12L 17s: Difference between revisions

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m == Intervals == {{MOS intervals}}
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{{MOS intro}}
{{MOS intro}}
Its [[chroma-positive]] generator is a near-perfect fourth of no more than 5\12 (500{{cent}}), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.
Its [[chroma-positive]] generator is a near-perfect fourth of no more than 5\12 (500{{cent}}), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.
== Intervals ==
{{MOS intervals}}


== Scale tree ==
== Scale tree ==
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6/1: [[Grackle]], ↓ [[gracecordial]];  
6/1: [[Grackle]], ↓ [[gracecordial]];  
}}
}}
{{todo|expand}}

Revision as of 07:06, 15 December 2024

↖ 11L 16s ↑ 12L 16s 13L 16s ↗
← 11L 17s 12L 17s 13L 17s →
↙ 11L 18s ↓ 12L 18s 13L 18s ↘
Scale structure
Step pattern LsLsLssLsLssLsLsLssLsLssLsLss
ssLsLssLsLssLsLsLssLsLssLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 12\29 to 5\12 (496.6 ¢ to 500.0 ¢)
Dark 7\12 to 17\29 (700.0 ¢ to 703.4 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 2:1 to 5:2 (minihard)
Related MOS scales
Parent 12L 5s
Sister 17L 12s
Daughters 29L 12s, 12L 29s
Neutralized 24L 5s
2-Flought 41L 17s, 12L 46s
Equal tunings
Equalized (L:s = 1:1) 12\29 (496.6 ¢)
Supersoft (L:s = 4:3) 41\99 (497.0 ¢)
Soft (L:s = 3:2) 29\70 (497.1 ¢)
Semisoft (L:s = 5:3) 46\111 (497.3 ¢)
Basic (L:s = 2:1) 17\41 (497.6 ¢)
Semihard (L:s = 5:2) 39\94 (497.9 ¢)
Hard (L:s = 3:1) 22\53 (498.1 ¢)
Superhard (L:s = 4:1) 27\65 (498.5 ¢)
Collapsed (L:s = 1:0) 5\12 (500.0 ¢)
View • Talk • Edit

12L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 17 small steps, repeating every octave. 12L 17s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 496.6 ¢ to 500 ¢, or from 700 ¢ to 703.4 ¢. Its chroma-positive generator is a near-perfect fourth of no more than 5\12 (500 ¢), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.

