17L 5s

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↖ 16L 4s ↑ 17L 4s 18L 4s ↗
← 16L 5s 17L 5s 18L 5s →
↙ 16L 6s ↓ 17L 6s 18L 6s ↘ 
┌╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║║│║║║│║║║││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLsLLLLsLLLsLLLs
sLLLsLLLsLLLLsLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\22 to 7\17 (490.9 ¢ to 494.1 ¢)
Dark 10\17 to 13\22 (705.9 ¢ to 709.1 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 5L 12s
Sister 5L 17s
Daughters 22L 17s, 17L 22s
Neutralized 12L 10s
2-Flought 39L 5s, 17L 27s
Equal tunings
Equalized (L:s = 1:1) 9\22 (490.9 ¢)
Supersoft (L:s = 4:3) 34\83 (491.6 ¢)
Soft (L:s = 3:2) 25\61 (491.8 ¢)
Semisoft (L:s = 5:3) 41\100 (492.0 ¢)
Basic (L:s = 2:1) 16\39 (492.3 ¢)
Semihard (L:s = 5:2) 39\95 (492.6 ¢)
Hard (L:s = 3:1) 23\56 (492.9 ¢)
Superhard (L:s = 4:1) 30\73 (493.2 ¢)
Collapsed (L:s = 1:0) 7\17 (494.1 ¢)

17L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 5 small steps, repeating every octave. 17L 5s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 490.9 ¢ to 494.1 ¢, or from 705.9 ¢ to 709.1 ¢. This scale is the parent of another MOS scale that exhibits the fractal-like acoustic effects for which Archagall temperament is named—however, this scale also has tuning areas that don't support these effects.

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 5s
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 70.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 70.6 ¢ to 109.1 ¢
Major 2-mosstep M2ms 2L 109.1 ¢ to 141.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 141.2 ¢ to 163.6 ¢
Major 3-mosstep M3ms 3L 163.6 ¢ to 211.8 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 211.8 ¢ to 218.2 ¢
Major 4-mosstep M4ms 4L 218.2 ¢ to 282.4 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 211.8 ¢ to 272.7 ¢
Major 5-mosstep M5ms 4L + s 272.7 ¢ to 282.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 282.4 ¢ to 327.3 ¢
Major 6-mosstep M6ms 5L + s 327.3 ¢ to 352.9 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 352.9 ¢ to 381.8 ¢
Major 7-mosstep M7ms 6L + s 381.8 ¢ to 423.5 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 423.5 ¢ to 436.4 ¢
Major 8-mosstep M8ms 7L + s 436.4 ¢ to 494.1 ¢
9-mosstep Diminished 9-mosstep d9ms 6L + 3s 423.5 ¢ to 490.9 ¢
Perfect 9-mosstep P9ms 7L + 2s 490.9 ¢ to 494.1 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 494.1 ¢ to 545.5 ¢
Major 10-mosstep M10ms 8L + 2s 545.5 ¢ to 564.7 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 564.7 ¢ to 600.0 ¢
Major 11-mosstep M11ms 9L + 2s 600.0 ¢ to 635.3 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 635.3 ¢ to 654.5 ¢
Major 12-mosstep M12ms 10L + 2s 654.5 ¢ to 705.9 ¢
13-mosstep Perfect 13-mosstep P13ms 10L + 3s 705.9 ¢ to 709.1 ¢
Augmented 13-mosstep A13ms 11L + 2s 709.1 ¢ to 776.5 ¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 705.9 ¢ to 763.6 ¢
Major 14-mosstep M14ms 11L + 3s 763.6 ¢ to 776.5 ¢
15-mosstep Minor 15-mosstep m15ms 11L + 4s 776.5 ¢ to 818.2 ¢
Major 15-mosstep M15ms 12L + 3s 818.2 ¢ to 847.1 ¢
16-mosstep Minor 16-mosstep m16ms 12L + 4s 847.1 ¢ to 872.7 ¢
Major 16-mosstep M16ms 13L + 3s 872.7 ¢ to 917.6 ¢
17-mosstep Minor 17-mosstep m17ms 13L + 4s 917.6 ¢ to 927.3 ¢
Major 17-mosstep M17ms 14L + 3s 927.3 ¢ to 988.2 ¢
18-mosstep Minor 18-mosstep m18ms 13L + 5s 917.6 ¢ to 981.8 ¢
Major 18-mosstep M18ms 14L + 4s 981.8 ¢ to 988.2 ¢
19-mosstep Minor 19-mosstep m19ms 14L + 5s 988.2 ¢ to 1036.4 ¢
Major 19-mosstep M19ms 15L + 4s 1036.4 ¢ to 1058.8 ¢
20-mosstep Minor 20-mosstep m20ms 15L + 5s 1058.8 ¢ to 1090.9 ¢
Major 20-mosstep M20ms 16L + 4s 1090.9 ¢ to 1129.4 ¢
21-mosstep Minor 21-mosstep m21ms 16L + 5s 1129.4 ¢ to 1145.5 ¢
Major 21-mosstep M21ms 17L + 4s 1145.5 ¢ to 1200.0 ¢
22-mosstep Perfect 22-mosstep P22ms 17L + 5s 1200.0 ¢

