17L 12s
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Scale structure
Step pattern
LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLsLLsLsLLsLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
17\29 to 10\17 (703.4¢ to 705.9¢)
Dark
7\17 to 12\29 (494.1¢ to 496.6¢)
TAMNAMS information
Descends from
5L 2s (diatonic)
Ancestor's step ratio range
5:2 to 3:1 (quasihard)
Related MOS scales
Parent
12L 5s
Sister
12L 17s
Daughters
29L 17s, 17L 29s
Neutralized
5L 24s
2-Flought
46L 12s, 17L 41s
Equal tunings
Equalized (L:s = 1:1)
17\29 (703.4¢)
Supersoft (L:s = 4:3)
61\104 (703.8¢)
Soft (L:s = 3:2)
44\75 (704.0¢)
Semisoft (L:s = 5:3)
71\121 (704.1¢)
Basic (L:s = 2:1)
27\46 (704.3¢)
Semihard (L:s = 5:2)
64\109 (704.6¢)
Hard (L:s = 3:1)
37\63 (704.8¢)
Superhard (L:s = 4:1)
47\80 (705.0¢)
Collapsed (L:s = 1:0)
10\17 (705.9¢)
 |
Todo: complete table populate scale tree with entries |
| ↖ 16L 11s | ↑ 17L 11s | 18L 11s ↗ |
| ← 16L 12s | 17L 12s | 18L 12s → |
| ↙ 16L 13s | ↓ 17L 13s | 18L 13s ↘ |
┌╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥┬┐ │║║│║│║║│║│║║│║│║│║║│║│║║│║│║││ │││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLsLLsLsLLsLsLsLLsLsLLsLsLL
17L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 12 small steps, repeating every octave. 17L 12s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 703.4¢ to 705.9¢, or from 494.1¢ to 496.6¢.
This mos, belonging to the leapday temperament, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of 17edo and 29edo and divides at 80edo into Margo Schulter's gentle region extending down to 29edo and a yet-unnamed region extending up to 17edo.
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 41.4¢ |
| Major 1-mosstep | M1ms | L | 41.4¢ to 70.6¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 70.6¢ to 82.8¢ |
| Major 2-mosstep | M2ms | 2L | 82.8¢ to 141.2¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 70.6¢ to 124.1¢ |
| Major 3-mosstep | M3ms | 2L + s | 124.1¢ to 141.2¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 141.2¢ to 165.5¢ |
| Major 4-mosstep | M4ms | 3L + s | 165.5¢ to 211.8¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 141.2¢ to 206.9¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 206.9¢ to 211.8¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 211.8¢ to 248.3¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 248.3¢ to 282.4¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 282.4¢ to 289.7¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 289.7¢ to 352.9¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 4L + 4s | 282.4¢ to 331.0¢ |
| Major 8-mosstep | M8ms | 5L + 3s | 331.0¢ to 352.9¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 352.9¢ to 372.4¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 372.4¢ to 423.5¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 5L + 5s | 352.9¢ to 413.8¢ |
| Major 10-mosstep | M10ms | 6L + 4s | 413.8¢ to 423.5¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 6L + 5s | 423.5¢ to 455.2¢ |
| Major 11-mosstep | M11ms | 7L + 4s | 455.2¢ to 494.1¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 7L + 5s | 494.1¢ to 496.6¢ |
| Augmented 12-mosstep | A12ms | 8L + 4s | 496.6¢ to 564.7¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 7L + 6s | 494.1¢ to 537.9¢ |
| Major 13-mosstep | M13ms | 8L + 5s | 537.9¢ to 564.7¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 8L + 6s | 564.7¢ to 579.3¢ |
| Major 14-mosstep | M14ms | 9L + 5s | 579.3¢ to 635.3¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 8L + 7s | 564.7¢ to 620.7¢ |
| Major 15-mosstep | M15ms | 9L + 6s | 620.7¢ to 635.3¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 9L + 7s | 635.3¢ to 662.1¢ |
| Major 16-mosstep | M16ms | 10L + 6s | 662.1¢ to 705.9¢ | |
