12L 5s

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Todo: review
Adopt scale tree template, add note that mode names are tuning-specific (they only apply to specific tunings)
↖ 11L 4s ↑12L 4s 13L 4s ↗
← 11L 5s12L 5s 13L 5s →
↙ 11L 6s ↓12L 6s 13L 6s ↘
┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║║│║║│║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLLsLLsLLs
sLLsLLsLLLsLLsLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 7\17 to 5\12 (494.1¢ to 500.0¢)
Dark 7\12 to 10\17 (700.0¢ to 705.9¢)
TAMNAMS information
Descends from 5L 2s (diatonic)
Required step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 5L 7s
Sister 5L 12s
Daughters 17L 12s, 12L 17s
Neutralized 7L 10s
2-Flought 29L 5s, 12L 22s
Equal tunings
Equalized (L:s = 1:1) 7\17 (494.1¢)
Supersoft (L:s = 4:3) 26\63 (495.2¢)
Soft (L:s = 3:2) 19\46 (495.7¢)
Semisoft (L:s = 5:3) 31\75 (496.0¢)
Basic (L:s = 2:1) 12\29 (496.6¢)
Semihard (L:s = 5:2) 29\70 (497.1¢)
Hard (L:s = 3:1) 17\41 (497.6¢)
Superhard (L:s = 4:1) 22\53 (498.1¢)
Collapsed (L:s = 1:0) 5\12 (500.0¢)

12L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 5 small steps, repeating every octave. 12L 5s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 494.1¢ to 500¢, or from 700¢ to 705.9¢. Temperaments supported by this scale include those under the Pythagorean and schismic families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the chroma.

The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).

Modes

Mode names are borrowed from the Subaru scale, proposed by Declan Paul Boushy.

Mode UDP Mode name
LLLsLLsLLLsLLsLLs 16|0 Harumi
LLLsLLsLLsLLLsLLs 15|1 Yuzuha
LLsLLLsLLsLLLsLLs 14|2 Maho
LLsLLLsLLsLLsLLLs 13|3 Sakura
LLsLLsLLLsLLsLLLs 12|4 Hanako
LLsLLsLLLsLLsLLsL 11|5 Saori
LLsLLsLLsLLLsLLsL 10|6 Machiko
LsLLLsLLsLLLsLLsL 9|7 Sae
LsLLLsLLsLLsLLLsL 8|8 Kaguya
LsLLsLLLsLLsLLLsL 7|9 Nae
LsLLsLLLsLLsLLsLL 6|10 Sachiko
LsLLsLLsLLLsLLsLL 5|11 Kaori
sLLLsLLsLLLsLLsLL 4|12 Kanako
sLLLsLLsLLsLLLsLL 3|13 Sakurajima
sLLsLLLsLLsLLLsLL 2|14 Kaho
sLLsLLLsLLsLLsLLL 1|15 Suzuha
sLLsLLsLLLsLLsLLL 0|16 Narumi

Scales

Scale tree

Generator ranges:

  • Bright generator: 494.1176 cents (7\17) to 500 cents (5\12)
  • Dark generator: 700 cents (7\12) to 705.8824 cents (10\17)
Bright generator Cents L s L/s Comments
7\17 494.118 1 1 1.000
40\97 494.845 6 5 1.200
33\80 495.000 5 4 1.250
59\143 495.105 9 7 1.286
26\63 495.238 4 3 1.333 Leapfrog
71\172 495.349 11 8 1.375
45\109 495.413 7 5 1.400 Leapweek
64\155 495.484 10 7 1.428
19\46 495.652 3 2 1.500
69\167 495.808 11 7 1.571 Leapday / polypyth
50\121 495.868 8 5 1.600
81\196 495.918 13 8 1.625 Golden neogothic (495.9044¢)
31\75 496.000 5 3 1.667
74\179 496.089 12 7 1.714
43\104 496.154 7 4 1.750
55\133 496.241 9 5 1.800
12\29 496.552 2 1 2.000 Basic 12L 5s
(Generators smaller than this are proper)
53\128 496.875 9 4 2.250
41\99 496.970 7 3 2.333 Undecental
70\169 497.041 12 5 2.400 Argent tuning (497.0563¢)
29\70 497.143 5 2 2.500
75\181 497.238 13 5 2.600 Unnamed golden tuning (497.2540¢)
46\111 497.297 8 3 2.667
63\152 497.368 11 4 2.750 Kwai
17\41 497.561 3 1 3.000 Garibaldi / andromeda
56\135 497.778 10 3 3.333
39\94 497.872 7 2 3.500 Garibaldi / cassandra
61\147 497.959 11 3 3.667
22\53 498.113 4 1 4.000 Garibaldi / helenus, Pythagorean tuning (498.0450¢)
49\118 498.305 9 2 4.500 Pontiac
27\65 498.462 5 1 5.000 Photia
32\77 498.701 6 1 6.000 Grackle
5\12 500.000 1 0 → inf