4L 15s

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↖ 3L 14s ↑ 4L 14s 5L 14s ↗
← 3L 15s 4L 15s 5L 15s →
↙ 3L 16s ↓ 4L 16s 5L 16s ↘ 
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Scale structure
Step pattern LsssLssssLssssLssss
ssssLssssLssssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 14\19 to 3\4 (884.2 ¢ to 900.0 ¢)
Dark 1\4 to 5\19 (300.0 ¢ to 315.8 ¢)
TAMNAMS information
Descends from 4L 3s (smitonic)
Ancestor's step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 4L 11s
Sister 15L 4s
Daughters 19L 4s, 4L 19s
Neutralized 8L 11s
2-Flought 23L 15s, 4L 34s
Equal tunings
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 ¢)

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

The intervals of 4L 15s 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 19-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 of 4L 15s
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

A chain of bright generators, each a perfect 14-mosstep, produces the following scale degrees. A chain of 19 bright generators contains the scale degrees of one of the modes of 4L 15s. Expanding the chain to 23 scale degrees produces the modes of either 19L 4s (for soft-of-basic tunings) or 4L 19s (for hard-of-basic tunings).

Generator chain of 4L 15s
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

Scale degrees of the modes of 4L 15s 
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

Scale tree and tuning spectrum of 4L 15s
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
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