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 ¢)
Descends from
6L 1s (archaeotonic)
Ancestor's step ratio range
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
The intervals of 13L 7s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 20-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
| 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
A chain of bright generators, each a perfect 3-mosstep, produces the following scale degrees. A chain of 20 bright generators contains the scale degrees of one of the modes of 13L 7s. Expanding the chain to 33 scale degrees produces the modes of either 20L 13s (for soft-of-basic tunings) or 13L 20s (for hard-of-basic tunings).
| 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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