12L 29s: Difference between revisions

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{{Infobox MOS}}{{MOS intro}} Its [[chroma-positive]] generator is an almost-perfect fourth, where large step is identified with the [[29-comma]] and the small step is identified with the [[pythagorean comma]]. [[Pythagorean tuning]] generates this scale, with a hardness of 1.8459.
{{Infobox MOS}}{{MOS intro}} Its [[chroma-positive]] generator is an almost-perfect fourth, where large step is identified with the [[29-comma]] and the small step is identified with the [[pythagorean comma]]. [[Pythagorean tuning]] generates this scale, with a hardness of 1.8459. This MOS is often associated with schismic temperaments and other accurate fifth-based temperaments. It is often known as '''pythamystonic'''.


== Intervals ==
== Intervals ==
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== Scale tree ==
== Scale tree ==
{{MOS tuning spectrum|9/5=Pythagorean tuning (701.955c)|3/2=[[Garibaldi]] / [[Cassandra]]|5/2=[[Schismic]]|7/3=[[Pontiac]]}}
{{MOS tuning spectrum|9/5=Pythagorean tuning (701.955c)|3/2=[[Garibaldi]] / [[Cassandra]]|5/2=[[Helmholtz]]|7/3=[[Pontiac]]|6/5=[[Cotoneum]]|4/3=[[Gary]] / Gariwizmic / [[Wizmic_microtemperaments#Cassawizmic|Cassawizmic]]|2/1=[[Mercator]]|1/0=[[Compton]] / [[Catler]]|4/1=[[Grackle]]|1/1=[[Countercomp]]|9/4=[[Ponta]]|8/3=[[Hemischis]]|11/4=[[Bischismic]]}}

Revision as of 16:21, 27 February 2026

↖ 11L 28s ↑ 12L 28s 13L 28s ↗
← 11L 29s 12L 29s 13L 29s →
↙ 11L 30s ↓ 12L 30s 13L 30s ↘
Scale structure
Step pattern ...41 steps...
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\41 to 5\12 (497.6 ¢ to 500.0 ¢)
Dark 7\12 to 24\41 (700.0 ¢ to 702.4 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 2:1 to 7:3
Related MOS scales
Parent 12L 17s
Sister 29L 12s
Daughters 41L 12s, 12L 41s
Neutralized 24L 17s
2-Flought 53L 29s, 12L 70s
Equal tunings
Equalized (L:s = 1:1) 17\41 (497.6 ¢)
Supersoft (L:s = 4:3) 56\135 (497.8 ¢)
Soft (L:s = 3:2) 39\94 (497.9 ¢)
Semisoft (L:s = 5:3) 61\147 (498.0 ¢)
Basic (L:s = 2:1) 22\53 (498.1 ¢)
Semihard (L:s = 5:2) 49\118 (498.3 ¢)
Hard (L:s = 3:1) 27\65 (498.5 ¢)
Superhard (L:s = 4:1) 32\77 (498.7 ¢)
Collapsed (L:s = 1:0) 5\12 (500.0 ¢)
View • Talk • Edit

12L 29s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 29 small steps, repeating every octave. 12L 29s is related to 5L 2s, expanding it by 34 tones. Generators that produce this scale range from 497.6 ¢ to 500 ¢, or from 700 ¢ to 702.4 ¢. Its chroma-positive generator is an almost-perfect fourth, where large step is identified with the 29-comma and the small step is identified with the pythagorean comma. Pythagorean tuning generates this scale, with a hardness of 1.8459. This MOS is often associated with schismic temperaments and other accurate fifth-based temperaments. It is often known as pythamystonic.

