8L 5s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖7L 4s ↑8L 4s 9L 4s↗
←7L 5s8L 5s 9L 5s→
↙7L 6s ↓8L 6s 9L 6s↘
Scale structure
Step pattern LLsLLsLsLLsLs
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\13 to 1\8 (92.3¢ to 150.0¢)
Small 0\8 to 1\13 (0.0¢ to 92.3¢)
Generator ranges
Bright 8\13 to 5\8 (738.5¢ to 750.0¢)
Dark 3\8 to 5\13 (450.0¢ to 461.5¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Related scales
Parent 5L 3s
Sister 5L 8s
Daughters 13L 8s, 8L 13s
Equal tunings
Equalized (L:s = 1:1) 8\13 (738.5¢)
Supersoft (L:s = 4:3) 29\47 (740.4¢)
Soft (L:s = 3:2) 21\34 (741.2¢)
Semisoft (L:s = 5:3) 34\55 (741.8¢)
Basic (L:s = 2:1) 13\21 (742.9¢)
Semihard (L:s = 5:2) 31\50 (744.0¢)
Hard (L:s = 3:1) 18\29 (744.8¢)
Superhard (L:s = 4:1) 23\37 (745.9¢)
Collapsed (L:s = 1:0) 5\8 (750.0¢)

8L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 5 small steps, repeating every octave. 8L 5s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 738.5¢ to 750¢, or from 450¢ to 461.5¢.

8L 5s represents the chromatic scale of Semidim, Tridec, Ammonite and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 semisixth, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to logarithmic phi, or even logarithmic phi itself.

Modes

Modes of 8L 5s
UDP Rotational order Step pattern
12|0 1 LLsLLsLsLLsLs
11|1 9 LLsLsLLsLLsLs
10|2 4 LLsLsLLsLsLLs
9|3 12 LsLLsLLsLsLLs
8|4 7 LsLLsLsLLsLLs
7|5 2 LsLLsLsLLsLsL
6|6 10 LsLsLLsLLsLsL
5|7 5 LsLsLLsLsLLsL
4|8 13 sLLsLLsLsLLsL
3|9 8 sLLsLsLLsLLsL
2|10 3 sLLsLsLLsLsLL
1|11 11 sLsLLsLLsLsLL
0|12 6 sLsLLsLsLLsLL

Scale tree

Scale tree and tuning spectrum of 8L 5s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\13 738.462 461.538 1:1 1.000 Equalized 8L 5s
45\73 739.726 460.274 6:5 1.200
37\60 740.000 460.000 5:4 1.250
66\107 740.187 459.813 9:7 1.286
29\47 740.426 459.574 4:3 1.333 Supersoft 8L 5s
79\128 740.625 459.375 11:8 1.375
50\81 740.741 459.259 7:5 1.400
71\115 740.870 459.130 10:7 1.429
21\34 741.176 458.824 3:2 1.500 Soft 8L 5s
76\123 741.463 458.537 11:7 1.571
55\89 741.573 458.427 8:5 1.600
89\144 741.667 458.333 13:8 1.625
34\55 741.818 458.182 5:3 1.667 Semisoft 8L 5s
81\131 741.985 458.015 12:7 1.714
47\76 742.105 457.895 7:4 1.750
60\97 742.268 457.732 9:5 1.800
13\21 742.857 457.143 2:1 2.000 Basic 8L 5s
Scales with tunings softer than this are proper
57\92 743.478 456.522 9:4 2.250
44\71 743.662 456.338 7:3 2.333
75\121 743.802 456.198 12:5 2.400
31\50 744.000 456.000 5:2 2.500 Semihard 8L 5s
80\129 744.186 455.814 13:5 2.600
49\79 744.304 455.696 8:3 2.667
67\108 744.444 455.556 11:4 2.750
18\29 744.828 455.172 3:1 3.000 Hard 8L 5s
59\95 745.263 454.737 10:3 3.333
41\66 745.455 454.545 7:2 3.500
64\103 745.631 454.369 11:3 3.667
23\37 745.946 454.054 4:1 4.000 Superhard 8L 5s
51\82 746.341 453.659 9:2 4.500
28\45 746.667 453.333 5:1 5.000
33\53 747.170 452.830 6:1 6.000
5\8 750.000 450.000 1:0 → ∞ Collapsed 8L 5s