Intervals

Intervals of 12L 17s
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 100.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 82.8 ¢
Major 2-mosstep M2ms L + s 82.8 ¢ to 100.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 100.0 ¢ to 124.1 ¢
Major 3-mosstep M3ms 2L + s 124.1 ¢ to 200.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 100.0 ¢ to 165.5 ¢
Major 4-mosstep M4ms 2L + 2s 165.5 ¢ to 200.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 200.0 ¢ to 206.9 ¢
Major 5-mosstep M5ms 3L + 2s 206.9 ¢ to 300.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 200.0 ¢ to 248.3 ¢
Major 6-mosstep M6ms 3L + 3s 248.3 ¢ to 300.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 200.0 ¢ to 289.7 ¢
Major 7-mosstep M7ms 3L + 4s 289.7 ¢ to 300.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 300.0 ¢ to 331.0 ¢
Major 8-mosstep M8ms 4L + 4s 331.0 ¢ to 400.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 300.0 ¢ to 372.4 ¢
Major 9-mosstep M9ms 4L + 5s 372.4 ¢ to 400.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 400.0 ¢ to 413.8 ¢
Major 10-mosstep M10ms 5L + 5s 413.8 ¢ to 500.0 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 400.0 ¢ to 455.2 ¢
Major 11-mosstep M11ms 5L + 6s 455.2 ¢ to 500.0 ¢
12-mosstep Diminished 12-mosstep d12ms 4L + 8s 400.0 ¢ to 496.6 ¢
Perfect 12-mosstep P12ms 5L + 7s 496.6 ¢ to 500.0 ¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 500.0 ¢ to 537.9 ¢
Major 13-mosstep M13ms 6L + 7s 537.9 ¢ to 600.0 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 500.0 ¢ to 579.3 ¢
Major 14-mosstep M14ms 6L + 8s 579.3 ¢ to 600.0 ¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 600.0 ¢ to 620.7 ¢
Major 15-mosstep M15ms 7L + 8s 620.7 ¢ to 700.0 ¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 600.0 ¢ to 662.1 ¢
Major 16-mosstep M16ms 7L + 9s 662.1 ¢ to 700.0 ¢
17-mosstep Perfect 17-mosstep P17ms 7L + 10s 700.0 ¢ to 703.4 ¢
Augmented 17-mosstep A17ms 8L + 9s 703.4 ¢ to 800.0 ¢
18-mosstep Minor 18-mosstep m18ms 7L + 11s 700.0 ¢ to 744.8 ¢
Major 18-mosstep M18ms 8L + 10s 744.8 ¢ to 800.0 ¢
19-mosstep Minor 19-mosstep m19ms 7L + 12s 700.0 ¢ to 786.2 ¢
Major 19-mosstep M19ms 8L + 11s 786.2 ¢ to 800.0 ¢
20-mosstep Minor 20-mosstep m20ms 8L + 12s 800.0 ¢ to 827.6 ¢
Major 20-mosstep M20ms 9L + 11s 827.6 ¢ to 900.0 ¢
21-mosstep Minor 21-mosstep m21ms 8L + 13s 800.0 ¢ to 869.0 ¢
Major 21-mosstep M21ms 9L + 12s 869.0 ¢ to 900.0 ¢
22-mosstep Minor 22-mosstep m22ms 9L + 13s 900.0 ¢ to 910.3 ¢
Major 22-mosstep M22ms 10L + 12s 910.3 ¢ to 1000.0 ¢
23-mosstep Minor 23-mosstep m23ms 9L + 14s 900.0 ¢ to 951.7 ¢
Major 23-mosstep M23ms 10L + 13s 951.7 ¢ to 1000.0 ¢
24-mosstep Minor 24-mosstep m24ms 9L + 15s 900.0 ¢ to 993.1 ¢
Major 24-mosstep M24ms 10L + 14s 993.1 ¢ to 1000.0 ¢
25-mosstep Minor 25-mosstep m25ms 10L + 15s 1000.0 ¢ to 1034.5 ¢
Major 25-mosstep M25ms 11L + 14s 1034.5 ¢ to 1100.0 ¢
26-mosstep Minor 26-mosstep m26ms 10L + 16s 1000.0 ¢ to 1075.9 ¢
Major 26-mosstep M26ms 11L + 15s 1075.9 ¢ to 1100.0 ¢
27-mosstep Minor 27-mosstep m27ms 11L + 16s 1100.0 ¢ to 1117.2 ¢
Major 27-mosstep M27ms 12L + 15s 1117.2 ¢ to 1200.0 ¢
28-mosstep Minor 28-mosstep m28ms 11L + 17s 1100.0 ¢ to 1158.6 ¢
Major 28-mosstep M28ms 12L + 16s 1158.6 ¢ to 1200.0 ¢
29-mosstep Perfect 29-mosstep P29ms 12L + 17s 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 12L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
12\29 496.552 703.448 1:1 1.000 Equalized 12L 17s
65\157 496.815 703.185 6:5 1.200
53\128 496.875 703.125 5:4 1.250
94\227 496.916 703.084 9:7 1.286
41\99 496.970 703.030 4:3 1.333 Supersoft 12L 17s
111\268 497.015 702.985 11:8 1.375
70\169 497.041 702.959 7:5 1.400
99\239 497.071 702.929 10:7 1.429
29\70 497.143 702.857 3:2 1.500 Soft 12L 17s
104\251 497.211 702.789 11:7 1.571
75\181 497.238 702.762 8:5 1.600
121\292 497.260 702.740 13:8 1.625
46\111 497.297 702.703 5:3 1.667 Semisoft 12L 17s
109\263 497.338 702.662 12:7 1.714
63\152 497.368 702.632 7:4 1.750
80\193 497.409 702.591 9:5 1.800
17\41 497.561 702.439 2:1 2.000 Basic 12L 17s
Scales with tunings softer than this are proper
73\176 497.727 702.273 9:4 2.250
56\135 497.778 702.222 7:3 2.333
95\229 497.817 702.183 12:5 2.400
39\94 497.872 702.128 5:2 2.500 Semihard 12L 17s
100\241 497.925 702.075 13:5 2.600
61\147 497.959 702.041 8:3 2.667
83\200 498.000 702.000 11:4 2.750
22\53 498.113 701.887 3:1 3.000 Hard 12L 17s
71\171 498.246 701.754 10:3 3.333
49\118 498.305 701.695 7:2 3.500
76\183 498.361 701.639 11:3 3.667
27\65 498.462 701.538 4:1 4.000 Superhard 12L 17s
59\142 498.592 701.408 9:2 4.500
32\77 498.701 701.299 5:1 5.000
37\89 498.876 701.124 6:1 6.000
5\12 500.000 700.000 1:0 → ∞ Collapsed 12L 17s
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