3L 10s
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Step pattern
LsssLsssLssss
ssssLsssLsssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
4\13 to 1\3 (369.2 ¢ to 400.0 ¢)
Dark
2\3 to 9\13 (800.0 ¢ to 830.8 ¢)
Descends from
3L 7s (sephiroid)
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Parent
3L 7s
Sister
10L 3s
Daughters
13L 3s, 3L 13s
Neutralized
6L 7s
2-Flought
16L 10s, 3L 23s
Equalized (L:s = 1:1)
4\13 (369.2 ¢)
Supersoft (L:s = 4:3)
13\42 (371.4 ¢)
Soft (L:s = 3:2)
9\29 (372.4 ¢)
Semisoft (L:s = 5:3)
14\45 (373.3 ¢)
Basic (L:s = 2:1)
5\16 (375.0 ¢)
Semihard (L:s = 5:2)
11\35 (377.1 ¢)
Hard (L:s = 3:1)
6\19 (378.9 ¢)
Superhard (L:s = 4:1)
7\22 (381.8 ¢)
Collapsed (L:s = 1:0)
1\3 (400.0 ¢)
↖ 2L 9s | ↑ 3L 9s | 4L 9s ↗ |
← 2L 10s | 3L 10s | 4L 10s → |
↙ 2L 11s | ↓ 3L 11s | 4L 11s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssLsssLsssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
3L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 10 small steps, repeating every octave. 3L 10s is a child scale of 3L 7s, expanding it by 3 tones. Generators that produce this scale range from 369.2 ¢ to 400 ¢, or from 800 ¢ to 830.8 ¢.
Some notable temperaments that form a mos with this pattern are magic and würschmidt. Of course, Magic[13] is still slightly improper and Würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13-tone-per-octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13-tone circles favor multiple times over.
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 92.3 ¢ |
Major 1-mosstep | M1ms | L | 92.3 ¢ to 400.0 ¢ | |
2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 184.6 ¢ |
Major 2-mosstep | M2ms | L + s | 184.6 ¢ to 400.0 ¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0 ¢ to 276.9 ¢ |
Major 3-mosstep | M3ms | L + 2s | 276.9 ¢ to 400.0 ¢ | |
4-mosstep | Diminished 4-mosstep | d4ms | 4s | 0.0 ¢ to 369.2 ¢ |
Perfect 4-mosstep | P4ms | L + 3s | 369.2 ¢ to 400.0 ¢ | |
5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 400.0 ¢ to 461.5 ¢ |
Major 5-mosstep | M5ms | 2L + 3s | 461.5 ¢ to 800.0 ¢ | |
6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 400.0 ¢ to 553.8 ¢ |
Major 6-mosstep | M6ms | 2L + 4s | 553.8 ¢ to 800.0 ¢ | |
7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 400.0 ¢ to 646.2 ¢ |
Major 7-mosstep | M7ms | 2L + 5s | 646.2 ¢ to 800.0 ¢ | |
8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 400.0 ¢ to 738.5 ¢ |
Major 8-mosstep | M8ms | 2L + 6s | 738.5 ¢ to 800.0 ¢ | |
9-mosstep | Perfect 9-mosstep | P9ms | 2L + 7s | 800.0 ¢ to 830.8 ¢ |
Augmented 9-mosstep | A9ms | 3L + 6s | 830.8 ¢ to 1200.0 ¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 800.0 ¢ to 923.1 ¢ |
Major 10-mosstep | M10ms | 3L + 7s | 923.1 ¢ to 1200.0 ¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 2L + 9s | 800.0 ¢ to 1015.4 ¢ |
Major 11-mosstep | M11ms | 3L + 8s | 1015.4 ¢ to 1200.0 ¢ | |
12-mosstep | Minor 12-mosstep | m12ms | 2L + 10s | 800.0 ¢ to 1107.7 ¢ |
Major 12-mosstep | M12ms | 3L + 9s | 1107.7 ¢ to 1200.0 ¢ | |
13-mosstep | Perfect 13-mosstep | P13ms | 3L + 10s | 1200.0 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
15 | Augmented 8-mosdegree | A8md |
14 | Augmented 4-mosdegree | A4md |
13 | Augmented 0-mosdegree | A0md |
12 | Augmented 9-mosdegree | A9md |
11 | Major 5-mosdegree | M5md |
10 | Major 1-mosdegree | M1md |
9 | Major 10-mosdegree | M10md |
8 | Major 6-mosdegree | M6md |
7 | Major 2-mosdegree | M2md |
6 | Major 11-mosdegree | M11md |
5 | Major 7-mosdegree | M7md |
4 | Major 3-mosdegree | M3md |
3 | Major 12-mosdegree | M12md |
2 | Major 8-mosdegree | M8md |
1 | Perfect 4-mosdegree | P4md |
0 | Perfect 0-mosdegree Perfect 13-mosdegree |
