4L 15s
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Step pattern
LsssLssssLssssLssss
ssssLssssLssssLsssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
14\19 to 3\4 (884.2 ¢ to 900.0 ¢)
Dark
1\4 to 5\19 (300.0 ¢ to 315.8 ¢)
Descends from
4L 3s (smitonic)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Parent
4L 11s
Sister
15L 4s
Daughters
19L 4s, 4L 19s
Neutralized
8L 11s
2-Flought
23L 15s, 4L 34s
Equalized (L:s = 1:1)
14\19 (884.2 ¢)
Supersoft (L:s = 4:3)
45\61 (885.2 ¢)
Soft (L:s = 3:2)
31\42 (885.7 ¢)
Semisoft (L:s = 5:3)
48\65 (886.2 ¢)
Basic (L:s = 2:1)
17\23 (887.0 ¢)
Semihard (L:s = 5:2)
37\50 (888.0 ¢)
Hard (L:s = 3:1)
20\27 (888.9 ¢)
Superhard (L:s = 4:1)
23\31 (890.3 ¢)
Collapsed (L:s = 1:0)
3\4 (900.0 ¢)
↖ 3L 14s | ↑ 4L 14s | 5L 14s ↗ |
← 3L 15s | 4L 15s | 5L 15s → |
↙ 3L 16s | ↓ 4L 16s | 5L 16s ↘ |
┌╥┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║│││║││││║││││║│││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssLssssLssssLsssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
4L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 15 small steps, repeating every octave. 4L 15s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 884.2 ¢ to 900 ¢, or from 300 ¢ to 315.8 ¢.
This scale is associated with myna temperament (pronounced /'maɪnə/), where stacking two bright generators and octave-reducing produces 7/5 (~582 ¢).
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 63.2 ¢ |
Major 1-mosstep | M1ms | L | 63.2 ¢ to 300.0 ¢ | |
2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 126.3 ¢ |
Major 2-mosstep | M2ms | L + s | 126.3 ¢ to 300.0 ¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0 ¢ to 189.5 ¢ |
Major 3-mosstep | M3ms | L + 2s | 189.5 ¢ to 300.0 ¢ | |
4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0 ¢ to 252.6 ¢ |
Major 4-mosstep | M4ms | L + 3s | 252.6 ¢ to 300.0 ¢ | |
5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 300.0 ¢ to 315.8 ¢ |
Augmented 5-mosstep | A5ms | 2L + 3s | 315.8 ¢ to 600.0 ¢ | |
6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 300.0 ¢ to 378.9 ¢ |
Major 6-mosstep | M6ms | 2L + 4s | 378.9 ¢ to 600.0 ¢ | |
7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 300.0 ¢ to 442.1 ¢ |
Major 7-mosstep | M7ms | 2L + 5s | 442.1 ¢ to 600.0 ¢ | |
8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 300.0 ¢ to 505.3 ¢ |
Major 8-mosstep | M8ms | 2L + 6s | 505.3 ¢ to 600.0 ¢ | |
9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 300.0 ¢ to 568.4 ¢ |
Major 9-mosstep | M9ms | 2L + 7s | 568.4 ¢ to 600.0 ¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 600.0 ¢ to 631.6 ¢ |
Major 10-mosstep | M10ms | 3L + 7s | 631.6 ¢ to 900.0 ¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 2L + 9s | 600.0 ¢ to 694.7 ¢ |
Major 11-mosstep | M11ms | 3L + 8s | 694.7 ¢ to 900.0 ¢ | |
12-mosstep | Minor 12-mosstep | m12ms | 2L + 10s | 600.0 ¢ to 757.9 ¢ |
Major 12-mosstep | M12ms | 3L + 9s | 757.9 ¢ to 900.0 ¢ | |
