3L 16s
| ↖ 2L 15s | ↑ 3L 15s | 4L 15s ↗ |
| ← 2L 16s | 3L 16s | 4L 16s → |
| ↙ 2L 17s | ↓ 3L 17s | 4L 17s ↘ |
Scale structure
ssssssLsssssLsssssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9 ¢ to 400 ¢, or from 800 ¢ to 821.1 ¢. This scale is associated with magic temperament, where 5 bright generators maps to 3/1 and the generator is a flat 5/4, and würschmidt temperament, where 8 bright generators map to 6/1 and the generator is a slightly sharp 5/4.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 18|0 | 1 | LsssssLsssssLssssss |
| 17|1 | 7 | LsssssLssssssLsssss |
| 16|2 | 13 | LssssssLsssssLsssss |
| 15|3 | 19 | sLsssssLsssssLsssss |
| 14|4 | 6 | sLsssssLssssssLssss |
| 13|5 | 12 | sLssssssLsssssLssss |
| 12|6 | 18 | ssLsssssLsssssLssss |
| 11|7 | 5 | ssLsssssLssssssLsss |
| 10|8 | 11 | ssLssssssLsssssLsss |
| 9|9 | 17 | sssLsssssLsssssLsss |
| 8|10 | 4 | sssLsssssLssssssLss |
| 7|11 | 10 | sssLssssssLsssssLss |
| 6|12 | 16 | ssssLsssssLsssssLss |
| 5|13 | 3 | ssssLsssssLssssssLs |
| 4|14 | 9 | ssssLssssssLsssssLs |
| 3|15 | 15 | sssssLsssssLsssssLs |
| 2|16 | 2 | sssssLsssssLssssssL |
| 1|17 | 8 | sssssLssssssLsssssL |
| 0|18 | 14 | ssssssLsssssLsssssL |
Scale tree
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Todo: review
Review entries from past page revision and enter them into the scale tree. |
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Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}
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| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 6\19 | 378.947 | 821.053 | 1:1 | 1.000 | Equalized 3L 16s | |||||
| 31\98 | 379.592 | 820.408 | 6:5 | 1.200 | ||||||
| 25\79 | 379.747 | 820.253 | 5:4 | 1.250 | ||||||
| 44\139 | 379.856 | 820.144 | 9:7 | 1.286 | ||||||
| 19\60 | 380.000 | 820.000 | 4:3 | 1.333 | Supersoft 3L 16s | |||||
| 51\161 | 380.124 | 819.876 | 11:8 | 1.375 | ||||||
| 32\101 | 380.198 | 819.802 | 7:5 | 1.400 | ||||||
| 45\142 | 380.282 | 819.718 | 10:7 | 1.429 | ||||||
| 13\41 | 380.488 | 819.512 | 3:2 | 1.500 | Soft 3L 16s | |||||
| 46\145 | 380.690 | 819.310 | 11:7 | 1.571 | ||||||
| 33\104 | 380.769 | 819.231 | 8:5 | 1.600 | ||||||
| 53\167 | 380.838 | 819.162 | 13:8 | 1.625 | ||||||
| 20\63 | 380.952 | 819.048 | 5:3 | 1.667 | Semisoft 3L 16s | |||||
| 47\148 | 381.081 | 818.919 | 12:7 | 1.714 | ||||||
| 27\85 | 381.176 | 818.824 | 7:4 | 1.750 | ||||||
| 34\107 | 381.308 | 818.692 | 9:5 | 1.800 | ||||||
| 7\22 | 381.818 | 818.182 | 2:1 | 2.000 | Basic 3L 16s Scales with tunings softer than this are proper | |||||
| 29\91 | 382.418 | 817.582 | 9:4 | 2.250 | ||||||
| 22\69 | 382.609 | 817.391 | 7:3 | 2.333 | ||||||
| 37\116 | 382.759 | 817.241 | 12:5 | 2.400 | ||||||
| 15\47 | 382.979 | 817.021 | 5:2 | 2.500 | Semihard 3L 16s | |||||
| 38\119 | 383.193 | 816.807 | 13:5 | 2.600 | ||||||
| 23\72 | 383.333 | 816.667 | 8:3 | 2.667 | ||||||
| 31\97 | 383.505 | 816.495 | 11:4 | 2.750 | ||||||
| 8\25 | 384.000 | 816.000 | 3:1 | 3.000 | Hard 3L 16s | |||||
| 25\78 | 384.615 | 815.385 | 10:3 | 3.333 | ||||||
| 17\53 | 384.906 | 815.094 | 7:2 | 3.500 | ||||||
| 26\81 | 385.185 | 814.815 | 11:3 | 3.667 | ||||||
| 9\28 | 385.714 | 814.286 | 4:1 | 4.000 | Superhard 3L 16s | |||||
| 19\59 | 386.441 | 813.559 | 9:2 | 4.500 | ||||||
| 10\31 | 387.097 | 812.903 | 5:1 | 5.000 | ||||||
| 11\34 | 388.235 | 811.765 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 16s | |||||