17L 7s

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↖ 16L 6s ↑ 17L 6s 18L 6s ↗
← 16L 7s 17L 7s 18L 7s →
↙ 16L 8s ↓ 17L 8s 18L 8s ↘
┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║║│║║│║║║│║║│║║││
││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLLsLLsLLLsLLsLLs
sLLsLLsLLLsLLsLLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\24 to 5\17 (350.0 ¢ to 352.9 ¢)
Dark 12\17 to 17\24 (847.1 ¢ to 850.0 ¢)
TAMNAMS information
Descends from 7L 3s (dicoid)
Ancestor's step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 7L 10s
Sister 7L 17s
Daughters 24L 17s, 17L 24s
Neutralized 10L 14s
2-Flought 41L 7s, 17L 31s
Equal tunings
Equalized (L:s = 1:1) 7\24 (350.0 ¢)
Supersoft (L:s = 4:3) 26\89 (350.6 ¢)
Soft (L:s = 3:2) 19\65 (350.8 ¢)
Semisoft (L:s = 5:3) 31\106 (350.9 ¢)
Basic (L:s = 2:1) 12\41 (351.2 ¢)
Semihard (L:s = 5:2) 29\99 (351.5 ¢)
Hard (L:s = 3:1) 17\58 (351.7 ¢)
Superhard (L:s = 4:1) 22\75 (352.0 ¢)
Collapsed (L:s = 1:0) 5\17 (352.9 ¢)

17L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 7 small steps, repeating every octave. 17L 7s is a grandchild scale of 7L 3s, expanding it by 14 tones. Generators that produce this scale range from 350 ¢ to 352.9 ¢, or from 847.1 ¢ to 850 ¢.

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 17L 7s
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 50.0 ¢
Major 1-mosstep M1ms L 50.0 ¢ to 70.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 70.6 ¢ to 100.0 ¢
Major 2-mosstep M2ms 2L 100.0 ¢ to 141.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 141.2 ¢ to 150.0 ¢
Major 3-mosstep M3ms 3L 150.0 ¢ to 211.8 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 141.2 ¢ to 200.0 ¢
Major 4-mosstep M4ms 3L + s 200.0 ¢ to 211.8 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 211.8 ¢ to 250.0 ¢
Major 5-mosstep M5ms 4L + s 250.0 ¢ to 282.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 282.4 ¢ to 300.0 ¢
Major 6-mosstep M6ms 5L + s 300.0 ¢ to 352.9 ¢
7-mosstep Diminished 7-mosstep d7ms 4L + 3s 282.4 ¢ to 350.0 ¢
Perfect 7-mosstep P7ms 5L + 2s 350.0 ¢ to 352.9 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 352.9 ¢ to 400.0 ¢
Major 8-mosstep M8ms 6L + 2s 400.0 ¢ to 423.5 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 423.5 ¢ to 450.0 ¢
Major 9-mosstep M9ms 7L + 2s 450.0 ¢ to 494.1 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 494.1 ¢ to 500.0 ¢
Major 10-mosstep M10ms 8L + 2s 500.0 ¢ to 564.7 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 494.1 ¢ to 550.0 ¢
Major 11-mosstep M11ms 8L + 3s 550.0 ¢ to 564.7 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 564.7 ¢ to 600.0 ¢
Major 12-mosstep M12ms 9L + 3s 600.0 ¢ to 635.3 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 635.3 ¢ to 650.0 ¢
Major 13-mosstep M13ms 10L + 3s 650.0 ¢ to 705.9 ¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 635.3 ¢ to 700.0 ¢
Major 14-mosstep M14ms 10L + 4s 700.0 ¢ to 705.9 ¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 705.9 ¢ to 750.0 ¢
Major 15-mosstep M15ms 11L + 4s 750.0 ¢ to 776.5 ¢
16-mosstep Minor 16-mosstep m16ms 11L + 5s 776.5 ¢ to 800.0 ¢
Major 16-mosstep M16ms 12L + 4s 800.0 ¢ to 847.1 ¢
17-mosstep Perfect 17-mosstep P17ms 12L + 5s 847.1 ¢ to 850.0 ¢
Augmented 17-mosstep A17ms 13L + 4s 850.0 ¢ to 917.6 ¢
18-mosstep Minor 18-mosstep m18ms 12L + 6s 847.1 ¢ to 900.0 ¢
Major 18-mosstep M18ms 13L + 5s 900.0 ¢ to 917.6 ¢
19-mosstep Minor 19-mosstep m19ms 13L + 6s 917.6 ¢ to 950.0 ¢
Major 19-mosstep M19ms 14L + 5s 950.0 ¢ to 988.2 ¢
20-mosstep Minor 20-mosstep m20ms 14L + 6s 988.2 ¢ to 1000.0 ¢
Major 20-mosstep M20ms 15L + 5s 1000.0 ¢ to 1058.8 ¢
21-mosstep Minor 21-mosstep m21ms 14L + 7s 988.2 ¢ to 1050.0 ¢
Major 21-mosstep M21ms 15L + 6s 1050.0 ¢ to 1058.8 ¢
22-mosstep Minor 22-mosstep m22ms 15L + 7s 1058.8 ¢ to 1100.0 ¢
Major 22-mosstep M22ms 16L + 6s 1100.0 ¢ to 1129.4 ¢
23-mosstep Minor 23-mosstep m23ms 16L + 7s 1129.4 ¢ to 1150.0 ¢
Major 23-mosstep M23ms 17L + 6s 1150.0 ¢ to 1200.0 ¢
24-mosstep Perfect 24-mosstep P24ms 17L + 7s 1200.0 ¢