13-mosstep | Minor 13-mosstep | m13ms | 2L + 11s | 600.0 ¢ to 821.1 ¢ |
Major 13-mosstep | M13ms | 3L + 10s | 821.1 ¢ to 900.0 ¢ | |
14-mosstep | Diminished 14-mosstep | d14ms | 2L + 12s | 600.0 ¢ to 884.2 ¢ |
Perfect 14-mosstep | P14ms | 3L + 11s | 884.2 ¢ to 900.0 ¢ | |
15-mosstep | Minor 15-mosstep | m15ms | 3L + 12s | 900.0 ¢ to 947.4 ¢ |
Major 15-mosstep | M15ms | 4L + 11s | 947.4 ¢ to 1200.0 ¢ | |
16-mosstep | Minor 16-mosstep | m16ms | 3L + 13s | 900.0 ¢ to 1010.5 ¢ |
Major 16-mosstep | M16ms | 4L + 12s | 1010.5 ¢ to 1200.0 ¢ | |
17-mosstep | Minor 17-mosstep | m17ms | 3L + 14s | 900.0 ¢ to 1073.7 ¢ |
Major 17-mosstep | M17ms | 4L + 13s | 1073.7 ¢ to 1200.0 ¢ | |
18-mosstep | Minor 18-mosstep | m18ms | 3L + 15s | 900.0 ¢ to 1136.8 ¢ |
Major 18-mosstep | M18ms | 4L + 14s | 1136.8 ¢ to 1200.0 ¢ | |
19-mosstep | Perfect 19-mosstep | P19ms | 4L + 15s | 1200.0 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
22 | Augmented 4-mosdegree | A4md |
21 | Augmented 9-mosdegree | A9md |
20 | Augmented 14-mosdegree | A14md |
19 | Augmented 0-mosdegree | A0md |
18 | Augmented 5-mosdegree | A5md |
17 | Major 10-mosdegree | M10md |
16 | Major 15-mosdegree | M15md |
15 | Major 1-mosdegree | M1md |
14 | Major 6-mosdegree | M6md |
13 | Major 11-mosdegree | M11md |
12 | Major 16-mosdegree | M16md |
11 | Major 2-mosdegree | M2md |
10 | Major 7-mosdegree | M7md |
9 | Major 12-mosdegree | M12md |
8 | Major 17-mosdegree | M17md |
7 | Major 3-mosdegree | M3md |
6 | Major 8-mosdegree | M8md |
5 | Major 13-mosdegree | M13md |
4 | Major 18-mosdegree | M18md |
3 | Major 4-mosdegree | M4md |
2 | Major 9-mosdegree | M9md |
1 | Perfect 14-mosdegree | P14md |
0 | Perfect 0-mosdegree Perfect 19-mosdegree |
P0md P19md |
−1 | Perfect 5-mosdegree | P5md |
−2 | Minor 10-mosdegree | m10md |
−3 | Minor 15-mosdegree | m15md |
−4 | Minor 1-mosdegree | m1md |
−5 | Minor 6-mosdegree | m6md |
−6 | Minor 11-mosdegree | m11md |
−7 | Minor 16-mosdegree | m16md |
−8 | Minor 2-mosdegree | m2md |
−9 | Minor 7-mosdegree | m7md |
−10 | Minor 12-mosdegree | m12md |
−11 | Minor 17-mosdegree | m17md |
−12 | Minor 3-mosdegree | m3md |
−13 | Minor 8-mosdegree | m8md |
−14 | Minor 13-mosdegree | m13md |
−15 | Minor 18-mosdegree | m18md |
−16 | Minor 4-mosdegree | m4md |
−17 | Minor 9-mosdegree | m9md |
−18 | Diminished 14-mosdegree | d14md |
−19 | Diminished 19-mosdegree | d19md |
−20 | Diminished 5-mosdegree | d5md |
−21 | Diminished 10-mosdegree | d10md |
−22 | Diminished 15-mosdegree | d15md |
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 | |||
18|0 | 1 | LsssLssssLssssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
17|1 | 15 | LssssLsssLssssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
16|2 | 10 | LssssLssssLsssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
15|3 | 5 | LssssLssssLssssLsss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
14|4 | 19 | sLsssLssssLssssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
