17L 3s

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↖ 16L 2s ↑ 17L 2s 18L 2s ↗
← 16L 3s 17L 3s 18L 3s →
↙ 16L 4s ↓ 17L 4s 18L 4s ↘ 
┌╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥┬┐
│║║║║║║│║║║║║║│║║║║║││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLsLLLLLLsLLLLLs
sLLLLLsLLLLLLsLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\20 to 6\17 (420.0 ¢ to 423.5 ¢)
Dark 11\17 to 13\20 (776.5 ¢ to 780.0 ¢)
TAMNAMS information
Related to 3L 5s (checkertonic)
With tunings 4:1 to 5:1
Related MOS scales
Parent 3L 14s
Sister 3L 17s
Daughters 20L 17s, 17L 20s
Neutralized 14L 6s
2-Flought 37L 3s, 17L 23s
Equal tunings
Equalized (L:s = 1:1) 7\20 (420.0 ¢)
Supersoft (L:s = 4:3) 27\77 (420.8 ¢)
Soft (L:s = 3:2) 20\57 (421.1 ¢)
Semisoft (L:s = 5:3) 33\94 (421.3 ¢)
Basic (L:s = 2:1) 13\37 (421.6 ¢)
Semihard (L:s = 5:2) 32\91 (422.0 ¢)
Hard (L:s = 3:1) 19\54 (422.2 ¢)
Superhard (L:s = 4:1) 25\71 (422.5 ¢)
Collapsed (L:s = 1:0) 6\17 (423.5 ¢)

17L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 3 small steps, repeating every octave. 17L 3s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 420 ¢ to 423.5 ¢, or from 776.5 ¢ to 780 ¢.

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 interval regions.

Intervals

Intervals of 17L 3s
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 60.0 ¢
Major 1-mosstep M1ms L 60.0 ¢ to 70.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 70.6 ¢ to 120.0 ¢
Major 2-mosstep M2ms 2L 120.0 ¢ to 141.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 141.2 ¢ to 180.0 ¢
Major 3-mosstep M3ms 3L 180.0 ¢ to 211.8 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 211.8 ¢ to 240.0 ¢
Major 4-mosstep M4ms 4L 240.0 ¢ to 282.4 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 282.4 ¢ to 300.0 ¢
Major 5-mosstep M5ms 5L 300.0 ¢ to 352.9 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 352.9 ¢ to 360.0 ¢
Major 6-mosstep M6ms 6L 360.0 ¢ to 423.5 ¢
7-mosstep Diminished 7-mosstep d7ms 5L + 2s 352.9 ¢ to 420.0 ¢
Perfect 7-mosstep P7ms 6L + s 420.0 ¢ to 423.5 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 423.5 ¢ to 480.0 ¢
Major 8-mosstep M8ms 7L + s 480.0 ¢ to 494.1 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 494.1 ¢ to 540.0 ¢
Major 9-mosstep M9ms 8L + s 540.0 ¢ to 564.7 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 564.7 ¢ to 600.0 ¢
Major 10-mosstep M10ms 9L + s 600.0 ¢ to 635.3 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 635.3 ¢ to 660.0 ¢
Major 11-mosstep M11ms 10L + s 660.0 ¢ to 705.9 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 705.9 ¢ to 720.0 ¢
Major 12-mosstep M12ms 11L + s 720.0 ¢ to 776.5 ¢
13-mosstep Perfect 13-mosstep P13ms 11L + 2s 776.5 ¢ to 780.0 ¢
Augmented 13-mosstep A13ms 12L + s 780.0 ¢ to 847.1 ¢
14-mosstep Minor 14-mosstep m14ms 11L + 3s 776.5 ¢ to 840.0 ¢
Major 14-mosstep M14ms 12L + 2s 840.0 ¢ to 847.1 ¢
15-mosstep Minor 15-mosstep m15ms 12L + 3s 847.1 ¢ to 900.0 ¢
Major 15-mosstep M15ms 13L + 2s 900.0 ¢ to 917.6 ¢
16-mosstep Minor 16-mosstep m16ms 13L + 3s 917.6 ¢ to 960.0 ¢
Major 16-mosstep M16ms 14L + 2s 960.0 ¢ to 988.2 ¢
17-mosstep Minor 17-mosstep m17ms 14L + 3s 988.2 ¢ to 1020.0 ¢
Major 17-mosstep M17ms 15L + 2s 1020.0 ¢ to 1058.8 ¢
18-mosstep Minor 18-mosstep m18ms 15L + 3s 1058.8 ¢ to 1080.0 ¢
Major 18-mosstep M18ms 16L + 2s 1080.0 ¢ to 1129.4 ¢
19-mosstep Minor 19-mosstep m19ms 16L + 3s 1129.4 ¢ to 1140.0 ¢
Major 19-mosstep M19ms 17L + 2s 1140.0 ¢ to 1200.0 ¢
20-mosstep Perfect 20-mosstep P20ms 17L + 3s 1200.0 ¢

