15L 2s

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↖ 14L 1s ↑ 15L 1s 16L 1s ↗
← 14L 2s 15L 2s 16L 2s →
↙ 14L 3s ↓ 15L 3s 16L 3s ↘ 
┌╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥┬┐
│║║║║║║║║│║║║║║║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLsLLLLLLLs
sLLLLLLLsLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\17 to 8\15 (635.3 ¢ to 640.0 ¢)
Dark 7\15 to 8\17 (560.0 ¢ to 564.7 ¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Ancestor's step ratio range 4:1 to 5:1
Related MOS scales
Parent 2L 13s
Sister 2L 15s
Daughters 17L 15s, 15L 17s
Neutralized 13L 4s
2-Flought 32L 2s, 15L 19s
Equal tunings
Equalized (L:s = 1:1) 9\17 (635.3 ¢)
Supersoft (L:s = 4:3) 35\66 (636.4 ¢)
Soft (L:s = 3:2) 26\49 (636.7 ¢)
Semisoft (L:s = 5:3) 43\81 (637.0 ¢)
Basic (L:s = 2:1) 17\32 (637.5 ¢)
Semihard (L:s = 5:2) 42\79 (638.0 ¢)
Hard (L:s = 3:1) 25\47 (638.3 ¢)
Superhard (L:s = 4:1) 33\62 (638.7 ¢)
Collapsed (L:s = 1:0) 8\15 (640.0 ¢)

15L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 2 small steps, repeating every octave. 15L 2s is related to 2L 7s, expanding it by 8 tones. Generators that produce this scale range from 635.3 ¢ to 640 ¢, or from 560 ¢ to 564.7 ¢.

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 of 15L 2s
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 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 80.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 80.0 ¢ to 141.2 ¢
Major 2-mosstep M2ms 2L 141.2 ¢ to 160.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 160.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms 3L 211.8 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 240.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms 4L 282.4 ¢ to 320.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 320.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms 5L 352.9 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 400.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms 6L 423.5 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 480.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms 7L 494.1 ¢ to 560.0 ¢
8-mosstep Perfect 8-mosstep P8ms 7L + s 560.0 ¢ to 564.7 ¢
Augmented 8-mosstep A8ms 8L 564.7 ¢ to 640.0 ¢
9-mosstep Diminished 9-mosstep d9ms 7L + 2s 560.0 ¢ to 635.3 ¢
Perfect 9-mosstep P9ms 8L + s 635.3 ¢ to 640.0 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 640.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 9L + s 705.9 ¢ to 720.0 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 720.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 10L + s 776.5 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 800.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 11L + s 847.1 ¢ to 880.0 ¢
13-mosstep Minor 13-mosstep m13ms 11L + 2s 880.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 12L + s 917.6 ¢ to 960.0 ¢
14-mosstep Minor 14-mosstep m14ms 12L + 2s 960.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 13L + s 988.2 ¢ to 1040.0 ¢
15-mosstep Minor 15-mosstep m15ms 13L + 2s 1040.0 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 14L + s 1058.8 ¢ to 1120.0 ¢
16-mosstep Minor 16-mosstep m16ms 14L + 2s 1120.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 15L + s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 15L + 2s 1200.0 ¢