Generator chain

Generator chain of 17L 7s
Bright gens Scale degree Abbrev.
40 Augmented 16-mosdegree A16md
39 Augmented 9-mosdegree A9md
38 Augmented 2-mosdegree A2md
37 Augmented 19-mosdegree A19md
36 Augmented 12-mosdegree A12md
35 Augmented 5-mosdegree A5md
34 Augmented 22-mosdegree A22md
33 Augmented 15-mosdegree A15md
32 Augmented 8-mosdegree A8md
31 Augmented 1-mosdegree A1md
30 Augmented 18-mosdegree A18md
29 Augmented 11-mosdegree A11md
28 Augmented 4-mosdegree A4md
27 Augmented 21-mosdegree A21md
26 Augmented 14-mosdegree A14md
25 Augmented 7-mosdegree A7md
24 Augmented 0-mosdegree A0md
23 Augmented 17-mosdegree A17md
22 Major 10-mosdegree M10md
21 Major 3-mosdegree M3md
20 Major 20-mosdegree M20md
19 Major 13-mosdegree M13md
18 Major 6-mosdegree M6md
17 Major 23-mosdegree M23md
16 Major 16-mosdegree M16md
15 Major 9-mosdegree M9md
14 Major 2-mosdegree M2md
13 Major 19-mosdegree M19md
12 Major 12-mosdegree M12md
11 Major 5-mosdegree M5md
10 Major 22-mosdegree M22md
9 Major 15-mosdegree M15md
8 Major 8-mosdegree M8md
7 Major 1-mosdegree M1md
6 Major 18-mosdegree M18md
5 Major 11-mosdegree M11md
4 Major 4-mosdegree M4md
3 Major 21-mosdegree M21md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 24-mosdegree
P0md
P24md
−1 Perfect 17-mosdegree P17md
−2 Minor 10-mosdegree m10md
−3 Minor 3-mosdegree m3md
−4 Minor 20-mosdegree m20md
−5 Minor 13-mosdegree m13md
−6 Minor 6-mosdegree m6md
−7 Minor 23-mosdegree m23md
−8 Minor 16-mosdegree m16md
−9 Minor 9-mosdegree m9md
−10 Minor 2-mosdegree m2md
−11 Minor 19-mosdegree m19md
−12 Minor 12-mosdegree m12md
−13 Minor 5-mosdegree m5md
−14 Minor 22-mosdegree m22md
−15 Minor 15-mosdegree m15md
−16 Minor 8-mosdegree m8md
−17 Minor 1-mosdegree m1md
−18 Minor 18-mosdegree m18md
−19 Minor 11-mosdegree m11md
−20 Minor 4-mosdegree m4md
−21 Minor 21-mosdegree m21md
−22 Minor 14-mosdegree m14md
−23 Diminished 7-mosdegree d7md
−24 Diminished 24-mosdegree d24md
−25 Diminished 17-mosdegree d17md
−26 Diminished 10-mosdegree d10md
−27 Diminished 3-mosdegree d3md
−28 Diminished 20-mosdegree d20md
−29 Diminished 13-mosdegree d13md
−30 Diminished 6-mosdegree d6md
−31 Diminished 23-mosdegree d23md
−32 Diminished 16-mosdegree d16md
−33 Diminished 9-mosdegree d9md
−34 Diminished 2-mosdegree d2md
−35 Diminished 19-mosdegree d19md
−36 Diminished 12-mosdegree d12md
−37 Diminished 5-mosdegree d5md
−38 Diminished 22-mosdegree d22md
−39 Diminished 15-mosdegree d15md
−40 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 17L 7s
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 23 24
23|0 1 LLLsLLsLLLsLLsLLLsLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
22|1 8 LLLsLLsLLLsLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
21|2 15 LLLsLLsLLsLLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|3 22 LLsLLLsLLsLLLsLLsLLLsLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|4 5 LLsLLLsLLsLLLsLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
