13L 7s
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Step pattern
LLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
3\20 to 2\13 (180.0 ¢ to 184.6 ¢)
Dark
11\13 to 17\20 (1015.4 ¢ to 1020.0 ¢)
Related to
6L 1s (archaeotonic)
With tunings
3:2 to 2:1 (hyposoft)
Parent
7L 6s
Sister
7L 13s
Daughters
20L 13s, 13L 20s
Neutralized
6L 14s
2-Flought
33L 7s, 13L 27s
Equalized (L:s = 1:1)
3\20 (180.0 ¢)
Supersoft (L:s = 4:3)
11\73 (180.8 ¢)
Soft (L:s = 3:2)
8\53 (181.1 ¢)
Semisoft (L:s = 5:3)
13\86 (181.4 ¢)
Basic (L:s = 2:1)
5\33 (181.8 ¢)
Semihard (L:s = 5:2)
12\79 (182.3 ¢)
Hard (L:s = 3:1)
7\46 (182.6 ¢)
Superhard (L:s = 4:1)
9\59 (183.1 ¢)
Collapsed (L:s = 1:0)
2\13 (184.6 ¢)
| ↖ 12L 6s | ↑ 13L 6s | 14L 6s ↗ |
| ← 12L 7s | 13L 7s | 14L 7s → |
| ↙ 12L 8s | ↓ 13L 8s | 14L 8s ↘ |
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║║│║║│║║│║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLsLLsLLsLLsLLsLLsLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
13L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 7 small steps, repeating every octave. 13L 7s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 180 ¢ to 184.6 ¢, or from 1015.4 ¢ to 1020 ¢.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
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 60.0 ¢ |
| Major 1-mosstep | M1ms | L | 60.0 ¢ to 92.3 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 92.3 ¢ to 120.0 ¢ |
| Major 2-mosstep | M2ms | 2L | 120.0 ¢ to 184.6 ¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | L + 2s | 92.3 ¢ to 180.0 ¢ |
| Perfect 3-mosstep | P3ms | 2L + s | 180.0 ¢ to 184.6 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 184.6 ¢ to 240.0 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 240.0 ¢ to 276.9 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 276.9 ¢ to 300.0 ¢ |
| Major 5-mosstep | M5ms | 4L + s | 300.0 ¢ to 369.2 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 276.9 ¢ to 360.0 ¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 360.0 ¢ to 369.2 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 369.2 ¢ to 420.0 ¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 420.0 ¢ to 461.5 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 5L + 3s | 461.5 ¢ to 480.0 ¢ |
| Major 8-mosstep | M8ms | 6L + 2s | 480.0 ¢ to 553.8 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 461.5 ¢ to 540.0 ¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 540.0 ¢ to 553.8 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 6L + 4s | 553.8 ¢ to 600.0 ¢ |
| Major 10-mosstep | M10ms | 7L + 3s | 600.0 ¢ to 646.2 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 7L + 4s | 646.2 ¢ to 660.0 ¢ |
| Major 11-mosstep | M11ms | 8L + 3s | 660.0 ¢ to 738.5 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 7L + 5s | 646.2 ¢ to 720.0 ¢ |
| Major 12-mosstep | M12ms | 8L + 4s | 720.0 ¢ to 738.5 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 8L + 5s | 738.5 ¢ to 780.0 ¢ |
| Major 13-mosstep | M13ms | 9L + 4s | 780.0 ¢ to 830.8 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 9L + 5s | 830.8 ¢ to 840.0 ¢ |
| Major 14-mosstep | M14ms | 10L + 4s | 840.0 ¢ to 923.1 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 9L + 6s | 830.8 ¢ to 900.0 ¢ |
| Major 15-mosstep | M15ms | 10L + 5s | 900.0 ¢ to 923.1 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 10L + 6s | 923.1 ¢ to 960.0 ¢ |
