12L 5s
| ↖ 11L 4s | ↑ 12L 4s | 13L 4s ↗ |
| ← 11L 5s | 12L 5s | 13L 5s → |
| ↙ 11L 6s | ↓ 12L 6s | 13L 6s ↘ |
┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║║│║║│║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLsLLLsLLsLLL
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).
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
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MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees |
Proposed tuning-specific names
Declan Paul Boushy has proposed names for these modes corresponding to step ratios 3:1 and 4:1.
Scales
- Edson17 – 29edo tuning
- Subaru scale – 41edo tuning
- Cotoneum17 – 217edo tuning
- Garibaldi17 – 94edo tuning
- Pythagorean17 – Pythagorean tuning
- Tanegashima scale – 53edo tuning
- Nestoria17 – 171edo tuning
Scale tree
| 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 Leapday | |||||
| 69\167 | 495.808 | 704.192 | 11:7 | 1.571 | Polypyth | |||||
| 50\121 | 495.868 | 704.132 | 8:5 | 1.600 | ||||||
| 81\196 | 495.918 | 704.082 | 13:8 | 1.625 | Golden neogothic (495.904 ¢) | |||||
| 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 (497.056 ¢) | |||||
| 29\70 | 497.143 | 702.857 | 5:2 | 2.500 | Semihard 12L 5s | |||||
| 75\181 | 497.238 | 702.762 | 13:5 | 2.600 | Unnamed golden tuning (497.254 ¢) | |||||
| 46\111 | 497.297 | 702.703 | 8:3 | 2.667 | ||||||
| 63\152 | 497.368 | 702.632 | 11:4 | 2.750 | Kwai | |||||
| 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 (498.045 ¢) | |||||
| 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, ↓↓ gracecordial | |||||
| 5\12 | 500.000 | 700.000 | 1:0 | → ∞ | Collapsed 12L 5s | |||||