13L 8s
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Step pattern
LLsLLsLsLLsLLsLsLLsLs
sLsLLsLsLLsLLsLsLLsLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
8\21 to 5\13 (457.1 ¢ to 461.5 ¢)
Dark
8\13 to 13\21 (738.5 ¢ to 742.9 ¢)
Descends from
5L 3s (oneirotonic)
Ancestor's step ratio range
3:2 to 2:1 (hyposoft)
Parent
8L 5s
Sister
8L 13s
Daughters
21L 13s, 13L 21s
Neutralized
5L 16s
2-Flought
34L 8s, 13L 29s
Equalized (L:s = 1:1)
8\21 (457.1 ¢)
Supersoft (L:s = 4:3)
29\76 (457.9 ¢)
Soft (L:s = 3:2)
21\55 (458.2 ¢)
Semisoft (L:s = 5:3)
34\89 (458.4 ¢)
Basic (L:s = 2:1)
13\34 (458.8 ¢)
Semihard (L:s = 5:2)
31\81 (459.3 ¢)
Hard (L:s = 3:1)
18\47 (459.6 ¢)
Superhard (L:s = 4:1)
23\60 (460.0 ¢)
Collapsed (L:s = 1:0)
5\13 (461.5 ¢)
| ↖ 12L 7s | ↑ 13L 7s | 14L 7s ↗ |
| ← 12L 8s | 13L 8s | 14L 8s → |
| ↙ 12L 9s | ↓ 13L 9s | 14L 9s ↘ |
┌╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║║│║│║║│║║│║│║║│║││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLsLLsLsLLsLLsLsLLsLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
13L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 8 small steps, repeating every octave. 13L 8s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 457.1 ¢ to 461.5 ¢, or from 738.5 ¢ to 742.9 ¢.
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 57.1 ¢ |
| Major 1-mosstep | M1ms | L | 57.1 ¢ to 92.3 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 92.3 ¢ to 114.3 ¢ |
| Major 2-mosstep | M2ms | 2L | 114.3 ¢ to 184.6 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 92.3 ¢ to 171.4 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 171.4 ¢ to 184.6 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 184.6 ¢ to 228.6 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 228.6 ¢ to 276.9 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 276.9 ¢ to 285.7 ¢ |
| Major 5-mosstep | M5ms | 4L + s | 285.7 ¢ to 369.2 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 276.9 ¢ to 342.9 ¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 342.9 ¢ to 369.2 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 369.2 ¢ to 400.0 ¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 400.0 ¢ to 461.5 ¢ | |
| 8-mosstep | Diminished 8-mosstep | d8ms | 4L + 4s | 369.2 ¢ to 457.1 ¢ |
| Perfect 8-mosstep | P8ms | 5L + 3s | 457.1 ¢ to 461.5 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 461.5 ¢ to 514.3 ¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 514.3 ¢ to 553.8 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 6L + 4s | 553.8 ¢ to 571.4 ¢ |
| Major 10-mosstep | M10ms | 7L + 3s | 571.4 ¢ to 646.2 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 6L + 5s | 553.8 ¢ to 628.6 ¢ |
| Major 11-mosstep | M11ms | 7L + 4s | 628.6 ¢ to 646.2 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 7L + 5s | 646.2 ¢ to 685.7 ¢ |
| Major 12-mosstep | M12ms | 8L + 4s | 685.7 ¢ to 738.5 ¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 8L + 5s | 738.5 ¢ to 742.9 ¢ |
| Augmented 13-mosstep | A13ms | 9L + 4s | 742.9 ¢ to 830.8 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 8L + 6s | 738.5 ¢ to 800.0 ¢ |
| Major 14-mosstep | M14ms | 9L + 5s | 800.0 ¢ to 830.8 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 9L + 6s | 830.8 ¢ to 857.1 ¢ |
| Major 15-mosstep | M15ms | 10L + 5s | 857.1 ¢ to 923.1 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 9L + 7s | 830.8 ¢ to 914.3 ¢ |
| Major 16-mosstep | M16ms | 10L + 6s | 914.3 ¢ to 923.1 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 10L + 7s | 923.1 ¢ to 971.4 ¢ |
