5L 21s: Difference between revisions

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{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
The generator of this scale is generally taken to be a sharpened [[8/7]], in [[slendric]] temperament and its various extensions ([[mothra]], [[rodan]], etc.), such that 3 generators reach [[3/2]].
== Scale properties ==
== Scale properties ==
{{TAMNAMS use}}
{{TAMNAMS use}}
Line 19: Line 21:
| 9/5 = [[Mothra]]
| 9/5 = [[Mothra]]
| 7/3 = [[Mosura]]
| 7/3 = [[Mosura]]
| 10/3 = [[Euslendric]], near 2.3.7 optimum
| 11/3 = [[Guiron]]
| 11/3 = [[Guiron]]
| 9/2 = [[Rodan]]}}
| 9/2 = [[Rodan]]}}

Latest revision as of 16:04, 16 July 2025

↖ 4L 20s ↑ 5L 20s 6L 20s ↗
← 4L 21s 5L 21s 6L 21s →
↙ 4L 22s ↓ 5L 22s 6L 22s ↘
Scale structure
Step pattern LssssLssssLssssLssssLsssss
sssssLssssLssssLssssLssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\26 to 1\5 (230.8 ¢ to 240.0 ¢)
Dark 4\5 to 21\26 (960.0 ¢ to 969.2 ¢)
TAMNAMS information
Related to 5L 1s (machinoid)
With tunings 5:1 to 1:0
Related MOS scales
Parent 5L 16s
Sister 21L 5s
Daughters 26L 5s, 5L 26s
Neutralized 10L 16s
2-Flought 31L 21s, 5L 47s
Equal tunings
Equalized (L:s = 1:1) 5\26 (230.8 ¢)
Supersoft (L:s = 4:3) 16\83 (231.3 ¢)
Soft (L:s = 3:2) 11\57 (231.6 ¢)
Semisoft (L:s = 5:3) 17\88 (231.8 ¢)
Basic (L:s = 2:1) 6\31 (232.3 ¢)
Semihard (L:s = 5:2) 13\67 (232.8 ¢)
Hard (L:s = 3:1) 7\36 (233.3 ¢)
Superhard (L:s = 4:1) 8\41 (234.1 ¢)
Collapsed (L:s = 1:0) 1\5 (240.0 ¢)
View • Talk • Edit

5L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 21 small steps, repeating every octave. 5L 21s is related to 5L 1s, expanding it by 20 tones. Generators that produce this scale range from 230.8 ¢ to 240 ¢, or from 960 ¢ to 969.2 ¢. The generator of this scale is generally taken to be a sharpened 8/7, in slendric temperament and its various extensions (mothra, rodan, etc.), such that 3 generators reach 3/2.

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 5L 21s
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 46.2 ¢
Major 1-mosstep M1ms L 46.2 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 92.3 ¢
Major 2-mosstep M2ms L + s 92.3 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 138.5 ¢
Major 3-mosstep M3ms L + 2s 138.5 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 184.6 ¢
Major 4-mosstep M4ms L + 3s 184.6 ¢ to 240.0 ¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0 ¢ to 230.8 ¢
Perfect 5-mosstep P5ms L + 4s 230.8 ¢ to 240.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 276.9 ¢
Major 6-mosstep M6ms 2L + 4s 276.9 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0 ¢ to 323.1 ¢
Major 7-mosstep M7ms 2L + 5s 323.1 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 240.0 ¢ to 369.2 ¢
Major 8-mosstep M8ms 2L + 6s 369.2 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 240.0 ¢ to 415.4 ¢
Major 9-mosstep M9ms 2L + 7s 415.4 ¢ to 480.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 240.0 ¢ to 461.5 ¢
Major 10-mosstep M10ms 2L + 8s 461.5 ¢ to 480.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 480.0 ¢ to 507.7 ¢
Major 11-mosstep M11ms 3L + 8s 507.7 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 480.0 ¢ to 553.8 ¢
Major 12-mosstep M12ms 3L + 9s 553.8 ¢ to 720.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 480.0 ¢ to 600.0 ¢
Major 13-mosstep M13ms 3L + 10s 600.0 ¢ to 720.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 480.0 ¢ to 646.2 ¢
Major 14-mosstep M14ms 3L + 11s 646.2 ¢ to 720.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 480.0 ¢ to 692.3 ¢
Major 15-mosstep M15ms 3L + 12s 692.3 ¢ to 720.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 720.0 ¢ to 738.5 ¢
Major 16-mosstep M16ms 4L + 12s 738.5 ¢ to 960.0 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 720.0 ¢ to 784.6 ¢
Major 17-mosstep M17ms 4L + 13s 784.6 ¢ to 960.0 ¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 720.0 ¢ to 830.8 ¢
Major 18-mosstep M18ms 4L + 14s 830.8 ¢ to 960.0 ¢
19-mosstep Minor 19-mosstep m19ms 3L + 16s 720.0 ¢ to 876.9 ¢
Major 19-mosstep M19ms 4L + 15s 876.9 ¢ to 960.0 ¢
20-mosstep Minor 20-mosstep m20ms 3L + 17s 720.0 ¢ to 923.1 ¢
Major 20-mosstep M20ms 4L + 16s 923.1 ¢ to 960.0 ¢
21-mosstep Perfect 21-mosstep P21ms 4L + 17s 960.0 ¢ to 969.2 ¢
Augmented 21-mosstep A21ms 5L + 16s 969.2 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 4L + 18s 960.0 ¢ to 1015.4 ¢
Major 22-mosstep M22ms 5L + 17s 1015.4 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 4L + 19s 960.0 ¢ to 1061.5 ¢
Major 23-mosstep M23ms 5L + 18s 1061.5 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 4L + 20s 960.0 ¢ to 1107.7 ¢
Major 24-mosstep M24ms 5L + 19s 1107.7 ¢ to 1200.0 ¢
25-mosstep Minor 25-mosstep m25ms 4L + 21s 960.0 ¢ to 1153.8 ¢
Major 25-mosstep M25ms 5L + 20s 1153.8 ¢ to 1200.0 ¢
26-mosstep Perfect 26-mosstep P26ms 5L + 21s 1200.0 ¢

