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17L 12s

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17L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 12 small steps, repeating every octave. 17L 12s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 703.4 ¢ to 705.9 ¢, or from 494.1 ¢ to 496.6 ¢.

↖ 16L 11s ↑ 17L 11s 18L 11s ↗
← 16L 12s 17L 12s 18L 12s →
↙ 16L 13s ↓ 17L 13s 18L 13s ↘
Scale structure
Step pattern LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLsLLsLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\29 to 10\17 (703.4 ¢ to 705.9 ¢)
Dark 7\17 to 12\29 (494.1 ¢ to 496.6 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 5:2 to 3:1 (quasihard)
Related MOS scales
Parent 12L 5s
Sister 12L 17s
Daughters 29L 17s, 17L 29s
Neutralized 5L 24s
2-Flought 46L 12s, 17L 41s
Equal tunings
Equalized (L:s = 1:1) 17\29 (703.4 ¢)
Supersoft (L:s = 4:3) 61\104 (703.8 ¢)
Soft (L:s = 3:2) 44\75 (704.0 ¢)
Semisoft (L:s = 5:3) 71\121 (704.1 ¢)
Basic (L:s = 2:1) 27\46 (704.3 ¢)
Semihard (L:s = 5:2) 64\109 (704.6 ¢)
Hard (L:s = 3:1) 37\63 (704.8 ¢)
Superhard (L:s = 4:1) 47\80 (705.0 ¢)
Collapsed (L:s = 1:0) 10\17 (705.9 ¢)
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This mos, belonging to the leapday temperament, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of 17edo and 29edo and divides at 80edo into Margo Schulter's gentle region extending down to 29edo and a yet-unnamed region extending up to 17edo.

Modes

Modes of 17L 12s
UDP Cyclic
order		 Step
pattern
28|0 1 LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
27|1 18 LLsLsLLsLsLsLLsLsLLsLsLLsLsLs
26|2 6 LLsLsLLsLsLsLLsLsLLsLsLsLLsLs
25|3 23 LLsLsLsLLsLsLLsLsLLsLsLsLLsLs
24|4 11 LLsLsLsLLsLsLLsLsLsLLsLsLLsLs
23|5 28 LsLLsLsLLsLsLLsLsLsLLsLsLLsLs
22|6 16 LsLLsLsLLsLsLsLLsLsLLsLsLLsLs
21|7 4 LsLLsLsLLsLsLsLLsLsLLsLsLsLLs
20|8 21 LsLLsLsLsLLsLsLLsLsLLsLsLsLLs
19|9 9 LsLLsLsLsLLsLsLLsLsLsLLsLsLLs
18|10 26 LsLsLLsLsLLsLsLLsLsLsLLsLsLLs
17|11 14 LsLsLLsLsLLsLsLsLLsLsLLsLsLLs
16|12 2 LsLsLLsLsLLsLsLsLLsLsLLsLsLsL
15|13 19 LsLsLLsLsLsLLsLsLLsLsLLsLsLsL
14|14 7 LsLsLLsLsLsLLsLsLLsLsLsLLsLsL
13|15 24 LsLsLsLLsLsLLsLsLLsLsLsLLsLsL
12|16 12 LsLsLsLLsLsLLsLsLsLLsLsLLsLsL
11|17 29 sLLsLsLLsLsLLsLsLsLLsLsLLsLsL
10|18 17 sLLsLsLLsLsLsLLsLsLLsLsLLsLsL
9|19 5 sLLsLsLLsLsLsLLsLsLLsLsLsLLsL
8|20 22 sLLsLsLsLLsLsLLsLsLLsLsLsLLsL
7|21 10 sLLsLsLsLLsLsLLsLsLsLLsLsLLsL
6|22 27 sLsLLsLsLLsLsLLsLsLsLLsLsLLsL
5|23 15 sLsLLsLsLLsLsLsLLsLsLLsLsLLsL
4|24 3 sLsLLsLsLLsLsLsLLsLsLLsLsLsLL
3|25 20 sLsLLsLsLsLLsLsLLsLsLLsLsLsLL
2|26 8 sLsLLsLsLsLLsLsLLsLsLsLLsLsLL
1|27 25 sLsLsLLsLsLLsLsLLsLsLsLLsLsLL
0|28 13 sLsLsLLsLsLLsLsLsLLsLsLLsLsLL

