13L 14s

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↖ 12L 13s ↑ 13L 13s 14L 13s ↗
← 12L 14s 13L 14s 14L 14s →
↙ 12L 15s ↓ 13L 15s 14L 15s ↘ 
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsLsLsLsLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 2\27 to 1\13 (88.9¢ to 92.3¢)
Dark 12\13 to 25\27 (1107.7¢ to 1111.1¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 4:1 to 9:2
Related MOS scales
Parent 13L 1s
Sister 14L 13s
Daughters 27L 13s, 13L 27s
Neutralized 26L 1s
2-Flought 40L 14s, 13L 41s
Equal tunings
Equalized (L:s = 1:1) 2\27 (88.9¢)
Supersoft (L:s = 4:3) 7\94 (89.4¢)
Soft (L:s = 3:2) 5\67 (89.6¢)
Semisoft (L:s = 5:3) 8\107 (89.7¢)
Basic (L:s = 2:1) 3\40 (90.0¢)
Semihard (L:s = 5:2) 7\93 (90.3¢)
Hard (L:s = 3:1) 4\53 (90.6¢)
Superhard (L:s = 4:1) 5\66 (90.9¢)
Collapsed (L:s = 1:0) 1\13 (92.3¢)

13L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 14 small steps, repeating every octave. 13L 14s is related to 1L 9s, expanding it by 17 tones. Generators that produce this scale range from 88.9¢ to 92.3¢, or from 1107.7¢ to 1111.1¢.

Modes

Modes of 13L 14s
UDP Cyclic
order		 Step
pattern
26|0 1 LsLsLsLsLsLsLsLsLsLsLsLsLss
25|1 3 LsLsLsLsLsLsLsLsLsLsLsLssLs
24|2 5 LsLsLsLsLsLsLsLsLsLsLssLsLs
23|3 7 LsLsLsLsLsLsLsLsLsLssLsLsLs
22|4 9 LsLsLsLsLsLsLsLsLssLsLsLsLs
21|5 11 LsLsLsLsLsLsLsLssLsLsLsLsLs
20|6 13 LsLsLsLsLsLsLssLsLsLsLsLsLs
19|7 15 LsLsLsLsLsLssLsLsLsLsLsLsLs
18|8 17 LsLsLsLsLssLsLsLsLsLsLsLsLs
17|9 19 LsLsLsLssLsLsLsLsLsLsLsLsLs
16|10 21 LsLsLssLsLsLsLsLsLsLsLsLsLs
15|11 23 LsLssLsLsLsLsLsLsLsLsLsLsLs
14|12 25 LssLsLsLsLsLsLsLsLsLsLsLsLs
13|13 27 sLsLsLsLsLsLsLsLsLsLsLsLsLs
12|14 2 sLsLsLsLsLsLsLsLsLsLsLsLssL
11|15 4 sLsLsLsLsLsLsLsLsLsLsLssLsL
10|16 6 sLsLsLsLsLsLsLsLsLsLssLsLsL
9|17 8 sLsLsLsLsLsLsLsLsLssLsLsLsL
8|18 10 sLsLsLsLsLsLsLsLssLsLsLsLsL
7|19 12 sLsLsLsLsLsLsLssLsLsLsLsLsL
6|20 14 sLsLsLsLsLsLssLsLsLsLsLsLsL
5|21 16 sLsLsLsLsLssLsLsLsLsLsLsLsL
4|22 18 sLsLsLsLssLsLsLsLsLsLsLsLsL
3|23 20 sLsLsLssLsLsLsLsLsLsLsLsLsL
2|24 22 sLsLssLsLsLsLsLsLsLsLsLsLsL
1|25 24 sLssLsLsLsLsLsLsLsLsLsLsLsL
0|26 26 ssLsLsLsLsLsLsLsLsLsLsLsLsL

