12L 17s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 11L 16s ↑12L 16s 13L 16s ↗
← 11L 17s12L 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
Descends from 5L 2s (diatonic)
Required step ratio range 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

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