3L 17s

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↖ 2L 16s ↑ 3L 16s 4L 16s ↗
← 2L 17s 3L 17s 4L 17s →
↙ 2L 18s ↓ 3L 18s 4L 18s ↘ 
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Scale structure
Step pattern LsssssLssssssLssssss
ssssssLssssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\20 to 2\3 (780.0 ¢ to 800.0 ¢)
Dark 1\3 to 7\20 (400.0 ¢ to 420.0 ¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Ancestor's step ratio range 5:1 to 1:0
Related MOS scales
Parent 3L 14s
Sister 17L 3s
Daughters 20L 3s, 3L 20s
Neutralized 6L 14s
2-Flought 23L 17s, 3L 37s
Equal tunings
Equalized (L:s = 1:1) 13\20 (780.0 ¢)
Supersoft (L:s = 4:3) 41\63 (781.0 ¢)
Soft (L:s = 3:2) 28\43 (781.4 ¢)
Semisoft (L:s = 5:3) 43\66 (781.8 ¢)
Basic (L:s = 2:1) 15\23 (782.6 ¢)
Semihard (L:s = 5:2) 32\49 (783.7 ¢)
Hard (L:s = 3:1) 17\26 (784.6 ¢)
Superhard (L:s = 4:1) 19\29 (786.2 ¢)
Collapsed (L:s = 1:0) 2\3 (800.0 ¢)

3L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 17 small steps, repeating every octave. 3L 17s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 780 ¢ to 800 ¢, or from 400 ¢ to 420 ¢.

This is the MOS which splits its small steps 6-6-5 between its large steps. Its most consonant generator is a 14/11 supermajor third, and its generator in general is a major third of no more than 7\20edo (420 ¢).

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 3L 17s 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 20-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 3L 17s
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 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 120.0 ¢
Major 2-mosstep M2ms L + s 120.0 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 180.0 ¢
Major 3-mosstep M3ms L + 2s 180.0 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 240.0 ¢
Major 4-mosstep M4ms L + 3s 240.0 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 300.0 ¢
Major 5-mosstep M5ms L + 4s 300.0 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 360.0 ¢
Major 6-mosstep M6ms L + 5s 360.0 ¢ to 400.0 ¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 400.0 ¢ to 420.0 ¢
Augmented 7-mosstep A7ms 2L + 5s 420.0 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 480.0 ¢
Major 8-mosstep M8ms 2L + 6s 480.0 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0 ¢ to 540.0 ¢
Major 9-mosstep M9ms 2L + 7s 540.0 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0 ¢ to 600.0 ¢
Major 10-mosstep M10ms 2L + 8s 600.0 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0 ¢ to 660.0 ¢
Major 11-mosstep M11ms 2L + 9s 660.0 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0 ¢ to 720.0 ¢
Major 12-mosstep M12ms 2L + 10s 720.0 ¢ to 800.0 ¢
13-mosstep Diminished 13-mosstep d13ms L + 12s 400.0 ¢ to 780.0 ¢
Perfect 13-mosstep P13ms 2L + 11s 780.0 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 800.0 ¢ to 840.0 ¢
Major 14-mosstep M14ms 3L + 11s 840.0 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 800.0 ¢ to 900.0 ¢
Major 15-mosstep M15ms 3L + 12s 900.0 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0 ¢ to 960.0 ¢
Major 16-mosstep M16ms 3L + 13s 960.0 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 2L + 15s 800.0 ¢ to 1020.0 ¢
Major 17-mosstep M17ms 3L + 14s 1020.0 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0 ¢ to 1080.0 ¢
Major 18-mosstep M18ms 3L + 15s 1080.0 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms 2L + 17s 800.0 ¢ to 1140.0 ¢
Major 19-mosstep M19ms 3L + 16s 1140.0 ¢ to 1200.0 ¢
20-mosstep Perfect 20-mosstep P20ms 3L + 17s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 13-mosstep, produces the following scale degrees. A chain of 20 bright generators contains the scale degrees of one of the modes of 3L 17s. Expanding the chain to 23 scale degrees produces the modes of either 20L 3s (for soft-of-basic tunings) or 3L 20s (for hard-of-basic tunings).