Intervals

Intervals of 13L 14s
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 44.4¢
Major 1-mosstep M1ms L 44.4¢ to 92.3¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0¢ to 88.9¢
Perfect 2-mosstep P2ms L + s 88.9¢ to 92.3¢
3-mosstep Minor 3-mosstep m3ms L + 2s 92.3¢ to 133.3¢
Major 3-mosstep M3ms 2L + s 133.3¢ to 184.6¢
4-mosstep Minor 4-mosstep m4ms L + 3s 92.3¢ to 177.8¢
Major 4-mosstep M4ms 2L + 2s 177.8¢ to 184.6¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 184.6¢ to 222.2¢
Major 5-mosstep M5ms 3L + 2s 222.2¢ to 276.9¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 184.6¢ to 266.7¢
Major 6-mosstep M6ms 3L + 3s 266.7¢ to 276.9¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 276.9¢ to 311.1¢
Major 7-mosstep M7ms 4L + 3s 311.1¢ to 369.2¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 276.9¢ to 355.6¢
Major 8-mosstep M8ms 4L + 4s 355.6¢ to 369.2¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 369.2¢ to 400.0¢
Major 9-mosstep M9ms 5L + 4s 400.0¢ to 461.5¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 369.2¢ to 444.4¢
Major 10-mosstep M10ms 5L + 5s 444.4¢ to 461.5¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 461.5¢ to 488.9¢
Major 11-mosstep M11ms 6L + 5s 488.9¢ to 553.8¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 461.5¢ to 533.3¢
Major 12-mosstep M12ms 6L + 6s 533.3¢ to 553.8¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 553.8¢ to 577.8¢
Major 13-mosstep M13ms 7L + 6s 577.8¢ to 646.2¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 553.8¢ to 622.2¢
Major 14-mosstep M14ms 7L + 7s 622.2¢ to 646.2¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 646.2¢ to 666.7¢
Major 15-mosstep M15ms 8L + 7s 666.7¢ to 738.5¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 646.2¢ to 711.1¢
Major 16-mosstep M16ms 8L + 8s 711.1¢ to 738.5¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 738.5¢ to 755.6¢
Major 17-mosstep M17ms 9L + 8s 755.6¢ to 830.8¢
18-mosstep Minor 18-mosstep m18ms 8L + 10s 738.5¢ to 800.0¢
Major 18-mosstep M18ms 9L + 9s 800.0¢ to 830.8¢
19-mosstep Minor 19-mosstep m19ms 9L + 10s 830.8¢ to 844.4¢
Major 19-mosstep M19ms 10L + 9s 844.4¢ to 923.1¢
20-mosstep Minor 20-mosstep m20ms 9L + 11s 830.8¢ to 888.9¢
Major 20-mosstep M20ms 10L + 10s 888.9¢ to 923.1¢
21-mosstep Minor 21-mosstep m21ms 10L + 11s 923.1¢ to 933.3¢
Major 21-mosstep M21ms 11L + 10s 933.3¢ to 1015.4¢
22-mosstep Minor 22-mosstep m22ms 10L + 12s 923.1¢ to 977.8¢
Major 22-mosstep M22ms 11L + 11s 977.8¢ to 1015.4¢
23-mosstep Minor 23-mosstep m23ms 11L + 12s 1015.4¢ to 1022.2¢
Major 23-mosstep M23ms 12L + 11s 1022.2¢ to 1107.7¢
24-mosstep Minor 24-mosstep m24ms 11L + 13s 1015.4¢ to 1066.7¢
Major 24-mosstep M24ms 12L + 12s 1066.7¢ to 1107.7¢
25-mosstep Perfect 25-mosstep P25ms 12L + 13s 1107.7¢ to 1111.1¢
Augmented 25-mosstep A25ms 13L + 12s 1111.1¢ to 1200.0¢
26-mosstep Minor 26-mosstep m26ms 12L + 14s 1107.7¢ to 1155.6¢
Major 26-mosstep M26ms 13L + 13s 1155.6¢ to 1200.0¢
27-mosstep Perfect 27-mosstep P27ms 13L + 14s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 13L 14s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\27 88.889 1111.111 1:1 1.000 Equalized 13L 14s
11\148 89.189 1110.811 6:5 1.200
9\121 89.256 1110.744 5:4 1.250
16\215 89.302 1110.698 9:7 1.286
7\94 89.362 1110.638 4:3 1.333 Supersoft 13L 14s
19\255 89.412 1110.588 11:8 1.375
12\161 89.441 1110.559 7:5 1.400
17\228 89.474 1110.526 10:7 1.429
5\67 89.552 1110.448 3:2 1.500 Soft 13L 14s
18\241 89.627 1110.373 11:7 1.571
13\174 89.655 1110.345 8:5 1.600
21\281 89.680 1110.320 13:8 1.625
8\107 89.720 1110.280 5:3 1.667 Semisoft 13L 14s
19\254 89.764 1110.236 12:7 1.714
11\147 89.796 1110.204 7:4 1.750
14\187 89.840 1110.160 9:5 1.800
3\40 90.000 1110.000 2:1 2.000 Basic 13L 14s
Scales with tunings softer than this are proper
13\173 90.173 1109.827 9:4 2.250
10\133 90.226 1109.774 7:3 2.333
17\226 90.265 1109.735 12:5 2.400
7\93 90.323 1109.677 5:2 2.500 Semihard 13L 14s
18\239 90.377 1109.623 13:5 2.600
11\146 90.411 1109.589 8:3 2.667
15\199 90.452 1109.548 11:4 2.750
4\53 90.566 1109.434 3:1 3.000 Hard 13L 14s
13\172 90.698 1109.302 10:3 3.333
9\119 90.756 1109.244 7:2 3.500
14\185 90.811 1109.189 11:3 3.667
5\66 90.909 1109.091 4:1 4.000 Superhard 13L 14s
11\145 91.034 1108.966 9:2 4.500
6\79 91.139 1108.861 5:1 5.000
7\92 91.304 1108.696 6:1 6.000
1\13 92.308 1107.692 1:0 → ∞ Collapsed 13L 14s


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