12L 5s
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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¢)
| ↖ 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).
Intervals
| 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
| 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
- 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 | |||||
| 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 | |||||