3L 17s
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Step pattern
LsssssLssssssLssssss
ssssssLssssssLsssssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
13\20 to 2\3 (780.0 ¢ to 800.0 ¢)
Dark
1\3 to 7\20 (400.0 ¢ to 420.0 ¢)
Descends from
3L 5s (checkertonic)
Ancestor's step ratio range
5:1 to 1:0
Parent
3L 14s
Sister
17L 3s
Daughters
20L 3s, 3L 20s
Neutralized
6L 14s
2-Flought
23L 17s, 3L 37s
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 ¢)
↖ 2L 16s | ↑ 3L 16s | 4L 16s ↗ |
← 2L 17s | 3L 17s | 4L 17s → |
↙ 2L 18s | ↓ 3L 18s | 4L 18s ↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║││││││║│││││││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssssLssssssLsssssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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
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
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
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
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 |