12L 5s
| Pattern | LLLsLLsLLLsLLsLLs | |
| Period | 2/1 | |
| Generator range | 7\17 (494.1¢) to 5\12 (500.0¢) | |
| Parent MOS | 5L 7s | |
| Daughter MOSes | 17L 12s, 12L 17s | |
| Sister MOS | 5L 12s | |
| Equal tunings | ||
| 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¢) | |
12L 5s is the MOS pattern of the Pythagorean/schismic enharmonic or mega-chromatic scale. In contrast to the superpyth enharmonic scale, in which the enharmonic diesis (negative diminished second) is larger than the chromatic semitone, here the reverse is true: the enharmonic diesis is smaller than the chromatic semitone, so the diatonic scale subset is actually proper.
This MOS separates its small steps by intervals of 3L-2L-3L-2L-2L. Its major third of -4 generators approximates an interval between 24/19 and 32/25, thus its generator is a perfect fourth between 7\17 (494.118 cents) and 5\12 (500 cents).
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
- 16|0 LLLsLLsLLLsLLsLLs
- 15|1 LLLsLLsLLsLLLsLLs
- 14|2 LLsLLLsLLsLLLsLLs
- 13|3 LLsLLLsLLsLLsLLLs
- 12|4 LLsLLsLLLsLLsLLLs
- 11|5 LLsLLsLLLsLLsLLsL
- 10|6 LLsLLsLLsLLLsLLsL
- 9|7 LsLLLsLLsLLLsLLsL
- 8|8 LsLLLsLLsLLsLLLsL
- 7|9 LsLLsLLLsLLsLLLsL
- 6|10 LsLLsLLLsLLsLLsLL
- 5|11 LsLLsLLsLLLsLLsLL
- 4|12 sLLLsLLsLLLsLLsLL
- 3|13 sLLLsLLsLLsLLLsLL
- 2|14 sLLsLLLsLLsLLLsLL
- 1|15 sLLsLLLsLLsLLsLLL
- 0|16 sLLsLLsLLLsLLsLLL
Scales
- Pythagorean17 – Pythagorean tuning
- Nestoria17 – 171edo tuning
- Cotoneum17 – 217edo tuning
- Garibaldi17 – 94edo tuning
Scale tree
Generator ranges:
- Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)
- Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)
| 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 | ||||||