13L 6s

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↖ 12L 5s ↑ 13L 5s 14L 5s ↗
← 12L 6s 13L 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)
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¢)

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 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

Intervals

Intervals of 13L 6s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 63.2¢
Major 1-mosstep M1ms L 63.2¢ to 92.3¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3¢ to 126.3¢
Major 2-mosstep M2ms 2L 126.3¢ to 184.6¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 184.6¢ to 189.5¢
Augmented 3-mosstep A3ms 3L 189.5¢ to 276.9¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 184.6¢ to 252.6¢
Major 4-mosstep M4ms 3L + s 252.6¢ to 276.9¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 276.9¢ to 315.8¢
Major 5-mosstep M5ms 4L + s 315.8¢ to 369.2¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 369.2¢ to 378.9¢
Major 6-mosstep M6ms 5L + s 378.9¢ to 461.5¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 369.2¢ to 442.1¢
Major 7-mosstep M7ms 5L + 2s 442.1¢ to 461.5¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 461.5¢ to 505.3¢
Major 8-mosstep M8ms 6L + 2s 505.3¢ to 553.8¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 553.8¢ to 568.4¢
Major 9-mosstep M9ms 7L + 2s 568.4¢ to 646.2¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 553.8¢ to 631.6¢
Major 10-mosstep M10ms 7L + 3s 631.6¢ to 646.2¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 646.2¢ to 694.7¢
Major 11-mosstep M11ms 8L + 3s 694.7¢ to 738.5¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 738.5¢ to 757.9¢
Major 12-mosstep M12ms 9L + 3s 757.9¢ to 830.8¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 738.5¢ to 821.1¢
Major 13-mosstep M13ms 9L + 4s 821.1¢ to 830.8¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 830.8¢ to 884.2¢
Major 14-mosstep M14ms 10L + 4s 884.2¢ to 923.1¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 923.1¢ to 947.4¢
Major 15-mosstep M15ms 11L + 4s 947.4¢ to 1015.4¢
16-mosstep Diminished 16-mosstep d16ms 10L + 6s 923.1¢ to 1010.5¢
Perfect 16-mosstep P16ms 11L + 5s 1010.5¢ to 1015.4¢
17-mosstep Minor 17-mosstep m17ms 11L + 6s 1015.4¢ to 1073.7¢
Major 17-mosstep M17ms 12L + 5s 1073.7¢ to 1107.7¢
18-mosstep Minor 18-mosstep m18ms 12L + 6s 1107.7¢ to 1136.8¢
Major 18-mosstep M18ms 13L + 5s 1136.8¢ to 1200.0¢
19-mosstep Perfect 19-mosstep P19ms 13L + 6s 1200.0¢

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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