12L 5s

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↖ 11L 4s↑ 12L 4s 13L 4s ↗
← 11L 5s12L 5s13L 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)
Ancestor's 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, also called p-enharmonic, 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).

Intervals

Intervals of 12L 5s
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 70.6¢
Major 1-mosstep M1ms L 70.6¢ to 100.0¢
2-mosstep Minor 2-mosstep m2ms L + s 100.0¢ to 141.2¢
Major 2-mosstep M2ms 2L 141.2¢ to 200.0¢
3-mosstep Minor 3-mosstep m3ms 2L + s 200.0¢ to 211.8¢
Major 3-mosstep M3ms 3L 211.8¢ to 300.0¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 200.0¢ to 282.4¢
Major 4-mosstep M4ms 3L + s 282.4¢ to 300.0¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 300.0¢ to 352.9¢
Major 5-mosstep M5ms 4L + s 352.9¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 400.0¢ to 423.5¢
Major 6-mosstep M6ms 5L + s 423.5¢ to 500.0¢
7-mosstep Diminished 7-mosstep d7ms 4L + 3s 400.0¢ to 494.1¢
Perfect 7-mosstep P7ms 5L + 2s 494.1¢ to 500.0¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 500.0¢ to 564.7¢
Major 8-mosstep M8ms 6L + 2s 564.7¢ to 600.0¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 600.0¢ to 635.3¢
Major 9-mosstep M9ms 7L + 2s 635.3¢ to 700.0¢
10-mosstep Perfect 10-mosstep P10ms 7L + 3s 700.0¢ to 705.9¢
Augmented 10-mosstep A10ms 8L + 2s 705.9¢ to 800.0¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 700.0¢ to 776.5¢
Major 11-mosstep M11ms 8L + 3s 776.5¢ to 800.0¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 800.0¢ to 847.1¢
Major 12-mosstep M12ms 9L + 3s 847.1¢ to 900.0¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 900.0¢ to 917.6¢
Major 13-mosstep M13ms 10L + 3s 917.6¢ to 1000.0¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 900.0¢ to 988.2¢
Major 14-mosstep M14ms 10L + 4s 988.2¢ to 1000.0¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 1000.0¢ to 1058.8¢
Major 15-mosstep M15ms 11L + 4s 1058.8¢ to 1100.0¢
16-mosstep Minor 16-mosstep m16ms 11L + 5s 1100.0¢ to 1129.4¢
Major 16-mosstep M16ms 12L + 4s 1129.4¢ to 1200.0¢
17-mosstep Perfect 17-mosstep P17ms 12L + 5s 1200.0¢

Modes

Scale degrees of the modes of 12L 5s 
UDP Cyclic
Order
Step
Pattern
Scale Degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
16|0 1 LLLsLLsLLLsLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|1 8 LLLsLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|2 15 LLsLLLsLLsLLLsLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|3 5 LLsLLLsLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
12|4 12 LLsLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
11|5 2 LLsLLsLLLsLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
10|6 9 LLsLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
9|7 16 LsLLLsLLsLLLsLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
8|8 6 LsLLLsLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
7|9 13 LsLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
6|10 3 LsLLsLLLsLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
5|11 10 LsLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
4|12 17 sLLLsLLsLLLsLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
3|13 7 sLLLsLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
2|14 14 sLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
1|15 4 sLLsLLLsLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|16 11 sLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Proposed Names

Declan Paul Boushy has proposed names for these modes (See Subaru scale and Tanegashima scale).

Scales

Scale tree

Scale Tree and Tuning Spectrum of 12L 5s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
7\17 494.118 705.882 1:1 1.000 Equalized 12L 5s
40\97 494.845 705.155 6:5 1.200
33\80 495.000 705.000 5:4 1.250
59\143 495.105 704.895 9:7 1.286
26\63 495.238 704.762 4:3 1.333 Supersoft 12L 5s
Leapfrog
71\172 495.349 704.651 11:8 1.375
45\109 495.413 704.587 7:5 1.400 Leapweek
64\155 495.484 704.516 10:7 1.429
19\46 495.652 704.348 3:2 1.500 Soft 12L 5s
69\167 495.808 704.192 11:7 1.571 Leapday / polypyth
50\121 495.868 704.132 8:5 1.600
81\196 495.918 704.082 13:8 1.625 Golden neogothic (495.9044¢)
31\75 496.000 704.000 5:3 1.667 Semisoft 12L 5s
74\179 496.089 703.911 12:7 1.714
43\104 496.154 703.846 7:4 1.750
55\133 496.241 703.759 9:5 1.800
12\29 496.552 703.448 2:1 2.000 Basic 12L 5s
Scales with tunings softer than this are proper
53\128 496.875 703.125 9:4 2.250
41\99 496.970 703.030 7:3 2.333 Undecental
70\169 497.041 702.959 12:5 2.400 Argent tuning (497.0563¢)
29\70 497.143 702.857 5:2 2.500 Semihard 12L 5s
75\181 497.238 702.762 13:5 2.600
46\111 497.297 702.703 8:3 2.667
63\152 497.368 702.632 11:4 2.750
17\41 497.561 702.439 3:1 3.000 Hard 12L 5s
Garibaldi / andromeda
56\135 497.778 702.222 10:3 3.333
39\94 497.872 702.128 7:2 3.500 Garibaldi / cassandra
61\147 497.959 702.041 11:3 3.667
22\53 498.113 701.887 4:1 4.000 Superhard 12L 5s
Garibaldi / helenus, Pythagorean tuning (498.0450¢)
49\118 498.305 701.695 9:2 4.500 Pontiac
27\65 498.462 701.538 5:1 5.000 Photia
32\77 498.701 701.299 6:1 6.000 Grackle
5\12 500.000 700.000 1:0 → ∞ Collapsed 12L 5s