15L 1s

From Xenharmonic Wiki
Jump to navigation Jump to search
← 14L 1s15L 1s 16L 1s →
↙ 14L 2s ↓15L 2s 16L 2s ↘
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║║║║║║║││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 1\16 to 1\15 (75.0¢ to 80.0¢)
Dark 14\15 to 15\16 (1120.0¢ to 1125.0¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Required step ratio range 6:1 to 7:1
Related MOS scales
Parent 1L 14s
Sister 1L 15s
Daughters 16L 15s, 15L 16s
Neutralized 14L 2s
2-Flought 31L 1s, 15L 17s
Equal tunings
Equalized (L:s = 1:1) 1\16 (75.0¢)
Supersoft (L:s = 4:3) 4\63 (76.2¢)
Soft (L:s = 3:2) 3\47 (76.6¢)
Semisoft (L:s = 5:3) 5\78 (76.9¢)
Basic (L:s = 2:1) 2\31 (77.4¢)
Semihard (L:s = 5:2) 5\77 (77.9¢)
Hard (L:s = 3:1) 3\46 (78.3¢)
Superhard (L:s = 4:1) 4\61 (78.7¢)
Collapsed (L:s = 1:0) 1\15 (80.0¢)

15L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 1 small step, repeating every octave. 15L 1s is related to 1L 9s, expanding it by 6 tones. Generators that produce this scale range from 75¢ to 80¢, or from 1120¢ to 1125¢. Scales of this form are always proper because there is only one small step. It is notable for corresponding to valentine[16].

Scale tree

Scale Tree and Tuning Spectrum of 15L 1s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\16 75.000 1125.000 1:1 1.000 Equalized 15L 1s
6\95 75.789 1124.211 6:5 1.200
5\79 75.949 1124.051 5:4 1.250
9\142 76.056 1123.944 9:7 1.286
4\63 76.190 1123.810 4:3 1.333 Supersoft 15L 1s
11\173 76.301 1123.699 11:8 1.375
7\110 76.364 1123.636 7:5 1.400
10\157 76.433 1123.567 10:7 1.429
3\47 76.596 1123.404 3:2 1.500 Soft 15L 1s
11\172 76.744 1123.256 11:7 1.571
8\125 76.800 1123.200 8:5 1.600
13\203 76.847 1123.153 13:8 1.625
5\78 76.923 1123.077 5:3 1.667 Semisoft 15L 1s
12\187 77.005 1122.995 12:7 1.714
7\109 77.064 1122.936 7:4 1.750
9\140 77.143 1122.857 9:5 1.800 Tertia / Tertiaseptal
2\31 77.419 1122.581 2:1 2.000 Basic 15L 1s
9\139 77.698 1122.302 9:4 2.250
7\108 77.778 1122.222 7:3 2.333
12\185 77.838 1122.162 12:5 2.400
5\77 77.922 1122.078 5:2 2.500 Semihard 15L 1s
13\200 78.000 1122.000 13:5 2.600
8\123 78.049 1121.951 8:3 2.667 Valentine
11\169 78.107 1121.893 11:4 2.750
3\46 78.261 1121.739 3:1 3.000 Hard 15L 1s
10\153 78.431 1121.569 10:3 3.333
7\107 78.505 1121.495 7:2 3.500
11\168 78.571 1121.429 11:3 3.667
4\61 78.689 1121.311 4:1 4.000 Superhard 15L 1s
9\137 78.832 1121.168 9:2 4.500
5\76 78.947 1121.053 5:1 5.000
6\91 79.121 1120.879 6:1 6.000
1\15 80.000 1120.000 1:0 → ∞ Collapsed 15L 1s