15L 2s
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Scale structure
Step pattern
LLLLLLLLsLLLLLLLs
sLLLLLLLsLLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
9\17 to 8\15 (635.3¢ to 640.0¢)
Dark
7\15 to 8\17 (560.0¢ to 564.7¢)
TAMNAMS information
Descends from
2L 7s (balzano)
Required step ratio range
4:1 to 5:1
Related MOS scales
Parent
2L 13s
Sister
2L 15s
Daughters
17L 15s
15L 17s
Equal tunings
Equalized (L:s = 1:1)
9\17 (635.3¢)
Supersoft (L:s = 4:3)
35\66 (636.4¢)
Soft (L:s = 3:2)
26\49 (636.7¢)
Semisoft (L:s = 5:3)
43\81 (637.0¢)
Basic (L:s = 2:1)
17\32 (637.5¢)
Semihard (L:s = 5:2)
42\79 (638.0¢)
Hard (L:s = 3:1)
25\47 (638.3¢)
Superhard (L:s = 4:1)
33\62 (638.7¢)
Collapsed (L:s = 1:0)
8\15 (640.0¢)
| ↖14L 1s | ↑15L 1s | 16L 1s↗ |
| ←14L 2s | 15L 2s | 16L 2s→ |
| ↙14L 3s | ↓15L 3s | 16L 3s↘ |
┌╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥┬┐ │║║║║║║║║│║║║║║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLsLLLLLLLL
15L 17s
15L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 2 small steps, repeating every octave. 15L 2s is related to 2L 7s, expanding it by 8 tones. Generators that produce this scale range from 635.3¢ to 640¢, or from 560¢ to 564.7¢.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 16|0 | 1 | LLLLLLLLsLLLLLLLs |
| 15|1 | 10 | LLLLLLLsLLLLLLLLs |
| 14|2 | 2 | LLLLLLLsLLLLLLLsL |
| 13|3 | 11 | LLLLLLsLLLLLLLLsL |
| 12|4 | 3 | LLLLLLsLLLLLLLsLL |
| 11|5 | 12 | LLLLLsLLLLLLLLsLL |
| 10|6 | 4 | LLLLLsLLLLLLLsLLL |
| 9|7 | 13 | LLLLsLLLLLLLLsLLL |
| 8|8 | 5 | LLLLsLLLLLLLsLLLL |
| 7|9 | 14 | LLLsLLLLLLLLsLLLL |
| 6|10 | 6 | LLLsLLLLLLLsLLLLL |
| 5|11 | 15 | LLsLLLLLLLLsLLLLL |
| 4|12 | 7 | LLsLLLLLLLsLLLLLL |
| 3|13 | 16 | LsLLLLLLLLsLLLLLL |
| 2|14 | 8 | LsLLLLLLLsLLLLLLL |
| 1|15 | 17 | sLLLLLLLLsLLLLLLL |
| 0|16 | 9 | sLLLLLLLsLLLLLLLL |
Scale tree
| Generator (edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 9\17 | 635.294 | 564.706 | 1:1 | 1.000 | Equalized 15L 2s | |||||
| 53\100 | 636.000 | 564.000 | 6:5 | 1.200 | ||||||
| 44\83 | 636.145 | 563.855 | 5:4 | 1.250 | ||||||
| 79\149 | 636.242 | 563.758 | 9:7 | 1.286 | ||||||
| 35\66 | 636.364 | 563.636 | 4:3 | 1.333 | Supersoft 15L 2s | |||||
| 96\181 | 636.464 | 563.536 | 11:8 | 1.375 | ||||||
| 61\115 | 636.522 | 563.478 | 7:5 | 1.400 | ||||||
| 87\164 | 636.585 | 563.415 | 10:7 | 1.429 | ||||||
| 26\49 | 636.735 | 563.265 | 3:2 | 1.500 | Soft 15L 2s | |||||
| 95\179 | 636.872 | 563.128 | 11:7 | 1.571 | ||||||
| 69\130 | 636.923 | 563.077 | 8:5 | 1.600 | ||||||
| 112\211 | 636.967 | 563.033 | 13:8 | 1.625 | ||||||
| 43\81 | 637.037 | 562.963 | 5:3 | 1.667 | Semisoft 15L 2s | |||||
| 103\194 | 637.113 | 562.887 | 12:7 | 1.714 | ||||||
| 60\113 | 637.168 | 562.832 | 7:4 | 1.750 | ||||||
| 77\145 | 637.241 | 562.759 | 9:5 | 1.800 | ||||||
| 17\32 | 637.500 | 562.500 | 2:1 | 2.000 | Basic 15L 2s Scales with tunings softer than this are proper | |||||
| 76\143 | 637.762 | 562.238 | 9:4 | 2.250 | ||||||
| 59\111 | 637.838 | 562.162 | 7:3 | 2.333 | ||||||
| 101\190 | 637.895 | 562.105 | 12:5 | 2.400 | ||||||
| 42\79 | 637.975 | 562.025 | 5:2 | 2.500 | Semihard 15L 2s | |||||
| 109\205 | 638.049 | 561.951 | 13:5 | 2.600 | ||||||
| 67\126 | 638.095 | 561.905 | 8:3 | 2.667 | ||||||
| 92\173 | 638.150 | 561.850 | 11:4 | 2.750 | ||||||
| 25\47 | 638.298 | 561.702 | 3:1 | 3.000 | Hard 15L 2s | |||||
| 83\156 | 638.462 | 561.538 | 10:3 | 3.333 | ||||||
| 58\109 | 638.532 | 561.468 | 7:2 | 3.500 | ||||||
| 91\171 | 638.596 | 561.404 | 11:3 | 3.667 | ||||||
| 33\62 | 638.710 | 561.290 | 4:1 | 4.000 | Superhard 15L 2s | |||||
| 74\139 | 638.849 | 561.151 | 9:2 | 4.500 | ||||||
| 41\77 | 638.961 | 561.039 | 5:1 | 5.000 | ||||||
| 49\92 | 639.130 | 560.870 | 6:1 | 6.000 | ||||||
| 8\15 | 640.000 | 560.000 | 1:0 | → ∞ | Collapsed 15L 2s | |||||
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