12L 41s: Difference between revisions

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{{Infobox MOS}}{{MOS intro}} Its [[chroma-positive]] generator is a almost-perfect fifth of no more than 31\53 (701.9{{cent}}), where the large step is identified with the [[41-comma|countercomp comma]], and the small step is identified with the [[pythagorean comma]]. This MOS is associated with flatter schismic temperaments like [[helmholtz]], [[pontiac]] or [[grackle]].
{{Infobox MOS}}{{MOS intro}} Its [[chroma-positive]] generator is a almost-perfect fifth of no more than 31\53 (701.9{{cent}}), where the large step is identified with the [[41-comma|countercomp comma]], and the small step is identified with the [[pythagorean comma]]. This mos is associated with flatter schismic temperaments like [[helmholtz]], [[pontiac]] or [[grackle]].


== Intervals ==
== Intervals ==
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== Scale tree ==
== Scale tree ==
{{MOS tuning spectrum|2/1=|3/1=[[Grackle]]|7/4=[[Bischismic]]|3/2=[[Helmholtz]]|4/3=[[Pontiac]]|5/4=[[Ponta]]|5/3=[[Hemischis]]|1/0=[[Compton]] / [[Catler]]|1/1=[[Mercator]]|6/1=[[Gracecordial]]}}
{{MOS tuning spectrum
| 5/4 = [[Ponta]]
| 4/3 = [[Pontiac]]
| 11/8 = [[Helmholtz]]
| 3/1 = [[Grackle]]
| 6/1 = [[Gracecordial]]
}}

Latest revision as of 16:53, 27 February 2026

↖ 11L 40s ↑ 12L 40s 13L 40s ↗
← 11L 41s 12L 41s 13L 41s →
↙ 11L 42s ↓ 12L 42s 13L 42s ↘
Scale structure
Step pattern ...53 steps...
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 22\53 to 5\12 (498.1 ¢ to 500.0 ¢)
Dark 7\12 to 31\53 (700.0 ¢ to 701.9 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 2:1 to 9:4
Related MOS scales
Parent 12L 29s
Sister 41L 12s
Daughters 53L 12s, 12L 53s
Neutralized 24L 29s
2-Flought 65L 41s, 12L 94s
Equal tunings
Equalized (L:s = 1:1) 22\53 (498.1 ¢)
Supersoft (L:s = 4:3) 71\171 (498.2 ¢)
Soft (L:s = 3:2) 49\118 (498.3 ¢)
Semisoft (L:s = 5:3) 76\183 (498.4 ¢)
Basic (L:s = 2:1) 27\65 (498.5 ¢)
Semihard (L:s = 5:2) 59\142 (498.6 ¢)
Hard (L:s = 3:1) 32\77 (498.7 ¢)
Superhard (L:s = 4:1) 37\89 (498.9 ¢)
Collapsed (L:s = 1:0) 5\12 (500.0 ¢)
View • Talk • Edit

12L 41s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 41 small steps, repeating every octave. 12L 41s is related to 5L 2s, expanding it by 46 tones. Generators that produce this scale range from 498.1 ¢ to 500 ¢, or from 700 ¢ to 701.9 ¢. Its chroma-positive generator is a almost-perfect fifth of no more than 31\53 (701.9 ¢), where the large step is identified with the countercomp comma, and the small step is identified with the pythagorean comma. This mos is associated with flatter schismic temperaments like helmholtz, pontiac or grackle.

