13L 9s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 12L 8s ↑ 13L 8s 14L 8s ↗
← 12L 9s 13L 9s 14L 9s →
↙ 12L 10s ↓ 13L 10s 14L 10s ↘ 
┌╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥┬┐
│║║│║│║║│║│║║│║│║║│║│║││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\22 to 3\13 (272.7¢ to 276.9¢)
Dark 10\13 to 17\22 (923.1¢ to 927.3¢)
TAMNAMS information
Descends from 4L 5s (gramitonic)
Ancestor's step ratio range 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 9L 4s
Sister 9L 13s
Daughters 22L 13s, 13L 22s
Neutralized 4L 18s
2-Flought 35L 9s, 13L 31s
Equal tunings
Equalized (L:s = 1:1) 5\22 (272.7¢)
Supersoft (L:s = 4:3) 18\79 (273.4¢)
Soft (L:s = 3:2) 13\57 (273.7¢)
Semisoft (L:s = 5:3) 21\92 (273.9¢)
Basic (L:s = 2:1) 8\35 (274.3¢)
Semihard (L:s = 5:2) 19\83 (274.7¢)
Hard (L:s = 3:1) 11\48 (275.0¢)
Superhard (L:s = 4:1) 14\61 (275.4¢)
Collapsed (L:s = 1:0) 3\13 (276.9¢)

13L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 9 small steps, repeating every octave. 13L 9s is a grandchild scale of 4L 5s, expanding it by 13 tones. Generators that produce this scale range from 272.7¢ to 276.9¢, or from 923.1¢ to 927.3¢.

Modes

Modes of 13L 9s
UDP Cyclic
order		 Step
pattern
21|0 1 LLsLsLLsLsLLsLsLLsLsLs
20|1 6 LLsLsLLsLsLLsLsLsLLsLs
19|2 11 LLsLsLLsLsLsLLsLsLLsLs
18|3 16 LLsLsLsLLsLsLLsLsLLsLs
17|4 21 LsLLsLsLLsLsLLsLsLLsLs
16|5 4 LsLLsLsLLsLsLLsLsLsLLs
15|6 9 LsLLsLsLLsLsLsLLsLsLLs
14|7 14 LsLLsLsLsLLsLsLLsLsLLs
13|8 19 LsLsLLsLsLLsLsLLsLsLLs
12|9 2 LsLsLLsLsLLsLsLLsLsLsL
11|10 7 LsLsLLsLsLLsLsLsLLsLsL
10|11 12 LsLsLLsLsLsLLsLsLLsLsL
9|12 17 LsLsLsLLsLsLLsLsLLsLsL
8|13 22 sLLsLsLLsLsLLsLsLLsLsL
7|14 5 sLLsLsLLsLsLLsLsLsLLsL
6|15 10 sLLsLsLLsLsLsLLsLsLLsL
5|16 15 sLLsLsLsLLsLsLLsLsLLsL
4|17 20 sLsLLsLsLLsLsLLsLsLLsL
3|18 3 sLsLLsLsLLsLsLLsLsLsLL
2|19 8 sLsLLsLsLLsLsLsLLsLsLL
1|20 13 sLsLLsLsLsLLsLsLLsLsLL
0|21 18 sLsLsLLsLsLLsLsLLsLsLL

Scale tree

Scale Tree and Tuning Spectrum of 13L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\22 272.727 927.273 1:1 1.000 Equalized 13L 9s
28\123 273.171 926.829 6:5 1.200
23\101 273.267 926.733 5:4 1.250
41\180 273.333 926.667 9:7 1.286
18\79 273.418 926.582 4:3 1.333 Supersoft 13L 9s
49\215 273.488 926.512 11:8 1.375
31\136 273.529 926.471 7:5 1.400
44\193 273.575 926.425 10:7 1.429
13\57 273.684 926.316 3:2 1.500 Soft 13L 9s
47\206 273.786 926.214 11:7 1.571
34\149 273.826 926.174 8:5 1.600
55\241 273.859 926.141 13:8 1.625
21\92 273.913 926.087 5:3 1.667 Semisoft 13L 9s
50\219 273.973 926.027 12:7 1.714
29\127 274.016 925.984 7:4 1.750
37\162 274.074 925.926 9:5 1.800
8\35 274.286 925.714 2:1 2.000 Basic 13L 9s
Scales with tunings softer than this are proper
35\153 274.510 925.490 9:4 2.250
27\118 274.576 925.424 7:3 2.333
46\201 274.627 925.373 12:5 2.400
19\83 274.699 925.301 5:2 2.500 Semihard 13L 9s
49\214 274.766 925.234 13:5 2.600
30\131 274.809 925.191 8:3 2.667
41\179 274.860 925.140 11:4 2.750
11\48 275.000 925.000 3:1 3.000 Hard 13L 9s
36\157 275.159 924.841 10:3 3.333
25\109 275.229 924.771 7:2 3.500
39\170 275.294 924.706 11:3 3.667
14\61 275.410 924.590 4:1 4.000 Superhard 13L 9s
31\135 275.556 924.444 9:2 4.500
17\74 275.676 924.324 5:1 5.000
20\87 275.862 924.138 6:1 6.000
3\13 276.923 923.077 1:0 → ∞ Collapsed 13L 9s
Retrieved from "https://en.xen.wiki/index.php?title=13L_9s&oldid=155830"