| Major 16-mosstep | M16ms | 11L + 5s | 960.0 ¢ to 1015.4 ¢ | |
| 17-mosstep | Perfect 17-mosstep | P17ms | 11L + 6s | 1015.4 ¢ to 1020.0 ¢ |
| Augmented 17-mosstep | A17ms | 12L + 5s | 1020.0 ¢ to 1107.7 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 11L + 7s | 1015.4 ¢ to 1080.0 ¢ |
| Major 18-mosstep | M18ms | 12L + 6s | 1080.0 ¢ to 1107.7 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 12L + 7s | 1107.7 ¢ to 1140.0 ¢ |
| Major 19-mosstep | M19ms | 13L + 6s | 1140.0 ¢ to 1200.0 ¢ | |
| 20-mosstep | Perfect 20-mosstep | P20ms | 13L + 7s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 32 | Augmented 16-mosdegree | A16md |
| 31 | Augmented 13-mosdegree | A13md |
| 30 | Augmented 10-mosdegree | A10md |
| 29 | Augmented 7-mosdegree | A7md |
| 28 | Augmented 4-mosdegree | A4md |
| 27 | Augmented 1-mosdegree | A1md |
| 26 | Augmented 18-mosdegree | A18md |
| 25 | Augmented 15-mosdegree | A15md |
| 24 | Augmented 12-mosdegree | A12md |
| 23 | Augmented 9-mosdegree | A9md |
| 22 | Augmented 6-mosdegree | A6md |
| 21 | Augmented 3-mosdegree | A3md |
| 20 | Augmented 0-mosdegree | A0md |
| 19 | Augmented 17-mosdegree | A17md |
| 18 | Major 14-mosdegree | M14md |
| 17 | Major 11-mosdegree | M11md |
| 16 | Major 8-mosdegree | M8md |
| 15 | Major 5-mosdegree | M5md |
| 14 | Major 2-mosdegree | M2md |
| 13 | Major 19-mosdegree | M19md |
| 12 | Major 16-mosdegree | M16md |
| 11 | Major 13-mosdegree | M13md |
| 10 | Major 10-mosdegree | M10md |
| 9 | Major 7-mosdegree | M7md |
| 8 | Major 4-mosdegree | M4md |
| 7 | Major 1-mosdegree | M1md |
| 6 | Major 18-mosdegree | M18md |
| 5 | Major 15-mosdegree | M15md |
| 4 | Major 12-mosdegree | M12md |
| 3 | Major 9-mosdegree | M9md |
| 2 | Major 6-mosdegree | M6md |
| 1 | Perfect 3-mosdegree | P3md |
| 0 | Perfect 0-mosdegree Perfect 20-mosdegree |
P0md P20md |
| −1 | Perfect 17-mosdegree | P17md |
| −2 | Minor 14-mosdegree | m14md |
| −3 | Minor 11-mosdegree | m11md |
| −4 | Minor 8-mosdegree | m8md |
| −5 | Minor 5-mosdegree | m5md |
| −6 | Minor 2-mosdegree | m2md |
| −7 | Minor 19-mosdegree | m19md |
| −8 | Minor 16-mosdegree | m16md |
| −9 | Minor 13-mosdegree | m13md |
| −10 | Minor 10-mosdegree | m10md |
| −11 | Minor 7-mosdegree | m7md |
| −12 | Minor 4-mosdegree | m4md |
| −13 | Minor 1-mosdegree | m1md |
| −14 | Minor 18-mosdegree | m18md |
| −15 | Minor 15-mosdegree | m15md |
| −16 | Minor 12-mosdegree | m12md |
| −17 | Minor 9-mosdegree | m9md |
| −18 | Minor 6-mosdegree | m6md |
| −19 | Diminished 3-mosdegree | d3md |
| −20 | Diminished 20-mosdegree | d20md |
| −21 | Diminished 17-mosdegree | d17md |
| −22 | Diminished 14-mosdegree | d14md |
| −23 | Diminished 11-mosdegree | d11md |
| −24 | Diminished 8-mosdegree | d8md |
| −25 | Diminished 5-mosdegree | d5md |
| −26 | Diminished 2-mosdegree | d2md |
| −27 | Diminished 19-mosdegree | d19md |
| −28 | Diminished 16-mosdegree | d16md |
| −29 | Diminished 13-mosdegree | d13md |
| −30 | Diminished 10-mosdegree | d10md |
| −31 | Diminished 7-mosdegree | d7md |
| −32 | Diminished 4-mosdegree | d4md |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |||
| 19|0 | 1 | LLsLLsLLsLLsLLsLLsLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Perf. |