Intervals

Intervals of 12L 41s
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 22.6 ¢
Major 1-mosstep M1ms L 22.6 ¢ to 100.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 45.3 ¢
Major 2-mosstep M2ms L + s 45.3 ¢ to 100.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 67.9 ¢
Major 3-mosstep M3ms L + 2s 67.9 ¢ to 100.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 90.6 ¢
Major 4-mosstep M4ms L + 3s 90.6 ¢ to 100.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 100.0 ¢ to 113.2 ¢
Major 5-mosstep M5ms 2L + 3s 113.2 ¢ to 200.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 100.0 ¢ to 135.8 ¢
Major 6-mosstep M6ms 2L + 4s 135.8 ¢ to 200.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 100.0 ¢ to 158.5 ¢
Major 7-mosstep M7ms 2L + 5s 158.5 ¢ to 200.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 100.0 ¢ to 181.1 ¢
Major 8-mosstep M8ms 2L + 6s 181.1 ¢ to 200.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 200.0 ¢ to 203.8 ¢
Major 9-mosstep M9ms 3L + 6s 203.8 ¢ to 300.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 200.0 ¢ to 226.4 ¢
Major 10-mosstep M10ms 3L + 7s 226.4 ¢ to 300.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 200.0 ¢ to 249.1 ¢
Major 11-mosstep M11ms 3L + 8s 249.1 ¢ to 300.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 200.0 ¢ to 271.7 ¢
Major 12-mosstep M12ms 3L + 9s 271.7 ¢ to 300.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 200.0 ¢ to 294.3 ¢
Major 13-mosstep M13ms 3L + 10s 294.3 ¢ to 300.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 300.0 ¢ to 317.0 ¢
Major 14-mosstep M14ms 4L + 10s 317.0 ¢ to 400.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 300.0 ¢ to 339.6 ¢
Major 15-mosstep M15ms 4L + 11s 339.6 ¢ to 400.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 300.0 ¢ to 362.3 ¢
Major 16-mosstep M16ms 4L + 12s 362.3 ¢ to 400.0 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 300.0 ¢ to 384.9 ¢
Major 17-mosstep M17ms 4L + 13s 384.9 ¢ to 400.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 400.0 ¢ to 407.5 ¢
Major 18-mosstep M18ms 5L + 13s 407.5 ¢ to 500.0 ¢
19-mosstep Minor 19-mosstep m19ms 4L + 15s 400.0 ¢ to 430.2 ¢
Major 19-mosstep M19ms 5L + 14s 430.2 ¢ to 500.0 ¢
20-mosstep Minor 20-mosstep m20ms 4L + 16s 400.0 ¢ to 452.8 ¢
Major 20-mosstep M20ms 5L + 15s 452.8 ¢ to 500.0 ¢
21-mosstep Minor 21-mosstep m21ms 4L + 17s 400.0 ¢ to 475.5 ¢
Major 21-mosstep M21ms 5L + 16s 475.5 ¢ to 500.0 ¢
22-mosstep Diminished 22-mosstep d22ms 4L + 18s 400.0 ¢ to 498.1 ¢
Perfect 22-mosstep P22ms 5L + 17s 498.1 ¢ to 500.0 ¢
23-mosstep Minor 23-mosstep m23ms 5L + 18s 500.0 ¢ to 520.8 ¢
Major 23-mosstep M23ms 6L + 17s 520.8 ¢ to 600.0 ¢
24-mosstep Minor 24-mosstep m24ms 5L + 19s 500.0 ¢ to 543.4 ¢
Major 24-mosstep M24ms 6L + 18s 543.4 ¢ to 600.0 ¢
25-mosstep Minor 25-mosstep m25ms 5L + 20s 500.0 ¢ to 566.0 ¢
Major 25-mosstep M25ms 6L + 19s 566.0 ¢ to 600.0 ¢
26-mosstep Minor 26-mosstep m26ms 5L + 21s 500.0 ¢ to 588.7 ¢
Major 26-mosstep M26ms 6L + 20s 588.7 ¢ to 600.0 ¢
27-mosstep Minor 27-mosstep m27ms 6L + 21s 600.0 ¢ to 611.3 ¢
Major 27-mosstep M27ms 7L + 20s 611.3 ¢ to 700.0 ¢
28-mosstep Minor 28-mosstep m28ms 6L + 22s 600.0 ¢ to 634.0 ¢
Major 28-mosstep M28ms 7L + 21s 634.0 ¢ to 700.0 ¢
29-mosstep Minor 29-mosstep m29ms 6L + 23s 600.0 ¢ to 656.6 ¢
Major 29-mosstep M29ms 7L + 22s 656.6 ¢ to 700.0 ¢
30-mosstep Minor 30-mosstep m30ms 6L + 24s 600.0 ¢ to 679.2 ¢
Major 30-mosstep M30ms 7L + 23s 679.2 ¢ to 700.0 ¢
31-mosstep Perfect 31-mosstep P31ms 7L + 24s 700.0 ¢ to 701.9 ¢
Augmented 31-mosstep A31ms 8L + 23s 701.9 ¢ to 800.0 ¢
32-mosstep Minor 32-mosstep m32ms 7L + 25s 700.0 ¢ to 724.5 ¢
Major 32-mosstep M32ms 8L + 24s 724.5 ¢ to 800.0 ¢
33-mosstep Minor 33-mosstep m33ms 7L + 26s 700.0 ¢ to 747.2 ¢
