13L 6s
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Scale structure
Step pattern
LLLsLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLsLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
16\19 to 11\13 (1010.5¢ to 1015.4¢)
Dark
2\13 to 3\19 (184.6¢ to 189.5¢)
TAMNAMS information
Descends from
6L 1s (archaeotonic)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
6L 7s
Sister
6L 13s
Daughters
19L 13s, 13L 19s
Neutralized
7L 12s
2-Flought
32L 6s, 13L 25s
Equal tunings
Equalized (L:s = 1:1)
16\19 (1010.5¢)
Supersoft (L:s = 4:3)
59\70 (1011.4¢)
Soft (L:s = 3:2)
43\51 (1011.8¢)
Semisoft (L:s = 5:3)
70\83 (1012.0¢)
Basic (L:s = 2:1)
27\32 (1012.5¢)
Semihard (L:s = 5:2)
65\77 (1013.0¢)
Hard (L:s = 3:1)
38\45 (1013.3¢)
Superhard (L:s = 4:1)
49\58 (1013.8¢)
Collapsed (L:s = 1:0)
11\13 (1015.4¢)
| ↖ 12L 5s | ↑ 13L 5s | 14L 5s ↗ |
| ← 12L 6s | 13L 6s | 14L 6s → |
| ↙ 12L 7s | ↓ 13L 7s | 14L 7s ↘ |
┌╥╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║│║║│║║│║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLsLLsLLsLLsLLL
13L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 6 small steps, repeating every octave. 13L 6s is a grandchild scale of 6L 1s, expanding it by 12 tones. Generators that produce this scale range from 1010.5¢ to 1015.4¢, or from 184.6¢ to 189.5¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 18|0 | 1 | LLLsLLsLLsLLsLLsLLs |
| 17|1 | 17 | LLsLLLsLLsLLsLLsLLs |
| 16|2 | 14 | LLsLLsLLLsLLsLLsLLs |
| 15|3 | 11 | LLsLLsLLsLLLsLLsLLs |
| 14|4 | 8 | LLsLLsLLsLLsLLLsLLs |
| 13|5 | 5 | LLsLLsLLsLLsLLsLLLs |
| 12|6 | 2 | LLsLLsLLsLLsLLsLLsL |
| 11|7 | 18 | LsLLLsLLsLLsLLsLLsL |
| 10|8 | 15 | LsLLsLLLsLLsLLsLLsL |
| 9|9 | 12 | LsLLsLLsLLLsLLsLLsL |
| 8|10 | 9 | LsLLsLLsLLsLLLsLLsL |
| 7|11 | 6 | LsLLsLLsLLsLLsLLLsL |
| 6|12 | 3 | LsLLsLLsLLsLLsLLsLL |
| 5|13 | 19 | sLLLsLLsLLsLLsLLsLL |
| 4|14 | 16 | sLLsLLLsLLsLLsLLsLL |
| 3|15 | 13 | sLLsLLsLLLsLLsLLsLL |
| 2|16 | 10 | sLLsLLsLLsLLLsLLsLL |
| 1|17 | 7 | sLLsLLsLLsLLsLLLsLL |
| 0|18 | 4 | sLLsLLsLLsLLsLLsLLL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 16\19 | 1010.526 | 189.474 | 1:1 | 1.000 | Equalized 13L 6s | |||||
| 91\108 | 1011.111 | 188.889 | 6:5 | 1.200 | ||||||
| 75\89 | 1011.236 | 188.764 | 5:4 | 1.250 | ||||||
| 134\159 | 1011.321 | 188.679 | 9:7 | 1.286 | ||||||
| 59\70 | 1011.429 | 188.571 | 4:3 | 1.333 | Supersoft 13L 6s | |||||
| 161\191 | 1011.518 | 188.482 | 11:8 | 1.375 | ||||||
| 102\121 | 1011.570 | 188.430 | 7:5 | 1.400 | ||||||
| 145\172 | 1011.628 | 188.372 | 10:7 | 1.429 | ||||||
| 43\51 | 1011.765 | 188.235 | 3:2 | 1.500 | Soft 13L 6s | |||||
| 156\185 | 1011.892 | 188.108 | 11:7 | 1.571 | ||||||
| 113\134 | 1011.940 | 188.060 | 8:5 | 1.600 | ||||||
| 183\217 | 1011.982 | 188.018 | 13:8 | 1.625 | ||||||
| 70\83 | 1012.048 | 187.952 | 5:3 | 1.667 | Semisoft 13L 6s | |||||
| 167\198 | 1012.121 | 187.879 | 12:7 | 1.714 | ||||||
| 97\115 | 1012.174 | 187.826 | 7:4 | 1.750 | ||||||
| 124\147 | 1012.245 | 187.755 | 9:5 | 1.800 | ||||||
| 27\32 | 1012.500 | 187.500 | 2:1 | 2.000 | Basic 13L 6s Scales with tunings softer than this are proper | |||||
| 119\141 | 1012.766 | 187.234 | 9:4 | 2.250 | ||||||
| 92\109 | 1012.844 | 187.156 | 7:3 | 2.333 | ||||||
| 157\186 | 1012.903 | 187.097 | 12:5 | 2.400 | ||||||
| 65\77 | 1012.987 | 187.013 | 5:2 | 2.500 | Semihard 13L 6s | |||||
| 168\199 | 1013.065 | 186.935 | 13:5 | 2.600 | ||||||
| 103\122 | 1013.115 | 186.885 | 8:3 | 2.667 | ||||||
| 141\167 | 1013.174 | 186.826 | 11:4 | 2.750 | ||||||
| 38\45 | 1013.333 | 186.667 | 3:1 | 3.000 | Hard 13L 6s | |||||
| 125\148 | 1013.514 | 186.486 | 10:3 | 3.333 | ||||||
| 87\103 | 1013.592 | 186.408 | 7:2 | 3.500 | ||||||
| 136\161 | 1013.665 | 186.335 | 11:3 | 3.667 | ||||||
| 49\58 | 1013.793 | 186.207 | 4:1 | 4.000 | Superhard 13L 6s | |||||
| 109\129 | 1013.953 | 186.047 | 9:2 | 4.500 | ||||||
| 60\71 | 1014.085 | 185.915 | 5:1 | 5.000 | ||||||
| 71\84 | 1014.286 | 185.714 | 6:1 | 6.000 | ||||||
| 11\13 | 1015.385 | 184.615 | 1:0 | → ∞ | Collapsed 13L 6s | |||||
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