8L 13s
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Step pattern
LsLssLsLssLssLsLssLss
ssLssLsLssLssLsLssLsL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
13\21 to 5\8 (742.9 ¢ to 750.0 ¢)
Dark
3\8 to 8\21 (450.0 ¢ to 457.1 ¢)
Descends from
5L 3s (oneirotonic)
Ancestor's step ratio range
1:1 to 3:2 (soft)
Parent
8L 5s
Sister
13L 8s
Daughters
21L 8s, 8L 21s
Neutralized
16L 5s
2-Flought
29L 13s, 8L 34s
Equalized (L:s = 1:1)
13\21 (742.9 ¢)
Supersoft (L:s = 4:3)
44\71 (743.7 ¢)
Soft (L:s = 3:2)
31\50 (744.0 ¢)
Semisoft (L:s = 5:3)
49\79 (744.3 ¢)
Basic (L:s = 2:1)
18\29 (744.8 ¢)
Semihard (L:s = 5:2)
41\66 (745.5 ¢)
Hard (L:s = 3:1)
23\37 (745.9 ¢)
Superhard (L:s = 4:1)
28\45 (746.7 ¢)
Collapsed (L:s = 1:0)
5\8 (750.0 ¢)
| ↖ 7L 12s | ↑ 8L 12s | 9L 12s ↗ |
| ← 7L 13s | 8L 13s | 9L 13s → |
| ↙ 7L 14s | ↓ 8L 14s | 9L 14s ↘ |
┌╥┬╥┬┬╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬┬┐ │║│║││║│║││║││║│║││║│││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssLssLsLssLssLsLssLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
8L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 13 small steps, repeating every octave. 8L 13s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 742.9 ¢ to 750 ¢, or from 450 ¢ to 457.1 ¢.
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 150.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 114.3 ¢ |
| Major 2-mosstep | M2ms | L + s | 114.3 ¢ to 150.0 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 150.0 ¢ to 171.4 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 171.4 ¢ to 300.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 150.0 ¢ to 228.6 ¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 228.6 ¢ to 300.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 150.0 ¢ to 285.7 ¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 285.7 ¢ to 300.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 300.0 ¢ to 342.9 ¢ |
| Major 6-mosstep | M6ms | 3L + 3s | 342.9 ¢ to 450.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 300.0 ¢ to 400.0 ¢ |
| Major 7-mosstep | M7ms | 3L + 4s | 400.0 ¢ to 450.0 ¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 3L + 5s | 450.0 ¢ to 457.1 ¢ |
| Augmented 8-mosstep | A8ms | 4L + 4s | 457.1 ¢ to 600.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 3L + 6s | 450.0 ¢ to 514.3 ¢ |
| Major 9-mosstep | M9ms | 4L + 5s | 514.3 ¢ to 600.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 3L + 7s | 450.0 ¢ to 571.4 ¢ |
| Major 10-mosstep | M10ms | 4L + 6s | 571.4 ¢ to 600.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 4L + 7s | 600.0 ¢ to 628.6 ¢ |
| Major 11-mosstep | M11ms | 5L + 6s | 628.6 ¢ to 750.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 4L + 8s | 600.0 ¢ to 685.7 ¢ |
| Major 12-mosstep | M12ms | 5L + 7s | 685.7 ¢ to 750.0 ¢ | |
| 13-mosstep | Diminished 13-mosstep | d13ms | 4L + 9s | 600.0 ¢ to 742.9 ¢ |
| Perfect 13-mosstep | P13ms | 5L + 8s | 742.9 ¢ to 750.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 5L + 9s | 750.0 ¢ to 800.0 ¢ |
| Major 14-mosstep | M14ms | 6L + 8s | 800.0 ¢ to 900.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 5L + 10s | 750.0 ¢ to 857.1 ¢ |
| Major 15-mosstep | M15ms | 6L + 9s | 857.1 ¢ to 900.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 6L + 10s | 900.0 ¢ to 914.3 ¢ |
