13L 14s
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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¢)
↖ 12L 13s | ↑ 13L 13s | 14L 13s ↗ |
← 12L 14s | 13L 14s | 14L 14s → |
↙ 12L 15s | ↓ 13L 15s | 14L 15s ↘ |
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║│║│║│║│║│║│║│║│║│││ │││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLsLsLsLsLsLsLsLsLsLsLsL
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
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 | 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
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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