |
┌╥╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLsLLLLLL
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
| UDP | Cyclic 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
| 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,
Wyschnegradsky's diatonicized chromatic | |||||
| 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 | Heinz is around here | |||||
| 56\103 | 9 | 2 | 4.500 | ||||||
| 31\57 | 5 | 1 | 5.000 | ||||||
| 37\68 | 6 | 1 | 6.000 | ||||||
| 6\11 | 1 | 0 | → inf | ||||||