13L 10s: Difference between revisions

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This is the MOS where the large steps split 2-1-1-2-1-1-2-1-1-1 between the small steps. Its generator is a submajor third between 7/23edo and 4/13edo (365.217 and 369.231 cents) and it is the major quartertone scale of the [[3L_7s|Modi Sephiratorum]] and the quartertone scale of Unidec temperament.
{{Infobox MOS
| Other names =
| Periods = 1
| nLargeSteps = 13
| nSmallSteps = 10
| Equalized = 7
| Paucitonic = 4
| Pattern = LLsLsLsLLsLsLsLLsLsLsLs
}}
The '''13L 10s''' [[MOS scale]] has its large steps split 2-1-1-2-1-1-2-1-1-1 between the small steps. Its generator is a submajor third between 7\23 (365.217{{cent}}) and 4\13 (369.231{{cent}}) and it is the major quartertone scale of [[3L 7s]] (sephiroid) and the quartertone scale of [[unidec]] temperament.


== Scale tree ==
{| class="wikitable"
{| class="wikitable"
|-
|-
| | 4/13
| 4/13
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 369.231
| 369.231
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 23/75
| 23/75
| | 368
| 368
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 19/62
| 19/62
| |  
|  
| | 367.742
| 367.742
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 34/111
| 34/111
| | 367.568
| 367.568
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 367.415
| 367.415
|-
|-
| |  
|  
| |  
|  
| | 15/49
| 15/49
| |  
|  
| |  
|  
| | 367.345
| 367.345
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 367.195
| 367.195
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 41/134
| 41/134
| | 367.164
| 367.164
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 367.1345
| 367.1345
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 26/85
| 26/85
| |  
|  
| | 367.059
| 367.059
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 37/121
| 37/121
| | 366.942
| 366.942
|-
|-
| |  
|  
| | 11/36
| 11/36
| |  
|  
| |  
|  
| |  
|  
| | 366.667
| 366.667
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 40/131
| 40/131
| | 366.412
| 366.412
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 366.392
| 366.392
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 29/95
| 29/95
| |  
|  
| | 366.316
| 366.316
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 366.256
| 366.256
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 47/154
| 47/154
| | 366.234
| 366.234
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 366.196
| 366.196
|-
|-
| |  
|  
| |  
|  
| | 18/59
| 18/59
| |  
|  
| |  
|  
| | 366.102
| 366.102
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 43/141
| 43/141
| | 365.957
| 365.957
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 25/82
| 25/82
| |  
|  
| | 365.854
| 365.854
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 32/105
| 32/105
| | 365.714
| 365.714
|-
|-
| | 7/23
| 7/23
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 365.217
| 365.217
|}
|}

Revision as of 03:42, 17 August 2022

↖ 12L 9s ↑ 13L 9s 14L 9s ↗
← 12L 10s 13L 10s 14L 10s →
↙ 12L 11s ↓ 13L 11s 14L 11s ↘
Scale structure
Step pattern LLsLsLsLLsLsLsLLsLsLsLs
sLsLsLsLLsLsLsLLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\23 to 4\13 (365.2 ¢ to 369.2 ¢)
Dark 9\13 to 16\23 (830.8 ¢ to 834.8 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 10L 3s
Sister 10L 13s
Daughters 23L 13s, 13L 23s
Neutralized 3L 20s
2-Flought 36L 10s, 13L 33s
Equal tunings
Equalized (L:s = 1:1) 7\23 (365.2 ¢)
Supersoft (L:s = 4:3) 25\82 (365.9 ¢)
Soft (L:s = 3:2) 18\59 (366.1 ¢)
Semisoft (L:s = 5:3) 29\95 (366.3 ¢)
Basic (L:s = 2:1) 11\36 (366.7 ¢)
Semihard (L:s = 5:2) 26\85 (367.1 ¢)
Hard (L:s = 3:1) 15\49 (367.3 ¢)
Superhard (L:s = 4:1) 19\62 (367.7 ¢)
Collapsed (L:s = 1:0) 4\13 (369.2 ¢)
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The 13L 10s MOS scale has its large steps split 2-1-1-2-1-1-2-1-1-1 between the small steps. Its generator is a submajor third between 7\23 (365.217 ¢) and 4\13 (369.231 ¢) and it is the major quartertone scale of 3L 7s (sephiroid) and the quartertone scale of unidec temperament.

Scale tree

4/13 369.231
23/75 368
19/62 367.742
34/111 367.568
367.415
15/49 367.345
367.195
41/134 367.164
367.1345
26/85 367.059
37/121 366.942
11/36 366.667
40/131 366.412
366.392
29/95 366.316
366.256
47/154 366.234
366.196
18/59 366.102
43/141 365.957
25/82 365.854
32/105 365.714
7/23 365.217
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