9L 3s: Difference between revisions

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<span style="font-size: 12.8000001907349px;">This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.</span>
{{Infobox MOS
| Name =
| Periods = 3
| nLargeSteps = 9
| nSmallSteps = 3
| Equalized = 1
| Paucitonic = 1
| Pattern = LLLsLLLsLLLs
}}
 
This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.


{| class="wikitable"
{| class="wikitable"
Line 5: Line 15:
| | 1/12
| | 1/12
| |  
| |  
| | <span style="font-size: 12.8px;">100</span>
| | 100
|-
|-
| | <span style="font-size: 12.8px;">5/57</span>
| | 5/57
| |  
| |  
| | 105.263
| | 105.263
|-
|-
| | <span style="font-size: 12.8px;">4/45</span>
| | 4/45
| |  
| |  
| | 106.667
| | 106.667
|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">7/78</span>
| | 7/78
| | 107.5385
| | 107.5385
|-
|-
Line 23: Line 33:
| | 108.108
| | 108.108
|-
|-
| | <span style="font-size: 12.8px;">3/33</span>
| | 3/33
| |  
| |  
| | 109.111
| | 109.111
Line 32: Line 42:
|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">8/87</span>
| | 8/87
| | 110.345
| | 110.345
|-
|-
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|-
|-
| |  
| |  
| | <span style="font-size: 12.8000001907349px;">5/54</span>
| | 5/54
| | 111.111
| | 111.111
|-
|-
Line 48: Line 58:
|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">7/75</span>
| | 7/75
| | 112
| | 112
|-
|-
Line 65: Line 75:
| | 2/21
| | 2/21
| |  
| |  
| | <span style="font-size: 12.8000001907349px;">114.286</span>
| | 114.286
|-
|-
| |  
| |  
Line 76: Line 86:
|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">7/72</span>
| | 7/72
| | 116.667
| | 116.667
|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">5/51</span>
| | 5/51
| | 117.647
| | 117.647
|-
|-
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|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">8/81</span>
| | 8/81
| | 118.5185
| | 118.5185
|-
|-
Line 103: Line 113:
| | 119.149
| | 119.149
|-
|-
| | <span style="font-size: 12.8px;">3/30</span>
| | 3/30
| |  
| |  
| | 120
| | 120
Line 112: Line 122:
|-
|-
| |  
| |  
| | <span style="font-size: 12.8px;">7/69</span>
| | 7/69
| | 121.739
| | 121.739
|-
|-
Line 119: Line 129:
| | 122.222
| | 122.222
|-
|-
| | <span style="font-size: 12.8px;">4/39</span>
| | 4/39
| |  
| |  
| | 123.138
| | 123.138
Line 127: Line 137:
| | 124.138
| | 124.138
|-
|-
| | <span style="font-size: 12.8px;">5/48</span>
| | 5/48
| |  
| |  
| | 125
| | 125
Line 133: Line 143:
| | 1/9
| | 1/9
| |  
| |  
| | <span style="font-size: 12.8px;">133.333</span>
| | 133.333
|}
|}

Revision as of 19:56, 27 March 2021

↖ 8L 2s ↑ 9L 2s 10L 2s ↗
← 8L 3s 9L 3s 10L 3s →
↙ 8L 4s ↓ 9L 4s 10L 4s ↘ 
┌╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║│║║║│║║║││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLLs
sLLLsLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 1\12 to 1\9 (100.0 ¢ to 133.3 ¢)
Dark 2\9 to 3\12 (266.7 ¢ to 300.0 ¢)
TAMNAMS information
Related to 3L 6s (tcherepnin)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 3L 6s
Sister 3L 9s
Daughters 12L 9s, 9L 12s
Neutralized 6L 6s
2-Flought 21L 3s, 9L 15s
Equal tunings
Equalized (L:s = 1:1) 1\12 (100.0 ¢)
Supersoft (L:s = 4:3) 4\45 (106.7 ¢)
Soft (L:s = 3:2) 3\33 (109.1 ¢)
Semisoft (L:s = 5:3) 5\54 (111.1 ¢)
Basic (L:s = 2:1) 2\21 (114.3 ¢)
Semihard (L:s = 5:2) 5\51 (117.6 ¢)
Hard (L:s = 3:1) 3\30 (120.0 ¢)
Superhard (L:s = 4:1) 4\39 (123.1 ¢)
Collapsed (L:s = 1:0) 1\9 (133.3 ¢)

This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.

1/12 100
5/57 105.263
4/45 106.667
7/78 107.5385
10/111 108.108
3/33 109.111
109.992
8/87 110.345
110.557
5/54 111.111
111.815
7/75 112
9/96 112.5
11/117 112.8205
13/138 113.0435
2/21 114.286
11/114 115.7895
9/93 116.129
7/72 116.667
5/51 117.647
118.274
8/81 118.5185
118.769
11/111 118.919
14/141 119.149
3/30 120
120.543
7/69 121.739
11/108 122.222
4/39 123.138
9/87 124.138
5/48 125
1/9 133.333
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