12L 17s
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Scale structure
Step pattern
LsLsLssLsLssLsLsLssLsLssLsLss
ssLsLssLsLssLsLsLssLsLssLsLsL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
12\29 to 5\12 (496.6¢ to 500.0¢)
Dark
7\12 to 17\29 (700.0¢ to 703.4¢)
TAMNAMS information
Descends from
5L 2s (diatonic)
Ancestor's step ratio range
2:1 to 5:2 (minihard)
Related MOS scales
Parent
12L 5s
Sister
17L 12s
Daughters
29L 12s, 12L 29s
Neutralized
24L 5s
2-Flought
41L 17s, 12L 46s
Equal tunings
Equalized (L:s = 1:1)
12\29 (496.6¢)
Supersoft (L:s = 4:3)
41\99 (497.0¢)
Soft (L:s = 3:2)
29\70 (497.1¢)
Semisoft (L:s = 5:3)
46\111 (497.3¢)
Basic (L:s = 2:1)
17\41 (497.6¢)
Semihard (L:s = 5:2)
39\94 (497.9¢)
Hard (L:s = 3:1)
22\53 (498.1¢)
Superhard (L:s = 4:1)
27\65 (498.5¢)
Collapsed (L:s = 1:0)
5\12 (500.0¢)
| ↖ 11L 16s | ↑ 12L 16s | 13L 16s ↗ |
| ← 11L 17s | 12L 17s | 13L 17s → |
| ↙ 11L 18s | ↓ 12L 18s | 13L 18s ↘ |
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║││║│║│║││║│║││║│║│││ │││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLssLsLssLsLsLssLsLssLsLsL
12L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 17 small steps, repeating every octave. 12L 17s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 496.6¢ to 500¢, or from 700¢ to 703.4¢. Its chroma-positive generator is a near-perfect fourth of no more than 5\12 (500 ¢), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.
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 100.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 82.8¢ |
| Major 2-mosstep | M2ms | L + s | 82.8¢ to 100.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 100.0¢ to 124.1¢ |
| Major 3-mosstep | M3ms | 2L + s | 124.1¢ to 200.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 100.0¢ to 165.5¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 165.5¢ to 200.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 200.0¢ to 206.9¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 206.9¢ to 300.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 200.0¢ to 248.3¢ |
| Major 6-mosstep | M6ms | 3L + 3s | 248.3¢ to 300.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 200.0¢ to 289.7¢ |
| Major 7-mosstep | M7ms | 3L + 4s | 289.7¢ to 300.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 3L + 5s | 300.0¢ to 331.0¢ |
| Major 8-mosstep | M8ms | 4L + 4s | 331.0¢ to 400.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 3L + 6s | 300.0¢ to 372.4¢ |
| Major 9-mosstep | M9ms | 4L + 5s | 372.4¢ to 400.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 4L + 6s | 400.0¢ to 413.8¢ |
| Major 10-mosstep | M10ms | 5L + 5s | 413.8¢ to 500.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 4L + 7s | 400.0¢ to 455.2¢ |
| Major 11-mosstep | M11ms | 5L + 6s | 455.2¢ to 500.0¢ | |
| 12-mosstep | Diminished 12-mosstep | d12ms | 4L + 8s | 400.0¢ to 496.6¢ |
| Perfect 12-mosstep | P12ms | 5L + 7s | 496.6¢ to 500.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 5L + 8s | 500.0¢ to 537.9¢ |
| Major 13-mosstep | M13ms | 6L + 7s | 537.9¢ to 600.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 5L + 9s | 500.0¢ to 579.3¢ |
| Major 14-mosstep | M14ms | 6L + 8s | 579.3¢ to 600.0¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 6L + 9s | 600.0¢ to 620.7¢ |
| Major 15-mosstep | M15ms | 7L + 8s | 620.7¢ to 700.0¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 6L + 10s | 600.0¢ to 662.1¢ |
| Major 16-mosstep | M16ms | 7L + 9s | 662.1¢ to 700.0¢ | |
| 17-mosstep | Perfect 17-mosstep | P17ms | 7L + 10s | 700.0¢ to 703.4¢ |
| Augmented 17-mosstep | A17ms | 8L + 9s | 703.4¢ to 800.0¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 7L + 11s | 700.0¢ to 744.8¢ |