Intervals

Intervals of 17L 12s
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 41.4 ¢
Major 1-mosstep M1ms L 41.4 ¢ to 70.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 70.6 ¢ to 82.8 ¢
Major 2-mosstep M2ms 2L 82.8 ¢ to 141.2 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 70.6 ¢ to 124.1 ¢
Major 3-mosstep M3ms 2L + s 124.1 ¢ to 141.2 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 141.2 ¢ to 165.5 ¢
Major 4-mosstep M4ms 3L + s 165.5 ¢ to 211.8 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 141.2 ¢ to 206.9 ¢
Major 5-mosstep M5ms 3L + 2s 206.9 ¢ to 211.8 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 211.8 ¢ to 248.3 ¢
Major 6-mosstep M6ms 4L + 2s 248.3 ¢ to 282.4 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 282.4 ¢ to 289.7 ¢
Major 7-mosstep M7ms 5L + 2s 289.7 ¢ to 352.9 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 282.4 ¢ to 331.0 ¢
Major 8-mosstep M8ms 5L + 3s 331.0 ¢ to 352.9 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 352.9 ¢ to 372.4 ¢
Major 9-mosstep M9ms 6L + 3s 372.4 ¢ to 423.5 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 352.9 ¢ to 413.8 ¢
Major 10-mosstep M10ms 6L + 4s 413.8 ¢ to 423.5 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 423.5 ¢ to 455.2 ¢
Major 11-mosstep M11ms 7L + 4s 455.2 ¢ to 494.1 ¢
12-mosstep Perfect 12-mosstep P12ms 7L + 5s 494.1 ¢ to 496.6 ¢
Augmented 12-mosstep A12ms 8L + 4s 496.6 ¢ to 564.7 ¢
13-mosstep Minor 13-mosstep m13ms 7L + 6s 494.1 ¢ to 537.9 ¢
Major 13-mosstep M13ms 8L + 5s 537.9 ¢ to 564.7 ¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 564.7 ¢ to 579.3 ¢
Major 14-mosstep M14ms 9L + 5s 579.3 ¢ to 635.3 ¢
15-mosstep Minor 15-mosstep m15ms 8L + 7s 564.7 ¢ to 620.7 ¢
Major 15-mosstep M15ms 9L + 6s 620.7 ¢ to 635.3 ¢
16-mosstep Minor 16-mosstep m16ms 9L + 7s 635.3 ¢ to 662.1 ¢
Major 16-mosstep M16ms 10L + 6s 662.1 ¢ to 705.9 ¢
17-mosstep Diminished 17-mosstep d17ms 9L + 8s 635.3 ¢ to 703.4 ¢
Perfect 17-mosstep P17ms 10L + 7s 703.4 ¢ to 705.9 ¢
18-mosstep Minor 18-mosstep m18ms 10L + 8s 705.9 ¢ to 744.8 ¢
Major 18-mosstep M18ms 11L + 7s 744.8 ¢ to 776.5 ¢
19-mosstep Minor 19-mosstep m19ms 11L + 8s 776.5 ¢ to 786.2 ¢
Major 19-mosstep M19ms 12L + 7s 786.2 ¢ to 847.1 ¢
20-mosstep Minor 20-mosstep m20ms 11L + 9s 776.5 ¢ to 827.6 ¢
Major 20-mosstep M20ms 12L + 8s 827.6 ¢ to 847.1 ¢
21-mosstep Minor 21-mosstep m21ms 12L + 9s 847.1 ¢ to 869.0 ¢
Major 21-mosstep M21ms 13L + 8s 869.0 ¢ to 917.6 ¢
22-mosstep Minor 22-mosstep m22ms 12L + 10s 847.1 ¢ to 910.3 ¢
Major 22-mosstep M22ms 13L + 9s 910.3 ¢ to 917.6 ¢
23-mosstep Minor 23-mosstep m23ms 13L + 10s 917.6 ¢ to 951.7 ¢
Major 23-mosstep M23ms 14L + 9s 951.7 ¢ to 988.2 ¢
24-mosstep Minor 24-mosstep m24ms 14L + 10s 988.2 ¢ to 993.1 ¢
Major 24-mosstep M24ms 15L + 9s 993.1 ¢ to 1058.8 ¢
25-mosstep Minor 25-mosstep m25ms 14L + 11s 988.2 ¢ to 1034.5 ¢
Major 25-mosstep M25ms 15L + 10s 1034.5 ¢ to 1058.8 ¢
26-mosstep Minor 26-mosstep m26ms 15L + 11s 1058.8 ¢ to 1075.9 ¢
Major 26-mosstep M26ms 16L + 10s 1075.9 ¢ to 1129.4 ¢
27-mosstep Minor 27-mosstep m27ms 15L + 12s 1058.8 ¢ to 1117.2 ¢
Major 27-mosstep M27ms 16L + 11s 1117.2 ¢ to 1129.4 ¢
28-mosstep Minor 28-mosstep m28ms 16L + 12s 1129.4 ¢ to 1158.6 ¢
Major 28-mosstep M28ms 17L + 11s 1158.6 ¢ to 1200.0 ¢
29-mosstep Perfect 29-mosstep P29ms 17L + 12s 1200.0 ¢

Scale tree

  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 17L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\29 703.448 496.552 1:1 1.000 Equalized 17L 12s
95\162 703.704 496.296 6:5 1.200
78\133 703.759 496.241 5:4 1.250
139\237 703.797 496.203 9:7 1.286
61\104 703.846 496.154 4:3 1.333 Supersoft 17L 12s
166\283 703.887 496.113 11:8 1.375
105\179 703.911 496.089 7:5 1.400
149\254 703.937 496.063 10:7 1.429
44\75 704.000 496.000 3:2 1.500 Soft 17L 12s
159\271 704.059 495.941 11:7 1.571
115\196 704.082 495.918 8:5 1.600
186\317 704.101 495.899 13:8 1.625
71\121 704.132 495.868 5:3 1.667 Semisoft 17L 12s
169\288 704.167 495.833 12:7 1.714
98\167 704.192 495.808 7:4 1.750
125\213 704.225 495.775 9:5 1.800
27\46 704.348 495.652 2:1 2.000 Basic 17L 12s
Scales with tunings softer than this are proper
118\201 704.478 495.522 9:4 2.250
91\155 704.516 495.484 7:3 2.333
155\264 704.545 495.455 12:5 2.400
64\109 704.587 495.413 5:2 2.500 Semihard 17L 12s
165\281 704.626 495.374 13:5 2.600
101\172 704.651 495.349 8:3 2.667
138\235 704.681 495.319 11:4 2.750
37\63 704.762 495.238 3:1 3.000 Hard 17L 12s
121\206 704.854 495.146 10:3 3.333
84\143 704.895 495.105 7:2 3.500
131\223 704.933 495.067 11:3 3.667
47\80 705.000 495.000 4:1 4.000 Superhard 17L 12s
104\177 705.085 494.915 9:2 4.500
57\97 705.155 494.845 5:1 5.000
67\114 705.263 494.737 6:1 6.000
10\17 705.882 494.118 1:0 → ∞ Collapsed 17L 12s
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