| 17-mosstep | Diminished 17-mosstep | d17ms | 9L + 8s | 635.3¢ to 703.4¢ |
| Perfect 17-mosstep | P17ms | 10L + 7s | 703.4¢ to 705.9¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 10L + 8s | 705.9¢ to 744.8¢ |
| Major 18-mosstep | M18ms | 11L + 7s | 744.8¢ to 776.5¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 11L + 8s | 776.5¢ to 786.2¢ |
| Major 19-mosstep | M19ms | 12L + 7s | 786.2¢ to 847.1¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 11L + 9s | 776.5¢ to 827.6¢ |
| Major 20-mosstep | M20ms | 12L + 8s | 827.6¢ to 847.1¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 12L + 9s | 847.1¢ to 869.0¢ |
| Major 21-mosstep | M21ms | 13L + 8s | 869.0¢ to 917.6¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 12L + 10s | 847.1¢ to 910.3¢ |
| Major 22-mosstep | M22ms | 13L + 9s | 910.3¢ to 917.6¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 13L + 10s | 917.6¢ to 951.7¢ |
| Major 23-mosstep | M23ms | 14L + 9s | 951.7¢ to 988.2¢ | |
| 24-mosstep | Minor 24-mosstep | m24ms | 14L + 10s | 988.2¢ to 993.1¢ |
| Major 24-mosstep | M24ms | 15L + 9s | 993.1¢ to 1058.8¢ | |
| 25-mosstep | Minor 25-mosstep | m25ms | 14L + 11s | 988.2¢ to 1034.5¢ |
| Major 25-mosstep | M25ms | 15L + 10s | 1034.5¢ to 1058.8¢ | |
| 26-mosstep | Minor 26-mosstep | m26ms | 15L + 11s | 1058.8¢ to 1075.9¢ |
| Major 26-mosstep | M26ms | 16L + 10s | 1075.9¢ to 1129.4¢ | |
| 27-mosstep | Minor 27-mosstep | m27ms | 15L + 12s | 1058.8¢ to 1117.2¢ |
| Major 27-mosstep | M27ms | 16L + 11s | 1117.2¢ to 1129.4¢ | |
| 28-mosstep | Minor 28-mosstep | m28ms | 16L + 12s | 1129.4¢ to 1158.6¢ |
| Major 28-mosstep | M28ms | 17L + 11s | 1158.6¢ to 1200.0¢ | |
| 29-mosstep | Perfect 29-mosstep | P29ms | 17L + 12s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 17\29 | 703.448 | 496.552 | 1:1 | 1.000 | Equalized 17L 12s | |||||
| 95\162 | 703.704 | 496.296 | 6:5 | 1.200 | ||||||
| 78\133 | 703.759 | 496.241 | 5:4 | 1.250 | ||||||
| 139\237 | 703.797 | 496.203 | 9:7 | 1.286 | ||||||
| 61\104 | 703.846 | 496.154 | 4:3 | 1.333 | Supersoft 17L 12s | |||||
| 166\283 | 703.887 | 496.113 | 11:8 | 1.375 | ||||||
| 105\179 | 703.911 | 496.089 | 7:5 | 1.400 | ||||||
| 149\254 | 703.937 | 496.063 | 10:7 | 1.429 | ||||||
| 44\75 | 704.000 | 496.000 | 3:2 | 1.500 | Soft 17L 12s | |||||
| 159\271 | 704.059 | 495.941 | 11:7 | 1.571 | ||||||
| 115\196 | 704.082 | 495.918 | 8:5 | 1.600 | ||||||
| 186\317 | 704.101 | 495.899 | 13:8 | 1.625 | Golden neogothic (704.096¢) | |||||
| 71\121 | 704.132 | 495.868 | 5:3 | 1.667 | Semisoft 17L 12s | |||||
| 169\288 | 704.167 | 495.833 | 12:7 | 1.714 | ||||||
| 98\167 | 704.192 | 495.808 | 7:4 | 1.750 | Polypyth | |||||
| 125\213 | 704.225 | 495.775 | 9:5 | 1.800 | ||||||
| 27\46 | 704.348 | 495.652 | 2:1 | 2.000 | Basic 17L 12s Scales with tunings softer than this are proper | |||||
| 118\201 | 704.478 | 495.522 | 9:4 | 2.250 | ||||||
| 91\155 | 704.516 | 495.484 | 7:3 | 2.333 | ||||||
| 155\264 | 704.545 | 495.455 | 12:5 | 2.400 | ||||||
| 64\109 | 704.587 | 495.413 | 5:2 | 2.500 | Semihard 17L 12s Leapweek | |||||
| 165\281 | 704.626 | 495.374 | 13:5 | 2.600 | ||||||
| 101\172 | 704.651 | 495.349 | 8:3 | 2.667 | ||||||
| 138\235 | 704.681 | 495.319 | 11:4 | 2.750 | ||||||
| 37\63 | 704.762 | 495.238 | 3:1 | 3.000 | Hard 17L 12s Leapfrog | |||||
| 121\206 | 704.854 | 495.146 | 10:3 | 3.333 | ||||||
| 84\143 | 704.895 | 495.105 | 7:2 | 3.500 | ||||||
| 131\223 | 704.933 | 495.067 | 11:3 | 3.667 | ||||||
| 47\80 | 705.000 | 495.000 | 4:1 | 4.000 | Superhard 17L 12s | |||||
| 104\177 | 705.085 | 494.915 | 9:2 | 4.500 | ||||||
| 57\97 | 705.155 | 494.845 | 5:1 | 5.000 | ||||||
| 67\114 | 705.263 | 494.737 | 6:1 | 6.000 | ||||||
| 10\17 | 705.882 | 494.118 | 1:0 | → ∞ | Collapsed 17L 12s | |||||