| Major 16-mosstep | M16ms | 7L + 9s | 914.3 ¢ to 1050.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 6L + 11s | 900.0 ¢ to 971.4 ¢ |
| Major 17-mosstep | M17ms | 7L + 10s | 971.4 ¢ to 1050.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 6L + 12s | 900.0 ¢ to 1028.6 ¢ |
| Major 18-mosstep | M18ms | 7L + 11s | 1028.6 ¢ to 1050.0 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 7L + 12s | 1050.0 ¢ to 1085.7 ¢ |
| Major 19-mosstep | M19ms | 8L + 11s | 1085.7 ¢ to 1200.0 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 7L + 13s | 1050.0 ¢ to 1142.9 ¢ |
| Major 20-mosstep | M20ms | 8L + 12s | 1142.9 ¢ to 1200.0 ¢ | |
| 21-mosstep | Perfect 21-mosstep | P21ms | 8L + 13s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 28 | Augmented 7-mosdegree | A7md |
| 27 | Augmented 15-mosdegree | A15md |
| 26 | Augmented 2-mosdegree | A2md |
| 25 | Augmented 10-mosdegree | A10md |
| 24 | Augmented 18-mosdegree | A18md |
| 23 | Augmented 5-mosdegree | A5md |
| 22 | Augmented 13-mosdegree | A13md |
| 21 | Augmented 0-mosdegree | A0md |
| 20 | Augmented 8-mosdegree | A8md |
| 19 | Major 16-mosdegree | M16md |
| 18 | Major 3-mosdegree | M3md |
| 17 | Major 11-mosdegree | M11md |
| 16 | Major 19-mosdegree | M19md |
| 15 | Major 6-mosdegree | M6md |
| 14 | Major 14-mosdegree | M14md |
| 13 | Major 1-mosdegree | M1md |
| 12 | Major 9-mosdegree | M9md |
| 11 | Major 17-mosdegree | M17md |
| 10 | Major 4-mosdegree | M4md |
| 9 | Major 12-mosdegree | M12md |
| 8 | Major 20-mosdegree | M20md |
| 7 | Major 7-mosdegree | M7md |
| 6 | Major 15-mosdegree | M15md |
| 5 | Major 2-mosdegree | M2md |
| 4 | Major 10-mosdegree | M10md |
| 3 | Major 18-mosdegree | M18md |
| 2 | Major 5-mosdegree | M5md |
| 1 | Perfect 13-mosdegree | P13md |
| 0 | Perfect 0-mosdegree Perfect 21-mosdegree |
P0md P21md |
| −1 | Perfect 8-mosdegree | P8md |
| −2 | Minor 16-mosdegree | m16md |
| −3 | Minor 3-mosdegree | m3md |
| −4 | Minor 11-mosdegree | m11md |
| −5 | Minor 19-mosdegree | m19md |
| −6 | Minor 6-mosdegree | m6md |
| −7 | Minor 14-mosdegree | m14md |
| −8 | Minor 1-mosdegree | m1md |
| −9 | Minor 9-mosdegree | m9md |
| −10 | Minor 17-mosdegree | m17md |
| −11 | Minor 4-mosdegree | m4md |
| −12 | Minor 12-mosdegree | m12md |
| −13 | Minor 20-mosdegree | m20md |
| −14 | Minor 7-mosdegree | m7md |
| −15 | Minor 15-mosdegree | m15md |
| −16 | Minor 2-mosdegree | m2md |
| −17 | Minor 10-mosdegree | m10md |
| −18 | Minor 18-mosdegree | m18md |
| −19 | Minor 5-mosdegree | m5md |
| −20 | Diminished 13-mosdegree | d13md |
| −21 | Diminished 21-mosdegree | d21md |
| −22 | Diminished 8-mosdegree | d8md |
| −23 | Diminished 16-mosdegree | d16md |
| −24 | Diminished 3-mosdegree | d3md |
| −25 | Diminished 11-mosdegree | d11md |
| −26 | Diminished 19-mosdegree | d19md |
| −27 | Diminished 6-mosdegree | d6md |
| −28 | Diminished 14-mosdegree | d14md |
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 | LsLssLsLssLssLsLssLss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 19|1 | 14 | LsLssLssLsLssLsLssLss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 18|2 | 6 | LsLssLssLsLssLssLsLss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 17|3 | 19 | LssLsLssLsLssLssLsLss | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 16|4 | 11 | LssLsLssLssLsLssLsLss | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 15|5 | 3 | LssLsLssLssLsLssLssLs | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. |