Intervals

Intervals of 12L 29s
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 29.3 ¢
Major 1-mosstep M1ms L 29.3 ¢ to 100.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 58.5 ¢
Major 2-mosstep M2ms L + s 58.5 ¢ to 100.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 87.8 ¢
Major 3-mosstep M3ms L + 2s 87.8 ¢ to 100.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 100.0 ¢ to 117.1 ¢
Major 4-mosstep M4ms 2L + 2s 117.1 ¢ to 200.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 100.0 ¢ to 146.3 ¢
Major 5-mosstep M5ms 2L + 3s 146.3 ¢ to 200.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 100.0 ¢ to 175.6 ¢
Major 6-mosstep M6ms 2L + 4s 175.6 ¢ to 200.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 200.0 ¢ to 204.9 ¢
Major 7-mosstep M7ms 3L + 4s 204.9 ¢ to 300.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 200.0 ¢ to 234.1 ¢
Major 8-mosstep M8ms 3L + 5s 234.1 ¢ to 300.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 200.0 ¢ to 263.4 ¢
Major 9-mosstep M9ms 3L + 6s 263.4 ¢ to 300.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 200.0 ¢ to 292.7 ¢
Major 10-mosstep M10ms 3L + 7s 292.7 ¢ to 300.0 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 300.0 ¢ to 322.0 ¢
Major 11-mosstep M11ms 4L + 7s 322.0 ¢ to 400.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 300.0 ¢ to 351.2 ¢
Major 12-mosstep M12ms 4L + 8s 351.2 ¢ to 400.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 300.0 ¢ to 380.5 ¢
Major 13-mosstep M13ms 4L + 9s 380.5 ¢ to 400.0 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 400.0 ¢ to 409.8 ¢
Major 14-mosstep M14ms 5L + 9s 409.8 ¢ to 500.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 400.0 ¢ to 439.0 ¢
Major 15-mosstep M15ms 5L + 10s 439.0 ¢ to 500.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 400.0 ¢ to 468.3 ¢
Major 16-mosstep M16ms 5L + 11s 468.3 ¢ to 500.0 ¢
17-mosstep Diminished 17-mosstep d17ms 4L + 13s 400.0 ¢ to 497.6 ¢
Perfect 17-mosstep P17ms 5L + 12s 497.6 ¢ to 500.0 ¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 500.0 ¢ to 526.8 ¢
Major 18-mosstep M18ms 6L + 12s 526.8 ¢ to 600.0 ¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 500.0 ¢ to 556.1 ¢
Major 19-mosstep M19ms 6L + 13s 556.1 ¢ to 600.0 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 500.0 ¢ to 585.4 ¢
Major 20-mosstep M20ms 6L + 14s 585.4 ¢ to 600.0 ¢
21-mosstep Minor 21-mosstep m21ms 6L + 15s 600.0 ¢ to 614.6 ¢
Major 21-mosstep M21ms 7L + 14s 614.6 ¢ to 700.0 ¢
22-mosstep Minor 22-mosstep m22ms 6L + 16s 600.0 ¢ to 643.9 ¢
Major 22-mosstep M22ms 7L + 15s 643.9 ¢ to 700.0 ¢
23-mosstep Minor 23-mosstep m23ms 6L + 17s 600.0 ¢ to 673.2 ¢
Major 23-mosstep M23ms 7L + 16s 673.2 ¢ to 700.0 ¢
24-mosstep Perfect 24-mosstep P24ms 7L + 17s 700.0 ¢ to 702.4 ¢
Augmented 24-mosstep A24ms 8L + 16s 702.4 ¢ to 800.0 ¢
25-mosstep Minor 25-mosstep m25ms 7L + 18s 700.0 ¢ to 731.7 ¢
Major 25-mosstep M25ms 8L + 17s 731.7 ¢ to 800.0 ¢
26-mosstep Minor 26-mosstep m26ms 7L + 19s 700.0 ¢ to 761.0 ¢
Major 26-mosstep M26ms 8L + 18s 761.0 ¢ to 800.0 ¢
27-mosstep Minor 27-mosstep m27ms 7L + 20s 700.0 ¢ to 790.2 ¢
Major 27-mosstep M27ms 8L + 19s 790.2 ¢ to 800.0 ¢
28-mosstep Minor 28-mosstep m28ms 8L + 20s 800.0 ¢ to 819.5 ¢
Major 28-mosstep M28ms 9L + 19s 819.5 ¢ to 900.0 ¢
29-mosstep Minor 29-mosstep m29ms 8L + 21s 800.0 ¢ to 848.8 ¢
Major 29-mosstep M29ms 9L + 20s 848.8 ¢ to 900.0 ¢
30-mosstep Minor 30-mosstep m30ms 8L + 22s 800.0 ¢ to 878.0 ¢
Major 30-mosstep M30ms 9L + 21s 878.0 ¢ to 900.0 ¢
31-mosstep Minor 31-mosstep m31ms 9L + 22s 900.0 ¢ to 907.3 ¢
Major 31-mosstep M31ms 10L + 21s 907.3 ¢ to 1000.0 ¢
32-mosstep Minor 32-mosstep m32ms 9L + 23s 900.0 ¢ to 936.6 ¢
Major 32-mosstep M32ms 10L + 22s 936.6 ¢ to 1000.0 ¢
33-mosstep Minor 33-mosstep m33ms 9L + 24s 900.0 ¢ to 965.9 ¢
Major 33-mosstep M33ms 10L + 23s 965.9 ¢ to 1000.0 ¢
34-mosstep Minor 34-mosstep m34ms 9L + 25s 900.0 ¢ to 995.1 ¢
Major 34-mosstep M34ms 10L + 24s 995.1 ¢ to 1000.0 ¢
35-mosstep Minor 35-mosstep m35ms 10L + 25s 1000.0 ¢ to 1024.4 ¢
Major 35-mosstep M35ms 11L + 24s 1024.4 ¢ to 1100.0 ¢
36-mosstep Minor 36-mosstep m36ms 10L + 26s 1000.0 ¢ to 1053.7 ¢
Major 36-mosstep M36ms 11L + 25s 1053.7 ¢ to 1100.0 ¢
37-mosstep Minor 37-mosstep m37ms 10L + 27s 1000.0 ¢ to 1082.9 ¢
Major 37-mosstep M37ms 11L + 26s 1082.9 ¢ to 1100.0 ¢
38-mosstep Minor 38-mosstep m38ms 11L + 27s 1100.0 ¢ to 1112.2 ¢
Major 38-mosstep M38ms 12L + 26s 1112.2 ¢ to 1200.0 ¢
39-mosstep Minor 39-mosstep m39ms 11L + 28s 1100.0 ¢ to 1141.5 ¢
Major 39-mosstep M39ms 12L + 27s 1141.5 ¢ to 1200.0 ¢
40-mosstep Minor 40-mosstep m40ms 11L + 29s 1100.0 ¢ to 1170.7 ¢
Major 40-mosstep M40ms 12L + 28s 1170.7 ¢ to 1200.0 ¢
41-mosstep Perfect 41-mosstep P41ms 12L + 29s 1200.0 ¢