| Major 18-mosstep | M18ms | 8L + 10s | 744.8¢ to 800.0¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 7L + 12s | 700.0¢ to 786.2¢ |
| Major 19-mosstep | M19ms | 8L + 11s | 786.2¢ to 800.0¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 8L + 12s | 800.0¢ to 827.6¢ |
| Major 20-mosstep | M20ms | 9L + 11s | 827.6¢ to 900.0¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 8L + 13s | 800.0¢ to 869.0¢ |
| Major 21-mosstep | M21ms | 9L + 12s | 869.0¢ to 900.0¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 9L + 13s | 900.0¢ to 910.3¢ |
| Major 22-mosstep | M22ms | 10L + 12s | 910.3¢ to 1000.0¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 9L + 14s | 900.0¢ to 951.7¢ |
| Major 23-mosstep | M23ms | 10L + 13s | 951.7¢ to 1000.0¢ | |
| 24-mosstep | Minor 24-mosstep | m24ms | 9L + 15s | 900.0¢ to 993.1¢ |
| Major 24-mosstep | M24ms | 10L + 14s | 993.1¢ to 1000.0¢ | |
| 25-mosstep | Minor 25-mosstep | m25ms | 10L + 15s | 1000.0¢ to 1034.5¢ |
| Major 25-mosstep | M25ms | 11L + 14s | 1034.5¢ to 1100.0¢ | |
| 26-mosstep | Minor 26-mosstep | m26ms | 10L + 16s | 1000.0¢ to 1075.9¢ |
| Major 26-mosstep | M26ms | 11L + 15s | 1075.9¢ to 1100.0¢ | |
| 27-mosstep | Minor 27-mosstep | m27ms | 11L + 16s | 1100.0¢ to 1117.2¢ |
| Major 27-mosstep | M27ms | 12L + 15s | 1117.2¢ to 1200.0¢ | |
| 28-mosstep | Minor 28-mosstep | m28ms | 11L + 17s | 1100.0¢ to 1158.6¢ |
| Major 28-mosstep | M28ms | 12L + 16s | 1158.6¢ to 1200.0¢ | |
| 29-mosstep | Perfect 29-mosstep | P29ms | 12L + 17s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 12\29 | 496.552 | 703.448 | 1:1 | 1.000 | Equalized 12L 17s | |||||
| 65\157 | 496.815 | 703.185 | 6:5 | 1.200 | ||||||
| 53\128 | 496.875 | 703.125 | 5:4 | 1.250 | ||||||
| 94\227 | 496.916 | 703.084 | 9:7 | 1.286 | ||||||
| 41\99 | 496.970 | 703.030 | 4:3 | 1.333 | Supersoft 12L 17s Undecental | |||||
| 111\268 | 497.015 | 702.985 | 11:8 | 1.375 | ||||||
| 70\169 | 497.041 | 702.959 | 7:5 | 1.400 | ||||||
| 99\239 | 497.071 | 702.929 | 10:7 | 1.429 | Argent tuning (497.056¢) | |||||
| 29\70 | 497.143 | 702.857 | 3:2 | 1.500 | Soft 12L 17s | |||||
| 104\251 | 497.211 | 702.789 | 11:7 | 1.571 | ||||||
| 75\181 | 497.238 | 702.762 | 8:5 | 1.600 | ||||||
| 121\292 | 497.260 | 702.740 | 13:8 | 1.625 | Unnamed golden tuning (497.254¢) | |||||
| 46\111 | 497.297 | 702.703 | 5:3 | 1.667 | Semisoft 12L 17s | |||||
| 109\263 | 497.338 | 702.662 | 12:7 | 1.714 | ||||||
| 63\152 | 497.368 | 702.632 | 7:4 | 1.750 | Kwai | |||||
| 80\193 | 497.409 | 702.591 | 9:5 | 1.800 | ||||||
| 17\41 | 497.561 | 702.439 | 2:1 | 2.000 | Basic 12L 17s Scales with tunings softer than this are proper | |||||
| 73\176 | 497.727 | 702.273 | 9:4 | 2.250 | Cotoneum | |||||
| 56\135 | 497.778 | 702.222 | 7:3 | 2.333 | ||||||
| 95\229 | 497.817 | 702.183 | 12:5 | 2.400 | ||||||
| 39\94 | 497.872 | 702.128 | 5:2 | 2.500 | Semihard 12L 17s Garibaldi / cassandra | |||||
| 100\241 | 497.925 | 702.075 | 13:5 | 2.600 | ||||||
| 61\147 | 497.959 | 702.041 | 8:3 | 2.667 | ||||||
| 83\200 | 498.000 | 702.000 | 11:4 | 2.750 | Pythagorean tuning (498.045¢) | |||||
| 22\53 | 498.113 | 701.887 | 3:1 | 3.000 | Hard 12L 17s Garibaldi / helenus | |||||
| 71\171 | 498.246 | 701.754 | 10:3 | 3.333 | Pontiac | |||||
| 49\118 | 498.305 | 701.695 | 7:2 | 3.500 | ||||||
| 76\183 | 498.361 | 701.639 | 11:3 | 3.667 | ||||||
| 27\65 | 498.462 | 701.538 | 4:1 | 4.000 | Superhard 12L 17s | |||||
| 59\142 | 498.592 | 701.408 | 9:2 | 4.500 | ||||||
| 32\77 | 498.701 | 701.299 | 5:1 | 5.000 | ||||||
| 37\89 | 498.876 | 701.124 | 6:1 | 6.000 | Grackle, ↓ gracecordial | |||||
| 5\12 | 500.000 | 700.000 | 1:0 | → ∞ | Collapsed 12L 17s | |||||