5L 17s

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↖ 4L 16s ↑ 5L 16s 6L 16s ↗
← 4L 17s 5L 17s 6L 17s →
↙ 4L 18s ↓ 5L 18s 6L 18s ↘ 
┌╥┬┬┬╥┬┬┬╥┬┬┬┬╥┬┬┬╥┬┬┬┬┐
│║│││║│││║││││║│││║│││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLsssLssssLsssLssss
ssssLsssLssssLsssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\22 to 3\5 (709.1 ¢ to 720.0 ¢)
Dark 2\5 to 9\22 (480.0 ¢ to 490.9 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 5L 12s
Sister 17L 5s
Daughters 22L 5s, 5L 22s
Neutralized 10L 12s
2-Flought 27L 17s, 5L 39s
Equal tunings
Equalized (L:s = 1:1) 13\22 (709.1 ¢)
Supersoft (L:s = 4:3) 42\71 (709.9 ¢)
Soft (L:s = 3:2) 29\49 (710.2 ¢)
Semisoft (L:s = 5:3) 45\76 (710.5 ¢)
Basic (L:s = 2:1) 16\27 (711.1 ¢)
Semihard (L:s = 5:2) 35\59 (711.9 ¢)
Hard (L:s = 3:1) 19\32 (712.5 ¢)
Superhard (L:s = 4:1) 22\37 (713.5 ¢)
Collapsed (L:s = 1:0) 3\5 (720.0 ¢)

5L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 17 small steps, repeating every octave. 5L 17s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 709.1 ¢ to 720 ¢, or from 480 ¢ to 490.9 ¢.

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 5L 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 54.5 ¢
Major 1-mosstep M1ms L 54.5 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 109.1 ¢
Major 2-mosstep M2ms L + s 109.1 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 163.6 ¢
Major 3-mosstep M3ms L + 2s 163.6 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 218.2 ¢
Major 4-mosstep M4ms L + 3s 218.2 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0 ¢ to 272.7 ¢
Major 5-mosstep M5ms 2L + 3s 272.7 ¢ to 480.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 327.3 ¢
Major 6-mosstep M6ms 2L + 4s 327.3 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0 ¢ to 381.8 ¢
Major 7-mosstep M7ms 2L + 5s 381.8 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 240.0 ¢ to 436.4 ¢
Major 8-mosstep M8ms 2L + 6s 436.4 ¢ to 480.0 ¢
9-mosstep Perfect 9-mosstep P9ms 2L + 7s 480.0 ¢ to 490.9 ¢
Augmented 9-mosstep A9ms 3L + 6s 490.9 ¢ to 720.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 480.0 ¢ to 545.5 ¢
Major 10-mosstep M10ms 3L + 7s 545.5 ¢ to 720.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 480.0 ¢ to 600.0 ¢
Major 11-mosstep M11ms 3L + 8s 600.0 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 480.0 ¢ to 654.5 ¢
Major 12-mosstep M12ms 3L + 9s 654.5 ¢ to 720.0 ¢
13-mosstep Diminished 13-mosstep d13ms 2L + 11s 480.0 ¢ to 709.1 ¢
Perfect 13-mosstep P13ms 3L + 10s 709.1 ¢ to 720.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 720.0 ¢ to 763.6 ¢
Major 14-mosstep M14ms 4L + 10s 763.6 ¢ to 960.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 720.0 ¢ to 818.2 ¢
Major 15-mosstep M15ms 4L + 11s 818.2 ¢ to 960.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 720.0 ¢ to 872.7 ¢
Major 16-mosstep M16ms 4L + 12s 872.7 ¢ to 960.0 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 720.0 ¢ to 927.3 ¢
Major 17-mosstep M17ms 4L + 13s 927.3 ¢ to 960.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 960.0 ¢ to 981.8 ¢
Major 18-mosstep M18ms 5L + 13s 981.8 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms 4L + 15s 960.0 ¢ to 1036.4 ¢
Major 19-mosstep M19ms 5L + 14s 1036.4 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms 4L + 16s 960.0 ¢ to 1090.9 ¢
Major 20-mosstep M20ms 5L + 15s 1090.9 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms 4L + 17s 960.0 ¢ to 1145.5 ¢
Major 21-mosstep M21ms 5L + 16s 1145.5 ¢ to 1200.0 ¢
22-mosstep Perfect 22-mosstep P22ms 5L + 17s 1200.0 ¢