Scales

Scale tree

Scale tree and tuning spectrum of 12L 29s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\41 497.561 702.439 1:1 1.000 Equalized 12L 29s
Countercomp
90\217 497.696 702.304 6:5 1.200 Cotoneum
73\176 497.727 702.273 5:4 1.250
129\311 497.749 702.251 9:7 1.286
56\135 497.778 702.222 4:3 1.333 Supersoft 12L 29s
Gary / Gariwizmic / Cassawizmic
151\364 497.802 702.198 11:8 1.375
95\229 497.817 702.183 7:5 1.400
134\323 497.833 702.167 10:7 1.429
39\94 497.872 702.128 3:2 1.500 Soft 12L 29s
Garibaldi / Cassandra
139\335 497.910 702.090 11:7 1.571
100\241 497.925 702.075 8:5 1.600
161\388 497.938 702.062 13:8 1.625
61\147 497.959 702.041 5:3 1.667 Semisoft 12L 29s
144\347 497.983 702.017 12:7 1.714
83\200 498.000 702.000 7:4 1.750
105\253 498.024 701.976 9:5 1.800 Pythagorean tuning (701.955c)
22\53 498.113 701.887 2:1 2.000 Basic 12L 29s
Scales with tunings softer than this are proper
Mercator
93\224 498.214 701.786 9:4 2.250 Ponta
71\171 498.246 701.754 7:3 2.333 Pontiac
120\289 498.270 701.730 12:5 2.400
49\118 498.305 701.695 5:2 2.500 Semihard 12L 29s
Helmholtz
125\301 498.339 701.661 13:5 2.600
76\183 498.361 701.639 8:3 2.667 Hemischis
103\248 498.387 701.613 11:4 2.750 Bischismic
27\65 498.462 701.538 3:1 3.000 Hard 12L 29s
86\207 498.551 701.449 10:3 3.333
59\142 498.592 701.408 7:2 3.500
91\219 498.630 701.370 11:3 3.667
32\77 498.701 701.299 4:1 4.000 Superhard 12L 29s
Grackle
69\166 498.795 701.205 9:2 4.500
37\89 498.876 701.124 5:1 5.000
42\101 499.010 700.990 6:1 6.000
5\12 500.000 700.000 1:0 → ∞ Collapsed 12L 29s
Compton / Catler
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