16L 1s

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← 15L 1s 16L 1s 17L 1s →
↙ 15L 2s ↓ 16L 2s 17L 2s ↘
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║║║║║║║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 1\17 to 1\16 (70.6¢ to 75.0¢)
Dark 15\16 to 16\17 (1125.0¢ to 1129.4¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 7:1 to 8:1
Related MOS scales
Parent 1L 15s
Sister 1L 16s
Daughters 17L 16s, 16L 17s
Neutralized 15L 2s
2-Flought 33L 1s, 16L 18s
Equal tunings
Equalized (L:s = 1:1) 1\17 (70.6¢)
Supersoft (L:s = 4:3) 4\67 (71.6¢)
Soft (L:s = 3:2) 3\50 (72.0¢)
Semisoft (L:s = 5:3) 5\83 (72.3¢)
Basic (L:s = 2:1) 2\33 (72.7¢)
Semihard (L:s = 5:2) 5\82 (73.2¢)
Hard (L:s = 3:1) 3\49 (73.5¢)
Superhard (L:s = 4:1) 4\65 (73.8¢)
Collapsed (L:s = 1:0) 1\16 (75.0¢)

16L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 1 small step, repeating every octave. 16L 1s is related to 1L 9s, expanding it by 7 tones. Generators that produce this scale range from 70.6¢ to 75¢, or from 1125¢ to 1129.4¢. Scales of this form are always proper because there is only one small step.

Modes

Modes of 16L 1s
UDP Cyclic
order
Step
pattern
16|0 1 LLLLLLLLLLLLLLLLs
15|1 2 LLLLLLLLLLLLLLLsL
14|2 3 LLLLLLLLLLLLLLsLL
13|3 4 LLLLLLLLLLLLLsLLL
12|4 5 LLLLLLLLLLLLsLLLL
11|5 6 LLLLLLLLLLLsLLLLL
10|6 7 LLLLLLLLLLsLLLLLL
9|7 8 LLLLLLLLLsLLLLLLL
8|8 9 LLLLLLLLsLLLLLLLL
7|9 10 LLLLLLLsLLLLLLLLL
6|10 11 LLLLLLsLLLLLLLLLL
5|11 12 LLLLLsLLLLLLLLLLL
4|12 13 LLLLsLLLLLLLLLLLL
3|13 14 LLLsLLLLLLLLLLLLL
2|14 15 LLsLLLLLLLLLLLLLL
1|15 16 LsLLLLLLLLLLLLLLL
0|16 17 sLLLLLLLLLLLLLLLL

Intervals

Intervals of 16L 1s
Intervals Steps
subtended
Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Diminished 1-mosstep d1ms s 0.0¢ to 70.6¢
Perfect 1-mosstep P1ms L 70.6¢ to 75.0¢
2-mosstep Minor 2-mosstep m2ms L + s 75.0¢ to 141.2¢
Major 2-mosstep M2ms 2L 141.2¢ to 150.0¢
3-mosstep Minor 3-mosstep m3ms 2L + s 150.0¢ to 211.8¢
Major 3-mosstep M3ms 3L 211.8¢ to 225.0¢
4-mosstep Minor 4-mosstep m4ms 3L + s 225.0¢ to 282.4¢
Major 4-mosstep M4ms 4L 282.4¢ to 300.0¢
5-mosstep Minor 5-mosstep m5ms 4L + s 300.0¢ to 352.9¢
Major 5-mosstep M5ms 5L 352.9¢ to 375.0¢
6-mosstep Minor 6-mosstep m6ms 5L + s 375.0¢ to 423.5¢
Major 6-mosstep M6ms 6L 423.5¢ to 450.0¢
7-mosstep Minor 7-mosstep m7ms 6L + s 450.0¢ to 494.1¢
Major 7-mosstep M7ms 7L 494.1¢ to 525.0¢
8-mosstep Minor 8-mosstep m8ms 7L + s 525.0¢ to 564.7¢
Major 8-mosstep M8ms 8L 564.7¢ to 600.0¢
9-mosstep Minor 9-mosstep m9ms 8L + s 600.0¢ to 635.3¢
Major 9-mosstep M9ms 9L 635.3¢ to 675.0¢
10-mosstep Minor 10-mosstep m10ms 9L + s 675.0¢ to 705.9¢
Major 10-mosstep M10ms 10L 705.9¢ to 750.0¢
11-mosstep Minor 11-mosstep m11ms 10L + s 750.0¢ to 776.5¢
Major 11-mosstep M11ms 11L 776.5¢ to 825.0¢
12-mosstep Minor 12-mosstep m12ms 11L + s 825.0¢ to 847.1¢
Major 12-mosstep M12ms 12L 847.1¢ to 900.0¢
13-mosstep Minor 13-mosstep m13ms 12L + s 900.0¢ to 917.6¢
Major 13-mosstep M13ms 13L 917.6¢ to 975.0¢
14-mosstep Minor 14-mosstep m14ms 13L + s 975.0¢ to 988.2¢
Major 14-mosstep M14ms 14L 988.2¢ to 1050.0¢
15-mosstep Minor 15-mosstep m15ms 14L + s 1050.0¢ to 1058.8¢
Major 15-mosstep M15ms 15L 1058.8¢ to 1125.0¢
16-mosstep Perfect 16-mosstep P16ms 15L + s 1125.0¢ to 1129.4¢
Augmented 16-mosstep A16ms 16L 1129.4¢ to 1200.0¢
17-mosstep Perfect 17-mosstep P17ms 16L + s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 16L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\17 70.588 1129.412 1:1 1.000 Equalized 16L 1s
6\101 71.287 1128.713 6:5 1.200
5\84 71.429 1128.571 5:4 1.250
9\151 71.523 1128.477 9:7 1.286
4\67 71.642 1128.358 4:3 1.333 Supersoft 16L 1s
11\184 71.739 1128.261 11:8 1.375
7\117 71.795 1128.205 7:5 1.400
10\167 71.856 1128.144 10:7 1.429
3\50 72.000 1128.000 3:2 1.500 Soft 16L 1s
11\183 72.131 1127.869 11:7 1.571
8\133 72.180 1127.820 8:5 1.600
13\216 72.222 1127.778 13:8 1.625
5\83 72.289 1127.711 5:3 1.667 Semisoft 16L 1s
12\199 72.362 1127.638 12:7 1.714
7\116 72.414 1127.586 7:4 1.750
9\149 72.483 1127.517 9:5 1.800
2\33 72.727 1127.273 2:1 2.000 Basic 16L 1s
9\148 72.973 1127.027 9:4 2.250
7\115 73.043 1126.957 7:3 2.333
12\197 73.096 1126.904 12:5 2.400
5\82 73.171 1126.829 5:2 2.500 Semihard 16L 1s
13\213 73.239 1126.761 13:5 2.600
8\131 73.282 1126.718 8:3 2.667
11\180 73.333 1126.667 11:4 2.750
3\49 73.469 1126.531 3:1 3.000 Hard 16L 1s
10\163 73.620 1126.380 10:3 3.333
7\114 73.684 1126.316 7:2 3.500
11\179 73.743 1126.257 11:3 3.667
4\65 73.846 1126.154 4:1 4.000 Superhard 16L 1s
9\146 73.973 1126.027 9:2 4.500
5\81 74.074 1125.926 5:1 5.000
6\97 74.227 1125.773 6:1 6.000
1\16 75.000 1125.000 1:0 → ∞ Collapsed 16L 1s


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