Generator chain

Generator chain of 5L 17s
Bright gens Scale degree Abbrev.
26 Augmented 8-mosdegree A8md
25 Augmented 17-mosdegree A17md
24 Augmented 4-mosdegree A4md
23 Augmented 13-mosdegree A13md
22 Augmented 0-mosdegree A0md
21 Augmented 9-mosdegree A9md
20 Major 18-mosdegree M18md
19 Major 5-mosdegree M5md
18 Major 14-mosdegree M14md
17 Major 1-mosdegree M1md
16 Major 10-mosdegree M10md
15 Major 19-mosdegree M19md
14 Major 6-mosdegree M6md
13 Major 15-mosdegree M15md
12 Major 2-mosdegree M2md
11 Major 11-mosdegree M11md
10 Major 20-mosdegree M20md
9 Major 7-mosdegree M7md
8 Major 16-mosdegree M16md
7 Major 3-mosdegree M3md
6 Major 12-mosdegree M12md
5 Major 21-mosdegree M21md
4 Major 8-mosdegree M8md
3 Major 17-mosdegree M17md
2 Major 4-mosdegree M4md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 22-mosdegree		 P0md
P22md
−1 Perfect 9-mosdegree P9md
−2 Minor 18-mosdegree m18md
−3 Minor 5-mosdegree m5md
−4 Minor 14-mosdegree m14md
−5 Minor 1-mosdegree m1md
−6 Minor 10-mosdegree m10md
−7 Minor 19-mosdegree m19md
−8 Minor 6-mosdegree m6md
−9 Minor 15-mosdegree m15md
−10 Minor 2-mosdegree m2md
−11 Minor 11-mosdegree m11md
−12 Minor 20-mosdegree m20md
−13 Minor 7-mosdegree m7md
−14 Minor 16-mosdegree m16md
−15 Minor 3-mosdegree m3md
−16 Minor 12-mosdegree m12md
−17 Minor 21-mosdegree m21md
−18 Minor 8-mosdegree m8md
−19 Minor 17-mosdegree m17md
−20 Minor 4-mosdegree m4md
−21 Diminished 13-mosdegree d13md
−22 Diminished 22-mosdegree d22md
−23 Diminished 9-mosdegree d9md
−24 Diminished 18-mosdegree d18md
−25 Diminished 5-mosdegree d5md
−26 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 5L 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 21 22
21|0 1 LsssLsssLssssLsssLssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|1 14 LsssLssssLsssLsssLssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|2 5 LsssLssssLsssLssssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf.
18|3 18 LssssLsssLsssLssssLsss Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf.
17|4 9 LssssLsssLssssLsssLsss Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf.
16|5 22 sLsssLsssLssssLsssLsss Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf.
15|6 13 sLsssLssssLsssLsssLsss Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf.
14|7 4 sLsssLssssLsssLssssLss Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Perf.
13|8 17 sLssssLsssLsssLssssLss Perf. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Perf.
12|9 8 sLssssLsssLssssLsssLss Perf. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf.
11|10 21 ssLsssLsssLssssLsssLss Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf.
10|11 12 ssLsssLssssLsssLsssLss Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf.
9|12 3 ssLsssLssssLsssLssssLs Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Min. Maj. Perf.
8|13 16 ssLssssLsssLsssLssssLs Perf. Min. Min. Maj. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Min. Maj. Perf.
7|14 7 ssLssssLsssLssssLsssLs Perf. Min. Min. Maj. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf.
6|15 20 sssLsssLsssLssssLsssLs Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf.
5|16 11 sssLsssLssssLsssLsssLs Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf.
4|17 2 sssLsssLssssLsssLssssL Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Min. Perf.
3|18 15 sssLssssLsssLsssLssssL Perf. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Min. Perf.
2|19 6 sssLssssLsssLssssLsssL Perf. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
1|20 19 ssssLsssLsssLssssLsssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|21 10 ssssLsssLssssLsssLsssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 5L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\22 709.091 490.909 1:1 1.000 Equalized 5L 17s
68\115 709.565 490.435 6:5 1.200
55\93 709.677 490.323 5:4 1.250
97\164 709.756 490.244 9:7 1.286
42\71 709.859 490.141 4:3 1.333 Supersoft 5L 17s
113\191 709.948 490.052 11:8 1.375
71\120 710.000 490.000 7:5 1.400
100\169 710.059 489.941 10:7 1.429
29\49 710.204 489.796 3:2 1.500 Soft 5L 17s
103\174 710.345 489.655 11:7 1.571
74\125 710.400 489.600 8:5 1.600
119\201 710.448 489.552 13:8 1.625
45\76 710.526 489.474 5:3 1.667 Semisoft 5L 17s
106\179 710.615 489.385 12:7 1.714
61\103 710.680 489.320 7:4 1.750
77\130 710.769 489.231 9:5 1.800
16\27 711.111 488.889 2:1 2.000 Basic 5L 17s
Scales with tunings softer than this are proper
67\113 711.504 488.496 9:4 2.250
51\86 711.628 488.372 7:3 2.333
86\145 711.724 488.276 12:5 2.400
35\59 711.864 488.136 5:2 2.500 Semihard 5L 17s
89\150 712.000 488.000 13:5 2.600
54\91 712.088 487.912 8:3 2.667
73\123 712.195 487.805 11:4 2.750
19\32 712.500 487.500 3:1 3.000 Hard 5L 17s
60\101 712.871 487.129 10:3 3.333
41\69 713.043 486.957 7:2 3.500
63\106 713.208 486.792 11:3 3.667
22\37 713.514 486.486 4:1 4.000 Superhard 5L 17s
47\79 713.924 486.076 9:2 4.500
25\42 714.286 485.714 5:1 5.000
28\47 714.894 485.106 6:1 6.000
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 17s
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