15L 4s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 14L 3s ↑ 15L 3s 16L 3s ↗
← 14L 4s 15L 4s 16L 4s →
↙ 14L 5s ↓ 15L 5s 16L 5s ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║║│║║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLLsLLLs
sLLLsLLLLsLLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\19 to 4\15 (315.8 ¢ to 320.0 ¢)
Dark 11\15 to 14\19 (880.0 ¢ to 884.2 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 4L 11s
Sister 4L 15s
Daughters 19L 15s, 15L 19s
Neutralized 11L 8s
2-Flought 34L 4s, 15L 23s
Equal tunings
Equalized (L:s = 1:1) 5\19 (315.8 ¢)
Supersoft (L:s = 4:3) 19\72 (316.7 ¢)
Soft (L:s = 3:2) 14\53 (317.0 ¢)
Semisoft (L:s = 5:3) 23\87 (317.2 ¢)
Basic (L:s = 2:1) 9\34 (317.6 ¢)
Semihard (L:s = 5:2) 22\83 (318.1 ¢)
Hard (L:s = 3:1) 13\49 (318.4 ¢)
Superhard (L:s = 4:1) 17\64 (318.8 ¢)
Collapsed (L:s = 1:0) 4\15 (320.0 ¢)

15L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 4 small steps, repeating every octave. 15L 4s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 315.8 ¢ to 320 ¢, or from 880 ¢ to 884.2 ¢.

It is notable as the MOS scale of Kleismic[19].

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 15L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 80.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 80.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms 2L 126.3 ¢ to 160.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 160.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms 3L 189.5 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 240.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms 4L 252.6 ¢ to 320.0 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 240.0 ¢ to 315.8 ¢
Perfect 5-mosstep P5ms 4L + s 315.8 ¢ to 320.0 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 320.0 ¢ to 378.9 ¢
Major 6-mosstep M6ms 5L + s 378.9 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 400.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 6L + s 442.1 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 480.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 7L + s 505.3 ¢ to 560.0 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 560.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 8L + s 568.4 ¢ to 640.0 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 560.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 8L + 2s 631.6 ¢ to 640.0 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 640.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 9L + 2s 694.7 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 720.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 10L + 2s 757.9 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 800.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 11L + 2s 821.1 ¢ to 880.0 ¢
14-mosstep Perfect 14-mosstep P14ms 11L + 3s 880.0 ¢ to 884.2 ¢
Augmented 14-mosstep A14ms 12L + 2s 884.2 ¢ to 960.0 ¢
15-mosstep Minor 15-mosstep m15ms 11L + 4s 880.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 12L + 3s 947.4 ¢ to 960.0 ¢
16-mosstep Minor 16-mosstep m16ms 12L + 4s 960.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 13L + 3s 1010.5 ¢ to 1040.0 ¢
17-mosstep Minor 17-mosstep m17ms 13L + 4s 1040.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 14L + 3s 1073.7 ¢ to 1120.0 ¢
18-mosstep Minor 18-mosstep m18ms 14L + 4s 1120.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 15L + 3s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 15L + 4s 1200.0 ¢

Generator chain

Generator chain of 15L 4s
Bright gens Scale degree Abbrev.
33 Augmented 13-mosdegree A13md
32 Augmented 8-mosdegree A8md
31 Augmented 3-mosdegree A3md
30 Augmented 17-mosdegree A17md
29 Augmented 12-mosdegree A12md
28 Augmented 7-mosdegree A7md
27 Augmented 2-mosdegree A2md
26 Augmented 16-mosdegree A16md
25 Augmented 11-mosdegree A11md
24 Augmented 6-mosdegree A6md
23 Augmented 1-mosdegree A1md
22 Augmented 15-mosdegree A15md
21 Augmented 10-mosdegree A10md
20 Augmented 5-mosdegree A5md
19 Augmented 0-mosdegree A0md
18 Augmented 14-mosdegree A14md
17 Major 9-mosdegree M9md
16 Major 4-mosdegree M4md
15 Major 18-mosdegree M18md
14 Major 13-mosdegree M13md
13 Major 8-mosdegree M8md
12 Major 3-mosdegree M3md
11 Major 17-mosdegree M17md
10 Major 12-mosdegree M12md
9 Major 7-mosdegree M7md
8 Major 2-mosdegree M2md
7 Major 16-mosdegree M16md
6 Major 11-mosdegree M11md
5 Major 6-mosdegree M6md
4 Major 1-mosdegree M1md
3 Major 15-mosdegree M15md
2 Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 14-mosdegree P14md
−2 Minor 9-mosdegree m9md
−3 Minor 4-mosdegree m4md
−4 Minor 18-mosdegree m18md
−5 Minor 13-mosdegree m13md
−6 Minor 8-mosdegree m8md
−7 Minor 3-mosdegree m3md
−8 Minor 17-mosdegree m17md
−9 Minor 12-mosdegree m12md
−10 Minor 7-mosdegree m7md
−11 Minor 2-mosdegree m2md
−12 Minor 16-mosdegree m16md
−13 Minor 11-mosdegree m11md
−14 Minor 6-mosdegree m6md
−15 Minor 1-mosdegree m1md
−16 Minor 15-mosdegree m15md
−17 Minor 10-mosdegree m10md
−18 Diminished 5-mosdegree d5md
−19 Diminished 19-mosdegree d19md
−20 Diminished 14-mosdegree d14md
−21 Diminished 9-mosdegree d9md
−22 Diminished 4-mosdegree d4md
−23 Diminished 18-mosdegree d18md
−24 Diminished 13-mosdegree d13md
−25 Diminished 8-mosdegree d8md
−26 Diminished 3-mosdegree d3md
−27 Diminished 17-mosdegree d17md
−28 Diminished 12-mosdegree d12md
−29 Diminished 7-mosdegree d7md
−30 Diminished 2-mosdegree d2md
−31 Diminished 16-mosdegree d16md
−32 Diminished 11-mosdegree d11md
−33 Diminished 6-mosdegree d6md

