9L 4s: Difference between revisions

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Infobox MOS, improve lead section, clean up table (uniformize precision, remove orphan lines), categories
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This MOS, generated by a subminor third of 2/9edo (266.667 cents) to 3/13edo (276.923), is the chromatic scale of [[Orwell|Orwell temperament]]. The generator for its harmonic entropy minimum is the cube root of 8/5.
{{Infobox MOS
| Name =
| Periods = 1
| nLargeSteps = 9
| nSmallSteps = 4
| Equalized = 3
| Collapsed = 2
| Pattern = LLLsLLsLLsLLs
}}


The '''9L 4s''' [[MOS scale]], generated by a subminor third of 2/9edo (266.667 cents) to 3/13edo (276.923), is the chromatic scale of [[Orwell|Orwell temperament]]. The generator for its harmonic entropy minimum is the cube root of 8/5.
== Scale tree ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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| |  
| |  
| | 16/71
| | 16/71
| | 270.4225
| | 270.423
|-
| |
| |
| |
| |
| |
| | 270.798
|-
|-
| |  
| |  
Line 44: Line 48:
| |  
| |  
| | 270.968
| | 270.968
|-
| |
| |
| |
| |
| |
| | 271.351
|-
|-
| |  
| |  
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| | 19/84
| | 19/84
| | 271.429
| | 271.429
|-
| |
| |
| |
| |
| |
| | 271.504
|-
|-
| |  
| |  
Line 93: Line 83:
| | 18/79
| | 18/79
| | 273.418
| | 273.418
|-
| |
| |
| |
| |
| |
| | 273.473
|-
|-
| |  
| |  
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| |  
| |  
| | 273.684
| | 273.684
|-
| |
| |
| |
| |
| |
| | 273.85
|-
|-
| |  
| |  
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| |  
| |  
| | 14/61
| | 14/61
| | 275.41
| | 275.410
|-
|-
| | 3/13
| | 3/13
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| | 276.923
| | 276.923
|}
|}
[[Category:13-tone scales]]

Revision as of 22:40, 12 February 2023

↖ 8L 3s ↑ 9L 3s 10L 3s ↗
← 8L 4s 9L 4s 10L 4s →
↙ 8L 5s ↓ 9L 5s 10L 5s ↘ 
┌╥╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║│║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLsLLs
sLLsLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\13 to 7\9 (923.1 ¢ to 933.3 ¢)
Dark 2\9 to 3\13 (266.7 ¢ to 276.9 ¢)
TAMNAMS information
Related to 4L 5s (gramitonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 4L 5s
Sister 4L 9s
Daughters 13L 9s, 9L 13s
Neutralized 5L 8s
2-Flought 22L 4s, 9L 17s
Equal tunings
Equalized (L:s = 1:1) 10\13 (923.1 ¢)
Supersoft (L:s = 4:3) 37\48 (925.0 ¢)
Soft (L:s = 3:2) 27\35 (925.7 ¢)
Semisoft (L:s = 5:3) 44\57 (926.3 ¢)
Basic (L:s = 2:1) 17\22 (927.3 ¢)
Semihard (L:s = 5:2) 41\53 (928.3 ¢)
Hard (L:s = 3:1) 24\31 (929.0 ¢)
Superhard (L:s = 4:1) 31\40 (930.0 ¢)
Collapsed (L:s = 1:0) 7\9 (933.3 ¢)

The 9L 4s MOS scale, generated by a subminor third of 2/9edo (266.667 cents) to 3/13edo (276.923), is the chromatic scale of Orwell temperament. The generator for its harmonic entropy minimum is the cube root of 8/5.

Scale tree

2/9 266.667
11/49 269.388
9/40 270
16/71 270.423
7/31 270.968
19/84 271.429
12/53 271.698
17/75 272
5/22 272.727
18/79 273.418
13/57 273.684
21/92 273.913
8/35 274.286
19/83 274.699
11/48 275
14/61 275.410
3/13 276.923
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