| 18|1 | 4 | LLsLLsLLsLLsLLsLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 17|2 | 7 | LLsLLsLLsLLsLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 16|3 | 10 | LLsLLsLLsLsLLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 15|4 | 13 | LLsLLsLsLLsLLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 14|5 | 16 | LLsLsLLsLLsLLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 13|6 | 19 | LsLLsLLsLLsLLsLLsLLs | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 12|7 | 2 | LsLLsLLsLLsLLsLLsLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Perf. |
| 11|8 | 5 | LsLLsLLsLLsLLsLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 10|9 | 8 | LsLLsLLsLLsLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 9|10 | 11 | LsLLsLLsLsLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 8|11 | 14 | LsLLsLsLLsLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 7|12 | 17 | LsLsLLsLLsLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 6|13 | 20 | sLLsLLsLLsLLsLLsLLsL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 5|14 | 3 | sLLsLLsLLsLLsLLsLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Perf. |
| 4|15 | 6 | sLLsLLsLLsLLsLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 3|16 | 9 | sLLsLLsLLsLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 2|17 | 12 | sLLsLLsLsLLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 1|18 | 15 | sLLsLsLLsLLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 0|19 | 18 | sLsLLsLLsLLsLLsLLsLL | Perf. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\20 | 180.000 | 1020.000 | 1:1 | 1.000 | Equalized 13L 7s | |||||
| 17\113 | 180.531 | 1019.469 | 6:5 | 1.200 | ||||||
| 14\93 | 180.645 | 1019.355 | 5:4 | 1.250 | ||||||
| 25\166 | 180.723 | 1019.277 | 9:7 | 1.286 | ||||||
| 11\73 | 180.822 | 1019.178 | 4:3 | 1.333 | Supersoft 13L 7s | |||||
| 30\199 | 180.905 | 1019.095 | 11:8 | 1.375 | ||||||
| 19\126 | 180.952 | 1019.048 | 7:5 | 1.400 | ||||||
| 27\179 | 181.006 | 1018.994 | 10:7 | 1.429 | ||||||
| 8\53 | 181.132 | 1018.868 | 3:2 | 1.500 | Soft 13L 7s | |||||
| 29\192 | 181.250 | 1018.750 | 11:7 | 1.571 | ||||||
| 21\139 | 181.295 | 1018.705 | 8:5 | 1.600 | ||||||
| 34\225 | 181.333 | 1018.667 | 13:8 | 1.625 | ||||||
| 13\86 | 181.395 | 1018.605 | 5:3 | 1.667 | Semisoft 13L 7s | |||||
| 31\205 | 181.463 | 1018.537 | 12:7 | 1.714 | ||||||
| 18\119 | 181.513 | 1018.487 | 7:4 | 1.750 | ||||||
| 23\152 | 181.579 | 1018.421 | 9:5 | 1.800 | ||||||
| 5\33 | 181.818 | 1018.182 | 2:1 | 2.000 | Basic 13L 7s Scales with tunings softer than this are proper | |||||
| 22\145 | 182.069 | 1017.931 | 9:4 | 2.250 | ||||||
| 17\112 | 182.143 | 1017.857 | 7:3 | 2.333 | ||||||
| 29\191 | 182.199 | 1017.801 | 12:5 | 2.400 | ||||||
| 12\79 | 182.278 | 1017.722 | 5:2 | 2.500 | Semihard 13L 7s | |||||
| 31\204 | 182.353 | 1017.647 | 13:5 | 2.600 | ||||||
| 19\125 | 182.400 | 1017.600 | 8:3 | 2.667 | ||||||
| 26\171 | 182.456 | 1017.544 | 11:4 | 2.750 | ||||||
| 7\46 | 182.609 | 1017.391 | 3:1 | 3.000 | Hard 13L 7s Mitonic / Minortone | |||||
| 23\151 | 182.781 | 1017.219 | 10:3 | 3.333 | ||||||
| 16\105 | 182.857 | 1017.143 | 7:2 | 3.500 | ||||||
| 25\164 | 182.927 | 1017.073 | 11:3 | 3.667 | ||||||
| 9\59 | 183.051 | 1016.949 | 4:1 | 4.000 | Superhard 13L 7s | |||||
| 20\131 | 183.206 | 1016.794 | 9:2 | 4.500 | ||||||
| 11\72 | 183.333 | 1016.667 | 5:1 | 5.000 | ||||||
| 13\85 | 183.529 | 1016.471 | 6:1 | 6.000 | ||||||
| 2\13 | 184.615 | 1015.385 | 1:0 | → ∞ | Collapsed 13L 7s | |||||
See also
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