Modes

Scale degrees of the modes of 15L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
18|0 1 LLLLsLLLLsLLLLsLLLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf.
17|1 6 LLLLsLLLLsLLLsLLLLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
16|2 11 LLLLsLLLsLLLLsLLLLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
15|3 16 LLLsLLLLsLLLLsLLLLs Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
14|4 2 LLLsLLLLsLLLLsLLLsL Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Perf.
13|5 7 LLLsLLLLsLLLsLLLLsL Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Perf.
12|6 12 LLLsLLLsLLLLsLLLLsL Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Perf.
11|7 17 LLsLLLLsLLLLsLLLLsL Perf. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Perf.
10|8 3 LLsLLLLsLLLLsLLLsLL Perf. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Perf.
9|9 8 LLsLLLLsLLLsLLLLsLL Perf. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Perf.
8|10 13 LLsLLLsLLLLsLLLLsLL Perf. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Perf.
7|11 18 LsLLLLsLLLLsLLLLsLL Perf. Maj. Min. Min. Min. Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Perf.
6|12 4 LsLLLLsLLLLsLLLsLLL Perf. Maj. Min. Min. Min. Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Min. Perf.
5|13 9 LsLLLLsLLLsLLLLsLLL Perf. Maj. Min. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Maj. Min. Min. Min. Perf.
4|14 14 LsLLLsLLLLsLLLLsLLL Perf. Maj. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Maj. Min. Min. Min. Perf.
3|15 19 sLLLLsLLLLsLLLLsLLL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Maj. Min. Min. Min. Perf.
2|16 5 sLLLLsLLLLsLLLsLLLL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|17 10 sLLLLsLLLsLLLLsLLLL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|18 15 sLLLsLLLLsLLLLsLLLL Perf. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 15L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\19 315.789 884.211 1:1 1.000 Equalized 15L 4s
29\110 316.364 883.636 6:5 1.200
24\91 316.484 883.516 5:4 1.250
43\163 316.564 883.436 9:7 1.286
19\72 316.667 883.333 4:3 1.333 Supersoft 15L 4s
52\197 316.751 883.249 11:8 1.375 Catakleismic
33\125 316.800 883.200 7:5 1.400
47\178 316.854 883.146 10:7 1.429
14\53 316.981 883.019 3:2 1.500 Soft 15L 4s
51\193 317.098 882.902 11:7 1.571
37\140 317.143 882.857 8:5 1.600
60\227 317.181 882.819 13:8 1.625
23\87 317.241 882.759 5:3 1.667 Semisoft 15L 4s
55\208 317.308 882.692 12:7 1.714
32\121 317.355 882.645 7:4 1.750
41\155 317.419 882.581 9:5 1.800
9\34 317.647 882.353 2:1 2.000 Basic 15L 4s
Scales with tunings softer than this are proper
40\151 317.881 882.119 9:4 2.250
31\117 317.949 882.051 7:3 2.333
53\200 318.000 882.000 12:5 2.400
22\83 318.072 881.928 5:2 2.500 Semihard 15L 4s
57\215 318.140 881.860 13:5 2.600
35\132 318.182 881.818 8:3 2.667
48\181 318.232 881.768 11:4 2.750
13\49 318.367 881.633 3:1 3.000 Hard 15L 4s
43\162 318.519 881.481 10:3 3.333
30\113 318.584 881.416 7:2 3.500
47\177 318.644 881.356 11:3 3.667
17\64 318.750 881.250 4:1 4.000 Superhard 15L 4s
38\143 318.881 881.119 9:2 4.500
21\79 318.987 881.013 5:1 5.000
25\94 319.149 880.851 6:1 6.000
4\15 320.000 880.000 1:0 → ∞ Collapsed 15L 4s
This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=15L_4s&oldid=195361"