Generator chain

Generator chain of 15L 2s
Bright gens Scale degree Abbrev.
31 Augmented 7-mosdegree A7md
30 Augmented 15-mosdegree A15md
29 Augmented 6-mosdegree A6md
28 Augmented 14-mosdegree A14md
27 Augmented 5-mosdegree A5md
26 Augmented 13-mosdegree A13md
25 Augmented 4-mosdegree A4md
24 Augmented 12-mosdegree A12md
23 Augmented 3-mosdegree A3md
22 Augmented 11-mosdegree A11md
21 Augmented 2-mosdegree A2md
20 Augmented 10-mosdegree A10md
19 Augmented 1-mosdegree A1md
18 Augmented 9-mosdegree A9md
17 Augmented 0-mosdegree A0md
16 Augmented 8-mosdegree A8md
15 Major 16-mosdegree M16md
14 Major 7-mosdegree M7md
13 Major 15-mosdegree M15md
12 Major 6-mosdegree M6md
11 Major 14-mosdegree M14md
10 Major 5-mosdegree M5md
9 Major 13-mosdegree M13md
8 Major 4-mosdegree M4md
7 Major 12-mosdegree M12md
6 Major 3-mosdegree M3md
5 Major 11-mosdegree M11md
4 Major 2-mosdegree M2md
3 Major 10-mosdegree M10md
2 Major 1-mosdegree M1md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 8-mosdegree P8md
−2 Minor 16-mosdegree m16md
−3 Minor 7-mosdegree m7md
−4 Minor 15-mosdegree m15md
−5 Minor 6-mosdegree m6md
−6 Minor 14-mosdegree m14md
−7 Minor 5-mosdegree m5md
−8 Minor 13-mosdegree m13md
−9 Minor 4-mosdegree m4md
−10 Minor 12-mosdegree m12md
−11 Minor 3-mosdegree m3md
−12 Minor 11-mosdegree m11md
−13 Minor 2-mosdegree m2md
−14 Minor 10-mosdegree m10md
−15 Minor 1-mosdegree m1md
−16 Diminished 9-mosdegree d9md
−17 Diminished 17-mosdegree d17md
−18 Diminished 8-mosdegree d8md
−19 Diminished 16-mosdegree d16md
−20 Diminished 7-mosdegree d7md
−21 Diminished 15-mosdegree d15md
−22 Diminished 6-mosdegree d6md
−23 Diminished 14-mosdegree d14md
−24 Diminished 5-mosdegree d5md
−25 Diminished 13-mosdegree d13md
−26 Diminished 4-mosdegree d4md
−27 Diminished 12-mosdegree d12md
−28 Diminished 3-mosdegree d3md
−29 Diminished 11-mosdegree d11md
−30 Diminished 2-mosdegree d2md
−31 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 15L 2s
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
16|0 1 LLLLLLLLsLLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|1 10 LLLLLLLsLLLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|2 2 LLLLLLLsLLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf.
13|3 11 LLLLLLsLLLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf.
12|4 3 LLLLLLsLLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf.
11|5 12 LLLLLsLLLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf.
10|6 4 LLLLLsLLLLLLLsLLL Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf.
9|7 13 LLLLsLLLLLLLLsLLL Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf.
8|8 5 LLLLsLLLLLLLsLLLL Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf.
7|9 14 LLLsLLLLLLLLsLLLL Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf.
6|10 6 LLLsLLLLLLLsLLLLL Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf.
5|11 15 LLsLLLLLLLLsLLLLL Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf.
4|12 7 LLsLLLLLLLsLLLLLL Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Perf.
3|13 16 LsLLLLLLLLsLLLLLL Perf. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Perf.
2|14 8 LsLLLLLLLsLLLLLLL Perf. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
1|15 17 sLLLLLLLLsLLLLLLL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
0|16 9 sLLLLLLLsLLLLLLLL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Dim. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 15L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\17 635.294 564.706 1:1 1.000 Equalized 15L 2s
53\100 636.000 564.000 6:5 1.200
44\83 636.145 563.855 5:4 1.250
79\149 636.242 563.758 9:7 1.286
35\66 636.364 563.636 4:3 1.333 Supersoft 15L 2s
96\181 636.464 563.536 11:8 1.375
61\115 636.522 563.478 7:5 1.400
87\164 636.585 563.415 10:7 1.429
26\49 636.735 563.265 3:2 1.500 Soft 15L 2s
95\179 636.872 563.128 11:7 1.571
69\130 636.923 563.077 8:5 1.600
112\211 636.967 563.033 13:8 1.625
43\81 637.037 562.963 5:3 1.667 Semisoft 15L 2s
103\194 637.113 562.887 12:7 1.714
60\113 637.168 562.832 7:4 1.750
77\145 637.241 562.759 9:5 1.800
17\32 637.500 562.500 2:1 2.000 Basic 15L 2s
Scales with tunings softer than this are proper
76\143 637.762 562.238 9:4 2.250
59\111 637.838 562.162 7:3 2.333
101\190 637.895 562.105 12:5 2.400
42\79 637.975 562.025 5:2 2.500 Semihard 15L 2s
109\205 638.049 561.951 13:5 2.600
67\126 638.095 561.905 8:3 2.667
92\173 638.150 561.850 11:4 2.750
25\47 638.298 561.702 3:1 3.000 Hard 15L 2s
83\156 638.462 561.538 10:3 3.333
58\109 638.532 561.468 7:2 3.500
91\171 638.596 561.404 11:3 3.667
33\62 638.710 561.290 4:1 4.000 Superhard 15L 2s
74\139 638.849 561.151 9:2 4.500
41\77 638.961 561.039 5:1 5.000
49\92 639.130 560.870 6:1 6.000
8\15 640.000 560.000 1:0 → ∞ Collapsed 15L 2s
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