| Major 17-mosstep | M17ms | 11L + 6s | 971.4 ¢ to 1015.4 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 11L + 7s | 1015.4 ¢ to 1028.6 ¢ |
| Major 18-mosstep | M18ms | 12L + 6s | 1028.6 ¢ to 1107.7 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 11L + 8s | 1015.4 ¢ to 1085.7 ¢ |
| Major 19-mosstep | M19ms | 12L + 7s | 1085.7 ¢ to 1107.7 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 12L + 8s | 1107.7 ¢ to 1142.9 ¢ |
| Major 20-mosstep | M20ms | 13L + 7s | 1142.9 ¢ to 1200.0 ¢ | |
| 21-mosstep | Perfect 21-mosstep | P21ms | 13L + 8s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 33 | Augmented 12-mosdegree | A12md |
| 32 | Augmented 4-mosdegree | A4md |
| 31 | Augmented 17-mosdegree | A17md |
| 30 | Augmented 9-mosdegree | A9md |
| 29 | Augmented 1-mosdegree | A1md |
| 28 | Augmented 14-mosdegree | A14md |
| 27 | Augmented 6-mosdegree | A6md |
| 26 | Augmented 19-mosdegree | A19md |
| 25 | Augmented 11-mosdegree | A11md |
| 24 | Augmented 3-mosdegree | A3md |
| 23 | Augmented 16-mosdegree | A16md |
| 22 | Augmented 8-mosdegree | A8md |
| 21 | Augmented 0-mosdegree | A0md |
| 20 | Augmented 13-mosdegree | A13md |
| 19 | Major 5-mosdegree | M5md |
| 18 | Major 18-mosdegree | M18md |
| 17 | Major 10-mosdegree | M10md |
| 16 | Major 2-mosdegree | M2md |
| 15 | Major 15-mosdegree | M15md |
| 14 | Major 7-mosdegree | M7md |
| 13 | Major 20-mosdegree | M20md |
| 12 | Major 12-mosdegree | M12md |
| 11 | Major 4-mosdegree | M4md |
| 10 | Major 17-mosdegree | M17md |
| 9 | Major 9-mosdegree | M9md |
| 8 | Major 1-mosdegree | M1md |
| 7 | Major 14-mosdegree | M14md |
| 6 | Major 6-mosdegree | M6md |
| 5 | Major 19-mosdegree | M19md |
| 4 | Major 11-mosdegree | M11md |
| 3 | Major 3-mosdegree | M3md |
| 2 | Major 16-mosdegree | M16md |
| 1 | Perfect 8-mosdegree | P8md |
| 0 | Perfect 0-mosdegree Perfect 21-mosdegree |
P0md P21md |
| −1 | Perfect 13-mosdegree | P13md |
| −2 | Minor 5-mosdegree | m5md |
| −3 | Minor 18-mosdegree | m18md |
| −4 | Minor 10-mosdegree | m10md |
| −5 | Minor 2-mosdegree | m2md |
| −6 | Minor 15-mosdegree | m15md |
| −7 | Minor 7-mosdegree | m7md |
| −8 | Minor 20-mosdegree | m20md |
| −9 | Minor 12-mosdegree | m12md |
| −10 | Minor 4-mosdegree | m4md |
| −11 | Minor 17-mosdegree | m17md |
| −12 | Minor 9-mosdegree | m9md |
| −13 | Minor 1-mosdegree | m1md |
| −14 | Minor 14-mosdegree | m14md |
| −15 | Minor 6-mosdegree | m6md |
| −16 | Minor 19-mosdegree | m19md |
| −17 | Minor 11-mosdegree | m11md |
| −18 | Minor 3-mosdegree | m3md |
| −19 | Minor 16-mosdegree | m16md |
| −20 | Diminished 8-mosdegree | d8md |
| −21 | Diminished 21-mosdegree | d21md |
| −22 | Diminished 13-mosdegree | d13md |
| −23 | Diminished 5-mosdegree | d5md |
| −24 | Diminished 18-mosdegree | d18md |
| −25 | Diminished 10-mosdegree | d10md |
| −26 | Diminished 2-mosdegree | d2md |
| −27 | Diminished 15-mosdegree | d15md |
| −28 | Diminished 7-mosdegree | d7md |
| −29 | Diminished 20-mosdegree | d20md |
| −30 | Diminished 12-mosdegree | d12md |
| −31 | Diminished 4-mosdegree | d4md |
| −32 | Diminished 17-mosdegree | d17md |
| −33 | Diminished 9-mosdegree | d9md |
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 | 21 | |||