13|5 | 14 | sLssssLsssLssssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
12|6 | 9 | sLssssLssssLsssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
11|7 | 4 | sLssssLssssLssssLss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
10|8 | 18 | ssLsssLssssLssssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
9|9 | 13 | ssLssssLsssLssssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
8|10 | 8 | ssLssssLssssLsssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
7|11 | 3 | ssLssssLssssLssssLs | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
6|12 | 17 | sssLsssLssssLssssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
5|13 | 12 | sssLssssLsssLssssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
4|14 | 7 | sssLssssLssssLsssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
3|15 | 2 | sssLssssLssssLssssL | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
2|16 | 16 | ssssLsssLssssLssssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
1|17 | 11 | ssssLssssLsssLssssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
0|18 | 6 | ssssLssssLssssLsssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
14\19 | 884.211 | 315.789 | 1:1 | 1.000 | Equalized 4L 15s | |||||
73\99 | 884.848 | 315.152 | 6:5 | 1.200 | ||||||
59\80 | 885.000 | 315.000 | 5:4 | 1.250 | ||||||
104\141 | 885.106 | 314.894 | 9:7 | 1.286 | ||||||
45\61 | 885.246 | 314.754 | 4:3 | 1.333 | Supersoft 4L 15s | |||||
121\164 | 885.366 | 314.634 | 11:8 | 1.375 | ||||||
76\103 | 885.437 | 314.563 | 7:5 | 1.400 | ||||||
107\145 | 885.517 | 314.483 | 10:7 | 1.429 | ||||||
31\42 | 885.714 | 314.286 | 3:2 | 1.500 | Soft 4L 15s | |||||
110\149 | 885.906 | 314.094 | 11:7 | 1.571 | ||||||
79\107 | 885.981 | 314.019 | 8:5 | 1.600 | ||||||
127\172 | 886.047 | 313.953 | 13:8 | 1.625 | ||||||
48\65 | 886.154 | 313.846 | 5:3 | 1.667 | Semisoft 4L 15s | |||||
113\153 | 886.275 | 313.725 | 12:7 | 1.714 | ||||||
65\88 | 886.364 | 313.636 | 7:4 | 1.750 | ||||||
82\111 | 886.486 | 313.514 | 9:5 | 1.800 | ||||||
17\23 | 886.957 | 313.043 | 2:1 | 2.000 | Basic 4L 15s Scales with tunings softer than this are proper | |||||
71\96 | 887.500 | 312.500 | 9:4 | 2.250 | ||||||
54\73 | 887.671 | 312.329 | 7:3 | 2.333 | ||||||
91\123 | 887.805 | 312.195 | 12:5 | 2.400 | ||||||
37\50 | 888.000 | 312.000 | 5:2 | 2.500 | Semihard 4L 15s | |||||
94\127 | 888.189 | 311.811 | 13:5 | 2.600 | ||||||
57\77 | 888.312 | 311.688 | 8:3 | 2.667 | ||||||
77\104 | 888.462 | 311.538 | 11:4 | 2.750 | ||||||
20\27 | 888.889 | 311.111 | 3:1 | 3.000 | Hard 4L 15s | |||||
63\85 | 889.412 | 310.588 | 10:3 | 3.333 | ||||||
43\58 | 889.655 | 310.345 | 7:2 | 3.500 | ||||||
66\89 | 889.888 | 310.112 | 11:3 | 3.667 | ||||||
23\31 | 890.323 | 309.677 | 4:1 | 4.000 | Superhard 4L 15s | |||||
49\66 | 890.909 | 309.091 | 9:2 | 4.500 | ||||||
26\35 | 891.429 | 308.571 | 5:1 | 5.000 | ||||||
29\39 | 892.308 | 307.692 | 6:1 | 6.000 | ||||||
3\4 | 900.000 | 300.000 | 1:0 | → ∞ | Collapsed 4L 15s |