Generator chain

Generator chain of 17L 5s
Bright gens Scale degree Abbrev.
38 Augmented 12-mosdegree A12md
37 Augmented 3-mosdegree A3md
36 Augmented 16-mosdegree A16md
35 Augmented 7-mosdegree A7md
34 Augmented 20-mosdegree A20md
33 Augmented 11-mosdegree A11md
32 Augmented 2-mosdegree A2md
31 Augmented 15-mosdegree A15md
30 Augmented 6-mosdegree A6md
29 Augmented 19-mosdegree A19md
28 Augmented 10-mosdegree A10md
27 Augmented 1-mosdegree A1md
26 Augmented 14-mosdegree A14md
25 Augmented 5-mosdegree A5md
24 Augmented 18-mosdegree A18md
23 Augmented 9-mosdegree A9md
22 Augmented 0-mosdegree A0md
21 Augmented 13-mosdegree A13md
20 Major 4-mosdegree M4md
19 Major 17-mosdegree M17md
18 Major 8-mosdegree M8md
17 Major 21-mosdegree M21md
16 Major 12-mosdegree M12md
15 Major 3-mosdegree M3md
14 Major 16-mosdegree M16md
13 Major 7-mosdegree M7md
12 Major 20-mosdegree M20md
11 Major 11-mosdegree M11md
10 Major 2-mosdegree M2md
9 Major 15-mosdegree M15md
8 Major 6-mosdegree M6md
7 Major 19-mosdegree M19md
6 Major 10-mosdegree M10md
5 Major 1-mosdegree M1md
4 Major 14-mosdegree M14md
3 Major 5-mosdegree M5md
2 Major 18-mosdegree M18md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 22-mosdegree		 P0md
P22md
−1 Perfect 13-mosdegree P13md
−2 Minor 4-mosdegree m4md
−3 Minor 17-mosdegree m17md
−4 Minor 8-mosdegree m8md
−5 Minor 21-mosdegree m21md
−6 Minor 12-mosdegree m12md
−7 Minor 3-mosdegree m3md
−8 Minor 16-mosdegree m16md
−9 Minor 7-mosdegree m7md
−10 Minor 20-mosdegree m20md
−11 Minor 11-mosdegree m11md
−12 Minor 2-mosdegree m2md
−13 Minor 15-mosdegree m15md
−14 Minor 6-mosdegree m6md
−15 Minor 19-mosdegree m19md
−16 Minor 10-mosdegree m10md
−17 Minor 1-mosdegree m1md
−18 Minor 14-mosdegree m14md
−19 Minor 5-mosdegree m5md
−20 Minor 18-mosdegree m18md
−21 Diminished 9-mosdegree d9md
−22 Diminished 22-mosdegree d22md
−23 Diminished 13-mosdegree d13md
−24 Diminished 4-mosdegree d4md
−25 Diminished 17-mosdegree d17md
−26 Diminished 8-mosdegree d8md
−27 Diminished 21-mosdegree d21md
−28 Diminished 12-mosdegree d12md
−29 Diminished 3-mosdegree d3md
−30 Diminished 16-mosdegree d16md
−31 Diminished 7-mosdegree d7md
−32 Diminished 20-mosdegree d20md
−33 Diminished 11-mosdegree d11md
−34 Diminished 2-mosdegree d2md
−35 Diminished 15-mosdegree d15md
−36 Diminished 6-mosdegree d6md
−37 Diminished 19-mosdegree d19md
−38 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 17L 5s
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 LLLLsLLLsLLLLsLLLsLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|1 10 LLLLsLLLsLLLsLLLLsLLLs 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 19 LLLsLLLLsLLLsLLLLsLLLs Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|3 6 LLLsLLLLsLLLsLLLsLLLLs Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
17|4 15 LLLsLLLsLLLLsLLLsLLLLs Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
