12L 17s: Difference between revisions

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== Scale tree ==
== Scale tree ==
{{Scale tree}}
{{Scale tree|Comments=
4/3: [[Undecental]];
10/7: Argent tuning (497.056¢);
13/8: Unnamed golden tuning (497.254¢);
7/4: [[Kwai]];
9/4: [[Cotoneum]];
5/2: [[Garibaldi]] / [[cassandra]];
11/4: [[Pythagorean tuning]] (498.045¢);
3/1: Garibaldi / [[helenus]];
10/3: [[Pontiac]];
6/1: [[Grackle]], ↓ [[gracecordial]];
}}

Revision as of 14:16, 2 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 ¢)

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.

Scale tree

Template:Scale tree