P0md P13md |
−1 | Perfect 9-mosdegree | P9md |
−2 | Minor 5-mosdegree | m5md |
−3 | Minor 1-mosdegree | m1md |
−4 | Minor 10-mosdegree | m10md |
−5 | Minor 6-mosdegree | m6md |
−6 | Minor 2-mosdegree | m2md |
−7 | Minor 11-mosdegree | m11md |
−8 | Minor 7-mosdegree | m7md |
−9 | Minor 3-mosdegree | m3md |
−10 | Minor 12-mosdegree | m12md |
−11 | Minor 8-mosdegree | m8md |
−12 | Diminished 4-mosdegree | d4md |
−13 | Diminished 13-mosdegree | d13md |
−14 | Diminished 9-mosdegree | d9md |
−15 | Diminished 5-mosdegree | d5md |
Modes
UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |||
12|0 | 1 | LsssLsssLssss | Perf. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Perf. |
11|1 | 5 | LsssLssssLsss | Perf. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
10|2 | 9 | LssssLsssLsss | Perf. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
9|3 | 13 | sLsssLsssLsss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
8|4 | 4 | sLsssLssssLss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
7|5 | 8 | sLssssLsssLss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
6|6 | 12 | ssLsssLsssLss | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
5|7 | 3 | ssLsssLssssLs | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
4|8 | 7 | ssLssssLsssLs | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
3|9 | 11 | sssLsssLsssLs | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
2|10 | 2 | sssLsssLssssL | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Perf. |
1|11 | 6 | sssLssssLsssL | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Perf. |
0|12 | 10 | ssssLsssLsssL | Perf. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Perf. |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
4\13 | 369.231 | 830.769 | 1:1 | 1.000 | Equalized 3L 10s | |||||
21\68 | 370.588 | 829.412 | 6:5 | 1.200 | ||||||
17\55 | 370.909 | 829.091 | 5:4 | 1.250 | ||||||
30\97 | 371.134 | 828.866 | 9:7 | 1.286 | ||||||
13\42 | 371.429 | 828.571 | 4:3 | 1.333 | Supersoft 3L 10s | |||||
35\113 | 371.681 | 828.319 | 11:8 | 1.375 | ||||||
22\71 | 371.831 | 828.169 | 7:5 | 1.400 | ||||||
31\100 | 372.000 | 828.000 | 10:7 | 1.429 | ||||||
9\29 | 372.414 | 827.586 | 3:2 | 1.500 | Soft 3L 10s Sephiroth | |||||
32\103 | 372.816 | 827.184 | 11:7 | 1.571 | ||||||
23\74 | 372.973 | 827.027 | 8:5 | 1.600 | ||||||
37\119 | 373.109 | 826.891 | 13:8 | 1.625 | Golden sephiroth | |||||
14\45 | 373.333 | 826.667 | 5:3 | 1.667 | Semisoft 3L 10s | |||||
33\106 | 373.585 | 826.415 | 12:7 | 1.714 | ||||||
19\61 | 373.770 | 826.230 | 7:4 | 1.750 | ||||||
24\77 | 374.026 | 825.974 | 9:5 | 1.800 | ||||||
5\16 | 375.000 | 825.000 | 2:1 | 2.000 | Basic 3L 10s Scales with tunings softer than this are proper | |||||
21\67 | 376.119 | 823.881 | 9:4 | 2.250 | ||||||
16\51 | 376.471 | 823.529 | 7:3 | 2.333 | ||||||
27\86 | 376.744 | 823.256 | 12:5 | 2.400 | ||||||
11\35 | 377.143 | 822.857 | 5:2 | 2.500 | Semihard 3L 10s | |||||
28\89 | 377.528 | 822.472 | 13:5 | 2.600 | Unnamed golden tuning | |||||
17\54 | 377.778 | 822.222 | 8:3 | 2.667 | Muggles | |||||
23\73 | 378.082 | 821.918 | 11:4 | 2.750 | ||||||
6\19 | 378.947 | 821.053 | 3:1 | 3.000 | Hard 3L 10s | |||||
19\60 | 380.000 | 820.000 | 10:3 | 3.333 | Magic / witchcraft | |||||
13\41 | 380.488 | 819.512 | 7:2 | 3.500 | Magic | |||||
20\63 | 380.952 | 819.048 | 11:3 | 3.667 | Magic / necromancy | |||||
7\22 | 381.818 | 818.182 | 4:1 | 4.000 | Superhard 3L 10s | |||||
15\47 | 382.979 | 817.021 | 9:2 | 4.500 | Marveltri | |||||
8\25 | 384.000 | 816.000 | 5:1 | 5.000 | ||||||
9\28 | 385.714 | 814.286 | 6:1 | 6.000 | Würschmidt ↓ | |||||
1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 10s |