16|5 2 LLLsLLLsLLLLsLLLsLLLsL Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf.
15|6 11 LLLsLLLsLLLsLLLLsLLLsL Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf.
14|7 20 LLsLLLLsLLLsLLLLsLLLsL Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf.
13|8 7 LLsLLLLsLLLsLLLsLLLLsL Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf.
12|9 16 LLsLLLsLLLLsLLLsLLLLsL Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf.
11|10 3 LLsLLLsLLLLsLLLsLLLsLL Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf.
10|11 12 LLsLLLsLLLsLLLLsLLLsLL Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf.
9|12 21 LsLLLLsLLLsLLLLsLLLsLL Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf.
8|13 8 LsLLLLsLLLsLLLsLLLLsLL Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf.
7|14 17 LsLLLsLLLLsLLLsLLLLsLL Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf.
6|15 4 LsLLLsLLLLsLLLsLLLsLLL Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf.
5|16 13 LsLLLsLLLsLLLLsLLLsLLL Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf.
4|17 22 sLLLLsLLLsLLLLsLLLsLLL Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf.
3|18 9 sLLLLsLLLsLLLsLLLLsLLL Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf.
2|19 18 sLLLsLLLLsLLLsLLLLsLLL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf.
1|20 5 sLLLsLLLLsLLLsLLLsLLLL 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 14 sLLLsLLLsLLLLsLLLsLLLL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 17L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\22 490.909 709.091 1:1 1.000 Equalized 17L 5s
52\127 491.339 708.661 6:5 1.200
43\105 491.429 708.571 5:4 1.250
77\188 491.489 708.511 9:7 1.286
34\83 491.566 708.434 4:3 1.333 Supersoft 17L 5s
93\227 491.630 708.370 11:8 1.375
59\144 491.667 708.333 7:5 1.400
84\205 491.707 708.293 10:7 1.429
25\61 491.803 708.197 3:2 1.500 Soft 17L 5s
91\222 491.892 708.108 11:7 1.571
66\161 491.925 708.075 8:5 1.600
107\261 491.954 708.046 13:8 1.625
41\100 492.000 708.000 5:3 1.667 Semisoft 17L 5s
98\239 492.050 707.950 12:7 1.714
57\139 492.086 707.914 7:4 1.750
73\178 492.135 707.865 9:5 1.800
16\39 492.308 707.692 2:1 2.000 Basic 17L 5s
Scales with tunings softer than this are proper
71\173 492.486 707.514 9:4 2.250
55\134 492.537 707.463 7:3 2.333
94\229 492.576 707.424 12:5 2.400
39\95 492.632 707.368 5:2 2.500 Semihard 17L 5s
101\246 492.683 707.317 13:5 2.600
62\151 492.715 707.285 8:3 2.667
85\207 492.754 707.246 11:4 2.750
23\56 492.857 707.143 3:1 3.000 Hard 17L 5s
76\185 492.973 707.027 10:3 3.333
53\129 493.023 706.977 7:2 3.500
83\202 493.069 706.931 11:3 3.667
30\73 493.151 706.849 4:1 4.000 Superhard 17L 5s
Archagall
67\163 493.252 706.748 9:2 4.500
37\90 493.333 706.667 5:1 5.000
44\107 493.458 706.542 6:1 6.000
7\17 494.118 705.882 1:0 → ∞ Collapsed 17L 5s
Todo: expand
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