5L 8s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖4L 7s ↑5L 7s 6L 7s↗
←4L 8s5L 8s 6L 8s→
↙4L 9s ↓5L 9s 6L 9s↘
Scale structure
Step pattern LsLssLsLssLss
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\13 to 1\5 (92.3¢ to 240.0¢)
Small 0\5 to 1\13 (0.0¢ to 92.3¢)
Generator ranges
Bright 5\13 to 2\5 (461.5¢ to 480.0¢)
Dark 3\5 to 8\13 (720.0¢ to 738.5¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Related scales
Parent 5L 3s
Sister 8L 5s
Daughters 13L 5s, 5L 13s
Equal tunings
Equalized (L:s = 1:1) 5\13 (461.5¢)
Supersoft (L:s = 4:3) 17\44 (463.6¢)
Soft (L:s = 3:2) 12\31 (464.5¢)
Semisoft (L:s = 5:3) 19\49 (465.3¢)
Basic (L:s = 2:1) 7\18 (466.7¢)
Semihard (L:s = 5:2) 16\41 (468.3¢)
Hard (L:s = 3:1) 9\23 (469.6¢)
Superhard (L:s = 4:1) 11\28 (471.4¢)
Collapsed (L:s = 1:0) 2\5 (480.0¢)

5L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 8 small steps, repeating every octave. 5L 8s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 461.5¢ to 480¢, or from 720¢ to 738.5¢.

5L 8s represents the chromatic scales of Semisept, A-Team and Vulture temperaments.

Modes

Modes of 5L 8s
UDP Rotational order Step pattern
12|0 1 LsLssLsLssLss
11|1 6 LsLssLssLsLss
10|2 11 LssLsLssLsLss
9|3 3 LssLsLssLssLs
8|4 8 LssLssLsLssLs
7|5 13 sLsLssLsLssLs
6|6 5 sLsLssLssLsLs
5|7 10 sLssLsLssLsLs
4|8 2 sLssLsLssLssL
3|9 7 sLssLssLsLssL
2|10 12 ssLsLssLsLssL
1|11 4 ssLsLssLssLsL
0|12 9 ssLssLsLssLsL

Scale tree

Scale tree and tuning spectrum of 5L 8s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\13 461.538 738.462 1:1 1.000 Equalized 5L 8s
27\70 462.857 737.143 6:5 1.200
22\57 463.158 736.842 5:4 1.250
39\101 463.366 736.634 9:7 1.286
17\44 463.636 736.364 4:3 1.333 Supersoft 5L 8s
46\119 463.866 736.134 11:8 1.375
29\75 464.000 736.000 7:5 1.400
41\106 464.151 735.849 10:7 1.429
12\31 464.516 735.484 3:2 1.500 Soft 5L 8s
43\111 464.865 735.135 11:7 1.571
31\80 465.000 735.000 8:5 1.600
50\129 465.116 734.884 13:8 1.625
19\49 465.306 734.694 5:3 1.667 Semisoft 5L 8s
45\116 465.517 734.483 12:7 1.714
26\67 465.672 734.328 7:4 1.750
33\85 465.882 734.118 9:5 1.800
7\18 466.667 733.333 2:1 2.000 Basic 5L 8s
Scales with tunings softer than this are proper
30\77 467.532 732.468 9:4 2.250
23\59 467.797 732.203 7:3 2.333
39\100 468.000 732.000 12:5 2.400
16\41 468.293 731.707 5:2 2.500 Semihard 5L 8s
41\105 468.571 731.429 13:5 2.600
25\64 468.750 731.250 8:3 2.667
34\87 468.966 731.034 11:4 2.750
9\23 469.565 730.435 3:1 3.000 Hard 5L 8s
29\74 470.270 729.730 10:3 3.333
20\51 470.588 729.412 7:2 3.500
31\79 470.886 729.114 11:3 3.667
11\28 471.429 728.571 4:1 4.000 Superhard 5L 8s
24\61 472.131 727.869 9:2 4.500
13\33 472.727 727.273 5:1 5.000
15\38 473.684 726.316 6:1 6.000
2\5 480.000 720.000 1:0 → ∞ Collapsed 5L 8s