13L 6s

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↖ 12L 5s ↑13L 5s 14L 5s ↗
← 12L 6s13L 6s 14L 6s →
↙ 12L 7s ↓13L 7s 14L 7s ↘
┌╥╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║│║║│║║│║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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)
Required 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¢)

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

Modes of 13L 6s
UDP Rotational 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

Scale Tree and Tuning Spectrum of 13L 6s
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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