| 20|0 | 1 | LLsLLsLsLLsLLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 19|1 | 9 | LLsLLsLsLLsLsLLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 18|2 | 17 | LLsLsLLsLLsLsLLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 17|3 | 4 | LLsLsLLsLLsLsLLsLsLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 16|4 | 12 | LLsLsLLsLsLLsLLsLsLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 15|5 | 20 | LsLLsLLsLsLLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 14|6 | 7 | LsLLsLLsLsLLsLsLLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 13|7 | 15 | LsLLsLsLLsLLsLsLLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 12|8 | 2 | LsLLsLsLLsLLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 11|9 | 10 | LsLLsLsLLsLsLLsLLsLsL | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 10|10 | 18 | LsLsLLsLLsLsLLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 9|11 | 5 | LsLsLLsLLsLsLLsLsLLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 8|12 | 13 | LsLsLLsLsLLsLLsLsLLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 7|13 | 21 | sLLsLLsLsLLsLLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 6|14 | 8 | sLLsLLsLsLLsLsLLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 5|15 | 16 | sLLsLsLLsLLsLsLLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 4|16 | 3 | sLLsLsLLsLLsLsLLsLsLL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 3|17 | 11 | sLLsLsLLsLsLLsLLsLsLL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 2|18 | 19 | sLsLLsLLsLsLLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 1|19 | 6 | sLsLLsLLsLsLLsLsLLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 0|20 | 14 | sLsLLsLsLLsLLsLsLLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 8\21 | 457.143 | 742.857 | 1:1 | 1.000 | Equalized 13L 8s | |||||
| 45\118 | 457.627 | 742.373 | 6:5 | 1.200 | ||||||
| 37\97 | 457.732 | 742.268 | 5:4 | 1.250 | ||||||
| 66\173 | 457.803 | 742.197 | 9:7 | 1.286 | ||||||
| 29\76 | 457.895 | 742.105 | 4:3 | 1.333 | Supersoft 13L 8s | |||||
| 79\207 | 457.971 | 742.029 | 11:8 | 1.375 | ||||||
| 50\131 | 458.015 | 741.985 | 7:5 | 1.400 | ||||||
| 71\186 | 458.065 | 741.935 | 10:7 | 1.429 | ||||||
| 21\55 | 458.182 | 741.818 | 3:2 | 1.500 | Soft 13L 8s | |||||
| 76\199 | 458.291 | 741.709 | 11:7 | 1.571 | ||||||
| 55\144 | 458.333 | 741.667 | 8:5 | 1.600 | ||||||
| 89\233 | 458.369 | 741.631 | 13:8 | 1.625 | ||||||
| 34\89 | 458.427 | 741.573 | 5:3 | 1.667 | Semisoft 13L 8s | |||||
| 81\212 | 458.491 | 741.509 | 12:7 | 1.714 | ||||||
| 47\123 | 458.537 | 741.463 | 7:4 | 1.750 | ||||||
| 60\157 | 458.599 | 741.401 | 9:5 | 1.800 | ||||||
| 13\34 | 458.824 | 741.176 | 2:1 | 2.000 | Basic 13L 8s Scales with tunings softer than this are proper | |||||
| 57\149 | 459.060 | 740.940 | 9:4 | 2.250 | ||||||
| 44\115 | 459.130 | 740.870 | 7:3 | 2.333 | ||||||
| 75\196 | 459.184 | 740.816 | 12:5 | 2.400 | ||||||
| 31\81 | 459.259 | 740.741 | 5:2 | 2.500 | Semihard 13L 8s | |||||
| 80\209 | 459.330 | 740.670 | 13:5 | 2.600 | ||||||
| 49\128 | 459.375 | 740.625 | 8:3 | 2.667 | ||||||
| 67\175 | 459.429 | 740.571 | 11:4 | 2.750 | ||||||
| 18\47 | 459.574 | 740.426 | 3:1 | 3.000 | Hard 13L 8s | |||||
| 59\154 | 459.740 | 740.260 | 10:3 | 3.333 | ||||||
| 41\107 | 459.813 | 740.187 | 7:2 | 3.500 | ||||||
| 64\167 | 459.880 | 740.120 | 11:3 | 3.667 | ||||||
| 23\60 | 460.000 | 740.000 | 4:1 | 4.000 | Superhard 13L 8s | |||||
| 51\133 | 460.150 | 739.850 | 9:2 | 4.500 | ||||||
| 28\73 | 460.274 | 739.726 | 5:1 | 5.000 | ||||||
| 33\86 | 460.465 | 739.535 | 6:1 | 6.000 | ||||||
| 5\13 | 461.538 | 738.462 | 1:0 | → ∞ | Collapsed 13L 8s | |||||
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