12L 17s
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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
Descends from
5L 2s (diatonic)
Required step ratio range
2:1 to 5:2 (minihard)
Related MOS scales
Parent
12L 5s
Sister
17L 12s
Daughters
29L 12s, 12L 29s
Neutralized
24L 5s
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¢)
| ↖11L 16s | ↑12L 16s | 13L 16s↗ |
| ←11L 17s | 12L 17s | 13L 17s→ |
| ↙11L 18s | ↓12L 18s | 13L 18s↘ |
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║││║│║│║││║│║││║│║│││ │││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLssLsLssLsLsLssLsLssLsLsL
12L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 17 small steps, repeating every octave. 12L 17s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 496.6¢ to 500¢, or from 700¢ to 703.4¢.
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
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 12\29 | 496.552 | 703.448 | 1:1 | 1.000 | Equalized 12L 17s | |||||
| 65\157 | 496.815 | 703.185 | 6:5 | 1.200 | ||||||
| 53\128 | 496.875 | 703.125 | 5:4 | 1.250 | ||||||
| 94\227 | 496.916 | 703.084 | 9:7 | 1.286 | ||||||
| 41\99 | 496.970 | 703.030 | 4:3 | 1.333 | Supersoft 12L 17s | |||||
| 111\268 | 497.015 | 702.985 | 11:8 | 1.375 | ||||||
| 70\169 | 497.041 | 702.959 | 7:5 | 1.400 | ||||||
| 99\239 | 497.071 | 702.929 | 10:7 | 1.429 | ||||||
| 29\70 | 497.143 | 702.857 | 3:2 | 1.500 | Soft 12L 17s | |||||
| 104\251 | 497.211 | 702.789 | 11:7 | 1.571 | ||||||
| 75\181 | 497.238 | 702.762 | 8:5 | 1.600 | ||||||
| 121\292 | 497.260 | 702.740 | 13:8 | 1.625 | ||||||
| 46\111 | 497.297 | 702.703 | 5:3 | 1.667 | Semisoft 12L 17s | |||||
| 109\263 | 497.338 | 702.662 | 12:7 | 1.714 | ||||||
| 63\152 | 497.368 | 702.632 | 7:4 | 1.750 | ||||||
| 80\193 | 497.409 | 702.591 | 9:5 | 1.800 | ||||||
| 17\41 | 497.561 | 702.439 | 2:1 | 2.000 | Basic 12L 17s Scales with tunings softer than this are proper | |||||
| 73\176 | 497.727 | 702.273 | 9:4 | 2.250 | ||||||
| 56\135 | 497.778 | 702.222 | 7:3 | 2.333 | ||||||
| 95\229 | 497.817 | 702.183 | 12:5 | 2.400 | ||||||
| 39\94 | 497.872 | 702.128 | 5:2 | 2.500 | Semihard 12L 17s | |||||
| 100\241 | 497.925 | 702.075 | 13:5 | 2.600 | ||||||
| 61\147 | 497.959 | 702.041 | 8:3 | 2.667 | ||||||
| 83\200 | 498.000 | 702.000 | 11:4 | 2.750 | ||||||
| 22\53 | 498.113 | 701.887 | 3:1 | 3.000 | Hard 12L 17s | |||||
| 71\171 | 498.246 | 701.754 | 10:3 | 3.333 | ||||||
| 49\118 | 498.305 | 701.695 | 7:2 | 3.500 | ||||||
| 76\183 | 498.361 | 701.639 | 11:3 | 3.667 | ||||||
| 27\65 | 498.462 | 701.538 | 4:1 | 4.000 | Superhard 12L 17s | |||||
| 59\142 | 498.592 | 701.408 | 9:2 | 4.500 | ||||||
| 32\77 | 498.701 | 701.299 | 5:1 | 5.000 | ||||||
| 37\89 | 498.876 | 701.124 | 6:1 | 6.000 | ||||||
| 5\12 | 500.000 | 700.000 | 1:0 | → ∞ | Collapsed 12L 17s | |||||