Generator chain

Generator chain of 17L 3s
Bright gens Scale degree Abbrev.
36 Augmented 12-mosdegree A12md
35 Augmented 5-mosdegree A5md
34 Augmented 18-mosdegree A18md
33 Augmented 11-mosdegree A11md
32 Augmented 4-mosdegree A4md
31 Augmented 17-mosdegree A17md
30 Augmented 10-mosdegree A10md
29 Augmented 3-mosdegree A3md
28 Augmented 16-mosdegree A16md
27 Augmented 9-mosdegree A9md
26 Augmented 2-mosdegree A2md
25 Augmented 15-mosdegree A15md
24 Augmented 8-mosdegree A8md
23 Augmented 1-mosdegree A1md
22 Augmented 14-mosdegree A14md
21 Augmented 7-mosdegree A7md
20 Augmented 0-mosdegree A0md
19 Augmented 13-mosdegree A13md
18 Major 6-mosdegree M6md
17 Major 19-mosdegree M19md
16 Major 12-mosdegree M12md
15 Major 5-mosdegree M5md
14 Major 18-mosdegree M18md
13 Major 11-mosdegree M11md
12 Major 4-mosdegree M4md
11 Major 17-mosdegree M17md
10 Major 10-mosdegree M10md
9 Major 3-mosdegree M3md
8 Major 16-mosdegree M16md
7 Major 9-mosdegree M9md
6 Major 2-mosdegree M2md
5 Major 15-mosdegree M15md
4 Major 8-mosdegree M8md
3 Major 1-mosdegree M1md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 20-mosdegree		 P0md
P20md
−1 Perfect 13-mosdegree P13md
−2 Minor 6-mosdegree m6md
−3 Minor 19-mosdegree m19md
−4 Minor 12-mosdegree m12md
−5 Minor 5-mosdegree m5md
−6 Minor 18-mosdegree m18md
−7 Minor 11-mosdegree m11md
−8 Minor 4-mosdegree m4md
−9 Minor 17-mosdegree m17md
−10 Minor 10-mosdegree m10md
−11 Minor 3-mosdegree m3md
−12 Minor 16-mosdegree m16md
−13 Minor 9-mosdegree m9md
−14 Minor 2-mosdegree m2md
−15 Minor 15-mosdegree m15md
−16 Minor 8-mosdegree m8md
−17 Minor 1-mosdegree m1md
−18 Minor 14-mosdegree m14md
−19 Diminished 7-mosdegree d7md
−20 Diminished 20-mosdegree d20md
−21 Diminished 13-mosdegree d13md
−22 Diminished 6-mosdegree d6md
−23 Diminished 19-mosdegree d19md
−24 Diminished 12-mosdegree d12md
−25 Diminished 5-mosdegree d5md
−26 Diminished 18-mosdegree d18md
−27 Diminished 11-mosdegree d11md
−28 Diminished 4-mosdegree d4md
−29 Diminished 17-mosdegree d17md
−30 Diminished 10-mosdegree d10md
−31 Diminished 3-mosdegree d3md
−32 Diminished 16-mosdegree d16md
−33 Diminished 9-mosdegree d9md
−34 Diminished 2-mosdegree d2md
−35 Diminished 15-mosdegree d15md
−36 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 17L 3s
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
19|0 1 LLLLLLsLLLLLLsLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|1 8 LLLLLLsLLLLLsLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|2 15 LLLLLsLLLLLLsLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|3 2 LLLLLsLLLLLLsLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
15|4 9 LLLLLsLLLLLsLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
14|5 16 LLLLsLLLLLLsLLLLLLsL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
13|6 3 LLLLsLLLLLLsLLLLLsLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
12|7 10 LLLLsLLLLLsLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
11|8 17 LLLsLLLLLLsLLLLLLsLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
10|9 4 LLLsLLLLLLsLLLLLsLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
9|10 11 LLLsLLLLLsLLLLLLsLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
8|11 18 LLsLLLLLLsLLLLLLsLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
7|12 5 LLsLLLLLLsLLLLLsLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
6|13 12 LLsLLLLLsLLLLLLsLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
5|14 19 LsLLLLLLsLLLLLLsLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
4|15 6 LsLLLLLLsLLLLLsLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf.
3|16 13 LsLLLLLsLLLLLLsLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf.
2|17 20 sLLLLLLsLLLLLLsLLLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf.
1|18 7 sLLLLLLsLLLLLsLLLLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|19 14 sLLLLLsLLLLLLsLLLLLL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 17L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\20 420.000 780.000 1:1 1.000 Equalized 17L 3s
41\117 420.513 779.487 6:5 1.200
34\97 420.619 779.381 5:4 1.250
61\174 420.690 779.310 9:7 1.286
27\77 420.779 779.221 4:3 1.333 Supersoft 17L 3s
74\211 420.853 779.147 11:8 1.375
47\134 420.896 779.104 7:5 1.400
67\191 420.942 779.058 10:7 1.429
20\57 421.053 778.947 3:2 1.500 Soft 17L 3s
73\208 421.154 778.846 11:7 1.571
53\151 421.192 778.808 8:5 1.600
86\245 421.224 778.776 13:8 1.625
33\94 421.277 778.723 5:3 1.667 Semisoft 17L 3s
79\225 421.333 778.667 12:7 1.714
46\131 421.374 778.626 7:4 1.750
59\168 421.429 778.571 9:5 1.800
13\37 421.622 778.378 2:1 2.000 Basic 17L 3s
Scales with tunings softer than this are proper
58\165 421.818 778.182 9:4 2.250
45\128 421.875 778.125 7:3 2.333
77\219 421.918 778.082 12:5 2.400
32\91 421.978 778.022 5:2 2.500 Semihard 17L 3s
83\236 422.034 777.966 13:5 2.600
51\145 422.069 777.931 8:3 2.667
70\199 422.111 777.889 11:4 2.750
19\54 422.222 777.778 3:1 3.000 Hard 17L 3s
63\179 422.346 777.654 10:3 3.333
44\125 422.400 777.600 7:2 3.500
69\196 422.449 777.551 11:3 3.667
25\71 422.535 777.465 4:1 4.000 Superhard 17L 3s
56\159 422.642 777.358 9:2 4.500
31\88 422.727 777.273 5:1 5.000
37\105 422.857 777.143 6:1 6.000
6\17 423.529 776.471 1:0 → ∞ Collapsed 17L 3s
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