12L 17s: Difference between revisions

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This is the MOS which splits the small steps 1-2-1-2-1-2-1-1-2-1-1-2 between the large steps. Its generator is a near-perfect fourth of no less than 5/12edo (500 cents), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.
{{Infobox MOS
| Other names =
| Periods = 1
| nLargeSteps = 12
| nSmallSteps = 17
| Equalized = 12
| Paucitonic = 5
| Pattern = LsLsLssLsLssLsLsLssLsLssLsLss
}}
The '''12L 17s''' [[MOS scale]] splits the small steps 1-1-2-1-2-1-1-2-1-2-1-2 between the large steps. Its [[chroma-positive]] generator is a near-perfect fourth of no more than 5\12 (500{{cent}}), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.


== Scale tree ==
{| class="wikitable"
{| class="wikitable"
|-
|-
| | 12/29
| 12/29
| |  
|
| |  
|
| |  
|
| |  
|
| | 496.552
| 496.552
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 53/128
| 53/128
| | 496.875
| 496.875
|-
|-
| |  
|
| |  
|
| |  
|
| | 41/99
| 41/99
| |  
|
| | 496.97
| 496.97
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 70/169
| 70/169
| | 497.041
| 497.041
|-
|-
| |  
|
| |  
|
| | 29/70
| 29/70
| |  
|
| |  
|
| | 497.143
| 497.143
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 497.211
| 497.211
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 75/181
| 75/181
| | 497.238
| 497.238
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 497.254
| 497.254
|-
|-
| |  
|
| |  
|
| |  
|
| | 46/111
| 46/111
| |  
|
| | 497.297
| 497.297
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 497.353
| 497.353
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 63/152
| 63/152
| | 497.368
| 497.368
|-
|-
| |  
|
| | 17/41
| 17/41
| |  
|
| |  
|
| |  
|
| | 497.561
| 497.561
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 56/135
| 56/135
| | 497.778
| 497.778
|-
|-
| |  
|
| |  
|
| |  
|
| | 39/94
| 39/94
| |  
|
| | 497.842
| 497.842
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 497.935
| 497.935
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 61/147
| 61/147
| | 497.959
| 497.959
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 497.985
| 497.985
|-
|-
| |  
|
| |  
|
| | 22/53
| 22/53
| |  
|
| |  
|
| | 498.113
| 498.113
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 498.178
| 498.178
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 49/118
| 49/118
| | 498.305
| 498.305
|-
|-
| |  
|
| |  
|
| |  
|
| | 27/65
| 27/65
| |  
|
| | 498.4615
| 498.4615
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 32/77
| 32/77
| | 498.701
| 498.701
|-
|-
| | 5/12
| 5/12
| |  
|
| |  
|
| |  
|
| |  
|
| | 500
| 500
|}
|}

Revision as of 20:35, 16 August 2022

↖ 11L 16s ↑ 12L 16s 13L 16s ↗
← 11L 17s 12L 17s 13L 17s →
↙ 11L 18s ↓ 12L 18s 13L 18s ↘ 
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐
│║│║│║││║│║││║│║│║││║│║││║│║│││
│││││││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLssLsLssLsLsLssLsLssLsLss
ssLsLssLsLssLsLsLssLsLssLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 12\29 to 5\12 (496.6 ¢ to 500.0 ¢)
Dark 7\12 to 17\29 (700.0 ¢ to 703.4 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 2:1 to 5:2 (minihard)
Related MOS scales
Parent 12L 5s
Sister 17L 12s
Daughters 29L 12s, 12L 29s
Neutralized 24L 5s
2-Flought 41L 17s, 12L 46s
Equal tunings
Equalized (L:s = 1:1) 12\29 (496.6 ¢)
Supersoft (L:s = 4:3) 41\99 (497.0 ¢)
Soft (L:s = 3:2) 29\70 (497.1 ¢)
Semisoft (L:s = 5:3) 46\111 (497.3 ¢)
Basic (L:s = 2:1) 17\41 (497.6 ¢)
Semihard (L:s = 5:2) 39\94 (497.9 ¢)
Hard (L:s = 3:1) 22\53 (498.1 ¢)
Superhard (L:s = 4:1) 27\65 (498.5 ¢)
Collapsed (L:s = 1:0) 5\12 (500.0 ¢)

The 12L 17s MOS scale splits the small steps 1-1-2-1-2-1-1-2-1-2-1-2 between the large steps. Its chroma-positive generator is a near-perfect fourth of no more than 5\12 (500 ¢), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.

Scale tree

12/29 496.552
53/128 496.875
41/99 496.97
70/169 497.041
29/70 497.143
497.211
75/181 497.238
497.254
46/111 497.297
497.353
63/152 497.368
17/41 497.561
56/135 497.778
39/94 497.842
497.935
61/147 497.959
497.985
22/53 498.113
498.178
49/118 498.305
27/65 498.4615
32/77 498.701
5/12 500
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