Generator chain of 3L 17s
Bright gens Scale degree Abbrev.
22 Augmented 6-mosdegree A6md
21 Augmented 13-mosdegree A13md
20 Augmented 0-mosdegree A0md
19 Augmented 7-mosdegree A7md
18 Major 14-mosdegree M14md
17 Major 1-mosdegree M1md
16 Major 8-mosdegree M8md
15 Major 15-mosdegree M15md
14 Major 2-mosdegree M2md
13 Major 9-mosdegree M9md
12 Major 16-mosdegree M16md
11 Major 3-mosdegree M3md
10 Major 10-mosdegree M10md
9 Major 17-mosdegree M17md
8 Major 4-mosdegree M4md
7 Major 11-mosdegree M11md
6 Major 18-mosdegree M18md
5 Major 5-mosdegree M5md
4 Major 12-mosdegree M12md
3 Major 19-mosdegree M19md
2 Major 6-mosdegree M6md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 20-mosdegree		 P0md
P20md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 1-mosdegree m1md
−4 Minor 8-mosdegree m8md
−5 Minor 15-mosdegree m15md
−6 Minor 2-mosdegree m2md
−7 Minor 9-mosdegree m9md
−8 Minor 16-mosdegree m16md
−9 Minor 3-mosdegree m3md
−10 Minor 10-mosdegree m10md
−11 Minor 17-mosdegree m17md
−12 Minor 4-mosdegree m4md
−13 Minor 11-mosdegree m11md
−14 Minor 18-mosdegree m18md
−15 Minor 5-mosdegree m5md
−16 Minor 12-mosdegree m12md
−17 Minor 19-mosdegree m19md
−18 Minor 6-mosdegree m6md
−19 Diminished 13-mosdegree d13md
−20 Diminished 20-mosdegree d20md
−21 Diminished 7-mosdegree d7md
−22 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 3L 17s 
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 LsssssLssssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|1 14 LssssssLsssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|2 7 LssssssLssssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
16|3 20 sLsssssLssssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
15|4 13 sLssssssLsssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
14|5 6 sLssssssLssssssLssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
13|6 19 ssLsssssLssssssLssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
12|7 12 ssLssssssLsssssLssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
11|8 5 ssLssssssLssssssLsss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
10|9 18 sssLsssssLssssssLsss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
9|10 11 sssLssssssLsssssLsss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
8|11 4 sssLssssssLssssssLss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
7|12 17 ssssLsssssLssssssLss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
6|13 10 ssssLssssssLsssssLss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
5|14 3 ssssLssssssLssssssLs Perf. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Perf.
4|15 16 sssssLsssssLssssssLs Perf. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Perf.
3|16 9 sssssLssssssLsssssLs Perf. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Maj. Perf.
2|17 2 sssssLssssssLssssssL Perf. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|18 15 ssssssLsssssLssssssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|19 8 ssssssLssssssLsssssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\20 780.000 420.000 1:1 1.000 Equalized 3L 17s
67\103 780.583 419.417 6:5 1.200
54\83 780.723 419.277 5:4 1.250
95\146 780.822 419.178 9:7 1.286
41\63 780.952 419.048 4:3 1.333 Supersoft 3L 17s
110\169 781.065 418.935 11:8 1.375
69\106 781.132 418.868 7:5 1.400
97\149 781.208 418.792 10:7 1.429
28\43 781.395 418.605 3:2 1.500 Soft 3L 17s
99\152 781.579 418.421 11:7 1.571
71\109 781.651 418.349 8:5 1.600
114\175 781.714 418.286 13:8 1.625
43\66 781.818 418.182 5:3 1.667 Semisoft 3L 17s
101\155 781.935 418.065 12:7 1.714
58\89 782.022 417.978 7:4 1.750
73\112 782.143 417.857 9:5 1.800
15\23 782.609 417.391 2:1 2.000 Basic 3L 17s
Scales with tunings softer than this are proper
62\95 783.158 416.842 9:4 2.250
47\72 783.333 416.667 7:3 2.333
79\121 783.471 416.529 12:5 2.400
32\49 783.673 416.327 5:2 2.500 Semihard 3L 17s
81\124 783.871 416.129 13:5 2.600
49\75 784.000 416.000 8:3 2.667
66\101 784.158 415.842 11:4 2.750
17\26 784.615 415.385 3:1 3.000 Hard 3L 17s
53\81 785.185 414.815 10:3 3.333
36\55 785.455 414.545 7:2 3.500
55\84 785.714 414.286 11:3 3.667
19\29 786.207 413.793 4:1 4.000 Superhard 3L 17s
40\61 786.885 413.115 9:2 4.500
21\32 787.500 412.500 5:1 5.000
23\35 788.571 411.429 6:1 6.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 17s
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