18|5 12 LLsLLLsLLsLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
17|6 19 LLsLLsLLLsLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
16|7 2 LLsLLsLLLsLLsLLLsLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
15|8 9 LLsLLsLLLsLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
14|9 16 LLsLLsLLsLLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
13|10 23 LsLLLsLLsLLLsLLsLLLsLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
12|11 6 LsLLLsLLsLLLsLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
11|12 13 LsLLLsLLsLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
10|13 20 LsLLsLLLsLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
9|14 3 LsLLsLLLsLLsLLLsLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
8|15 10 LsLLsLLLsLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
7|16 17 LsLLsLLsLLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
6|17 24 sLLLsLLsLLLsLLsLLLsLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
5|18 7 sLLLsLLsLLLsLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
4|19 14 sLLLsLLsLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
3|20 21 sLLsLLLsLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
2|21 4 sLLsLLLsLLsLLLsLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|22 11 sLLsLLLsLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|23 18 sLLsLLsLLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 17L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\24 350.000 850.000 1:1 1.000 Equalized 17L 7s
40\137 350.365 849.635 6:5 1.200
33\113 350.442 849.558 5:4 1.250
59\202 350.495 849.505 9:7 1.286
26\89 350.562 849.438 4:3 1.333 Supersoft 17L 7s
71\243 350.617 849.383 11:8 1.375
45\154 350.649 849.351 7:5 1.400
64\219 350.685 849.315 10:7 1.429
19\65 350.769 849.231 3:2 1.500 Soft 17L 7s
69\236 350.847 849.153 11:7 1.571
50\171 350.877 849.123 8:5 1.600
81\277 350.903 849.097 13:8 1.625
31\106 350.943 849.057 5:3 1.667 Semisoft 17L 7s
74\253 350.988 849.012 12:7 1.714
43\147 351.020 848.980 7:4 1.750
55\188 351.064 848.936 9:5 1.800
12\41 351.220 848.780 2:1 2.000 Basic 17L 7s
Scales with tunings softer than this are proper
53\181 351.381 848.619 9:4 2.250
41\140 351.429 848.571 7:3 2.333
70\239 351.464 848.536 12:5 2.400
29\99 351.515 848.485 5:2 2.500 Semihard 17L 7s
75\256 351.562 848.438 13:5 2.600
46\157 351.592 848.408 8:3 2.667
63\215 351.628 848.372 11:4 2.750
17\58 351.724 848.276 3:1 3.000 Hard 17L 7s
56\191 351.832 848.168 10:3 3.333
39\133 351.880 848.120 7:2 3.500
61\208 351.923 848.077 11:3 3.667
22\75 352.000 848.000 4:1 4.000 Superhard 17L 7s
49\167 352.096 847.904 9:2 4.500
27\92 352.174 847.826 5:1 5.000
32\109 352.294 847.706 6:1 6.000
5\17 352.941 847.059 1:0 → ∞ Collapsed 17L 7s
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