Major 33-mosstep M33ms 8L + 25s 747.2 ¢ to 800.0 ¢
34-mosstep Minor 34-mosstep m34ms 7L + 27s 700.0 ¢ to 769.8 ¢
Major 34-mosstep M34ms 8L + 26s 769.8 ¢ to 800.0 ¢
35-mosstep Minor 35-mosstep m35ms 7L + 28s 700.0 ¢ to 792.5 ¢
Major 35-mosstep M35ms 8L + 27s 792.5 ¢ to 800.0 ¢
36-mosstep Minor 36-mosstep m36ms 8L + 28s 800.0 ¢ to 815.1 ¢
Major 36-mosstep M36ms 9L + 27s 815.1 ¢ to 900.0 ¢
37-mosstep Minor 37-mosstep m37ms 8L + 29s 800.0 ¢ to 837.7 ¢
Major 37-mosstep M37ms 9L + 28s 837.7 ¢ to 900.0 ¢
38-mosstep Minor 38-mosstep m38ms 8L + 30s 800.0 ¢ to 860.4 ¢
Major 38-mosstep M38ms 9L + 29s 860.4 ¢ to 900.0 ¢
39-mosstep Minor 39-mosstep m39ms 8L + 31s 800.0 ¢ to 883.0 ¢
Major 39-mosstep M39ms 9L + 30s 883.0 ¢ to 900.0 ¢
40-mosstep Minor 40-mosstep m40ms 9L + 31s 900.0 ¢ to 905.7 ¢
Major 40-mosstep M40ms 10L + 30s 905.7 ¢ to 1000.0 ¢
41-mosstep Minor 41-mosstep m41ms 9L + 32s 900.0 ¢ to 928.3 ¢
Major 41-mosstep M41ms 10L + 31s 928.3 ¢ to 1000.0 ¢
42-mosstep Minor 42-mosstep m42ms 9L + 33s 900.0 ¢ to 950.9 ¢
Major 42-mosstep M42ms 10L + 32s 950.9 ¢ to 1000.0 ¢
43-mosstep Minor 43-mosstep m43ms 9L + 34s 900.0 ¢ to 973.6 ¢
Major 43-mosstep M43ms 10L + 33s 973.6 ¢ to 1000.0 ¢
44-mosstep Minor 44-mosstep m44ms 9L + 35s 900.0 ¢ to 996.2 ¢
Major 44-mosstep M44ms 10L + 34s 996.2 ¢ to 1000.0 ¢
45-mosstep Minor 45-mosstep m45ms 10L + 35s 1000.0 ¢ to 1018.9 ¢
Major 45-mosstep M45ms 11L + 34s 1018.9 ¢ to 1100.0 ¢
46-mosstep Minor 46-mosstep m46ms 10L + 36s 1000.0 ¢ to 1041.5 ¢
Major 46-mosstep M46ms 11L + 35s 1041.5 ¢ to 1100.0 ¢
47-mosstep Minor 47-mosstep m47ms 10L + 37s 1000.0 ¢ to 1064.2 ¢
Major 47-mosstep M47ms 11L + 36s 1064.2 ¢ to 1100.0 ¢
48-mosstep Minor 48-mosstep m48ms 10L + 38s 1000.0 ¢ to 1086.8 ¢
Major 48-mosstep M48ms 11L + 37s 1086.8 ¢ to 1100.0 ¢
49-mosstep Minor 49-mosstep m49ms 11L + 38s 1100.0 ¢ to 1109.4 ¢
Major 49-mosstep M49ms 12L + 37s 1109.4 ¢ to 1200.0 ¢
50-mosstep Minor 50-mosstep m50ms 11L + 39s 1100.0 ¢ to 1132.1 ¢
Major 50-mosstep M50ms 12L + 38s 1132.1 ¢ to 1200.0 ¢
51-mosstep Minor 51-mosstep m51ms 11L + 40s 1100.0 ¢ to 1154.7 ¢
Major 51-mosstep M51ms 12L + 39s 1154.7 ¢ to 1200.0 ¢
52-mosstep Minor 52-mosstep m52ms 11L + 41s 1100.0 ¢ to 1177.4 ¢
Major 52-mosstep M52ms 12L + 40s 1177.4 ¢ to 1200.0 ¢
53-mosstep Perfect 53-mosstep P53ms 12L + 41s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 41s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
22\53 498.113 701.887 1:1 1.000 Equalized 12L 41s
115\277 498.195 701.805 6:5 1.200
93\224 498.214 701.786 5:4 1.250 Ponta
164\395 498.228 701.772 9:7 1.286
71\171 498.246 701.754 4:3 1.333 Supersoft 12L 41s
Pontiac
191\460 498.261 701.739 11:8 1.375 Helmholtz
120\289 498.270 701.730 7:5 1.400
169\407 498.280 701.720 10:7 1.429
49\118 498.305 701.695 3:2 1.500 Soft 12L 41s
174\419 498.329 701.671 11:7 1.571
125\301 498.339 701.661 8:5 1.600
201\484 498.347 701.653 13:8 1.625
76\183 498.361 701.639 5:3 1.667 Semisoft 12L 41s
179\431 498.376 701.624 12:7 1.714
103\248 498.387 701.613 7:4 1.750
130\313 498.403 701.597 9:5 1.800
27\65 498.462 701.538 2:1 2.000 Basic 12L 41s
Scales with tunings softer than this are proper
113\272 498.529 701.471 9:4 2.250
86\207 498.551 701.449 7:3 2.333
145\349 498.567 701.433 12:5 2.400
59\142 498.592 701.408 5:2 2.500 Semihard 12L 41s
150\361 498.615 701.385 13:5 2.600
91\219 498.630 701.370 8:3 2.667
123\296 498.649 701.351 11:4 2.750
32\77 498.701 701.299 3:1 3.000 Hard 12L 41s
Grackle
101\243 498.765 701.235 10:3 3.333
69\166 498.795 701.205 7:2 3.500
106\255 498.824 701.176 11:3 3.667
37\89 498.876 701.124 4:1 4.000 Superhard 12L 41s
79\190 498.947 701.053 9:2 4.500
42\101 499.010 700.990 5:1 5.000
47\113 499.115 700.885 6:1 6.000 Gracecordial
5\12 500.000 700.000 1:0 → ∞ Collapsed 12L 41s
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