| 14|6 | 16 | LssLssLsLssLsLssLssLs | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. |
| 13|7 | 8 | LssLssLsLssLssLsLssLs | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. |
| 12|8 | 21 | sLsLssLsLssLssLsLssLs | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. |
| 11|9 | 13 | sLsLssLssLsLssLsLssLs | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. |
| 10|10 | 5 | sLsLssLssLsLssLssLsLs | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. |
| 9|11 | 18 | sLssLsLssLsLssLssLsLs | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. |
| 8|12 | 10 | sLssLsLssLssLsLssLsLs | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. |
| 7|13 | 2 | sLssLsLssLssLsLssLssL | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. |
| 6|14 | 15 | sLssLssLsLssLsLssLssL | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. |
| 5|15 | 7 | sLssLssLsLssLssLsLssL | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. |
| 4|16 | 20 | ssLsLssLsLssLssLsLssL | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. |
| 3|17 | 12 | ssLsLssLssLsLssLsLssL | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. |
| 2|18 | 4 | ssLsLssLssLsLssLssLsL | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 1|19 | 17 | ssLssLsLssLsLssLssLsL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 0|20 | 9 | ssLssLsLssLssLsLssLsL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 13\21 | 742.857 | 457.143 | 1:1 | 1.000 | Equalized 8L 13s | |||||
| 70\113 | 743.363 | 456.637 | 6:5 | 1.200 | ||||||
| 57\92 | 743.478 | 456.522 | 5:4 | 1.250 | ||||||
| 101\163 | 743.558 | 456.442 | 9:7 | 1.286 | ||||||
| 44\71 | 743.662 | 456.338 | 4:3 | 1.333 | Supersoft 8L 13s | |||||
| 119\192 | 743.750 | 456.250 | 11:8 | 1.375 | ||||||
| 75\121 | 743.802 | 456.198 | 7:5 | 1.400 | ||||||
| 106\171 | 743.860 | 456.140 | 10:7 | 1.429 | ||||||
| 31\50 | 744.000 | 456.000 | 3:2 | 1.500 | Soft 8L 13s | |||||
| 111\179 | 744.134 | 455.866 | 11:7 | 1.571 | ||||||
| 80\129 | 744.186 | 455.814 | 8:5 | 1.600 | ||||||
| 129\208 | 744.231 | 455.769 | 13:8 | 1.625 | ||||||
| 49\79 | 744.304 | 455.696 | 5:3 | 1.667 | Semisoft 8L 13s | |||||
| 116\187 | 744.385 | 455.615 | 12:7 | 1.714 | ||||||
| 67\108 | 744.444 | 455.556 | 7:4 | 1.750 | ||||||
| 85\137 | 744.526 | 455.474 | 9:5 | 1.800 | ||||||
| 18\29 | 744.828 | 455.172 | 2:1 | 2.000 | Basic 8L 13s Scales with tunings softer than this are proper | |||||
| 77\124 | 745.161 | 454.839 | 9:4 | 2.250 | ||||||
| 59\95 | 745.263 | 454.737 | 7:3 | 2.333 | ||||||
| 100\161 | 745.342 | 454.658 | 12:5 | 2.400 | ||||||
| 41\66 | 745.455 | 454.545 | 5:2 | 2.500 | Semihard 8L 13s | |||||
| 105\169 | 745.562 | 454.438 | 13:5 | 2.600 | ||||||
| 64\103 | 745.631 | 454.369 | 8:3 | 2.667 | ||||||
| 87\140 | 745.714 | 454.286 | 11:4 | 2.750 | ||||||
| 23\37 | 745.946 | 454.054 | 3:1 | 3.000 | Hard 8L 13s | |||||
| 74\119 | 746.218 | 453.782 | 10:3 | 3.333 | ||||||
| 51\82 | 746.341 | 453.659 | 7:2 | 3.500 | ||||||
| 79\127 | 746.457 | 453.543 | 11:3 | 3.667 | ||||||
| 28\45 | 746.667 | 453.333 | 4:1 | 4.000 | Superhard 8L 13s | |||||
| 61\98 | 746.939 | 453.061 | 9:2 | 4.500 | ||||||
| 33\53 | 747.170 | 452.830 | 5:1 | 5.000 | ||||||
| 38\61 | 747.541 | 452.459 | 6:1 | 6.000 | ||||||
| 5\8 | 750.000 | 450.000 | 1:0 | → ∞ | Collapsed 8L 13s | |||||
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