Generator chain

Generator chain of 5L 21s
Bright gens Scale degree Abbrev.
30 Augmented 20-mosdegree A20md
29 Augmented 15-mosdegree A15md
28 Augmented 10-mosdegree A10md
27 Augmented 5-mosdegree A5md
26 Augmented 0-mosdegree A0md
25 Augmented 21-mosdegree A21md
24 Major 16-mosdegree M16md
23 Major 11-mosdegree M11md
22 Major 6-mosdegree M6md
21 Major 1-mosdegree M1md
20 Major 22-mosdegree M22md
19 Major 17-mosdegree M17md
18 Major 12-mosdegree M12md
17 Major 7-mosdegree M7md
16 Major 2-mosdegree M2md
15 Major 23-mosdegree M23md
14 Major 18-mosdegree M18md
13 Major 13-mosdegree M13md
12 Major 8-mosdegree M8md
11 Major 3-mosdegree M3md
10 Major 24-mosdegree M24md
9 Major 19-mosdegree M19md
8 Major 14-mosdegree M14md
7 Major 9-mosdegree M9md
6 Major 4-mosdegree M4md
5 Major 25-mosdegree M25md
4 Major 20-mosdegree M20md
3 Major 15-mosdegree M15md
2 Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 26-mosdegree		 P0md
P26md
−1 Perfect 21-mosdegree P21md
−2 Minor 16-mosdegree m16md
−3 Minor 11-mosdegree m11md
−4 Minor 6-mosdegree m6md
−5 Minor 1-mosdegree m1md
−6 Minor 22-mosdegree m22md
−7 Minor 17-mosdegree m17md
−8 Minor 12-mosdegree m12md
−9 Minor 7-mosdegree m7md
−10 Minor 2-mosdegree m2md
−11 Minor 23-mosdegree m23md
−12 Minor 18-mosdegree m18md
−13 Minor 13-mosdegree m13md
−14 Minor 8-mosdegree m8md
−15 Minor 3-mosdegree m3md
−16 Minor 24-mosdegree m24md
−17 Minor 19-mosdegree m19md
−18 Minor 14-mosdegree m14md
−19 Minor 9-mosdegree m9md
−20 Minor 4-mosdegree m4md
−21 Minor 25-mosdegree m25md
−22 Minor 20-mosdegree m20md
−23 Minor 15-mosdegree m15md
−24 Minor 10-mosdegree m10md
−25 Diminished 5-mosdegree d5md
−26 Diminished 26-mosdegree d26md
−27 Diminished 21-mosdegree d21md
−28 Diminished 16-mosdegree d16md
−29 Diminished 11-mosdegree d11md
−30 Diminished 6-mosdegree d6md

Modes

Scale degrees of the modes of 5L 21s
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 20 21 22 23 24 25 26
25|0 1 LssssLssssLssssLssssLsssss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf.
24|1 6 LssssLssssLssssLsssssLssss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
23|2 11 LssssLssssLsssssLssssLssss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
22|3 16 LssssLsssssLssssLssssLssss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
21|4 21 LsssssLssssLssssLssssLssss Perf. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
20|5 26 sLssssLssssLssssLssssLssss Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
19|6 5 sLssssLssssLssssLsssssLsss Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
18|7 10 sLssssLssssLsssssLssssLsss Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
17|8 15 sLssssLsssssLssssLssssLsss Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
16|9 20 sLsssssLssssLssssLssssLsss Perf. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
15|10 25 ssLssssLssssLssssLssssLsss Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
14|11 4 ssLssssLssssLssssLsssssLss Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
13|12 9 ssLssssLssssLsssssLssssLss Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
12|13 14 ssLssssLsssssLssssLssssLss Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
11|14 19 ssLsssssLssssLssssLssssLss Perf. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
10|15 24 sssLssssLssssLssssLssssLss Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
9|16 3 sssLssssLssssLssssLsssssLs Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Perf.
8|17 8 sssLssssLssssLsssssLssssLs Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Maj. Min. Min. Min. Maj. Maj. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf.
7|18 13 sssLssssLsssssLssssLssssLs Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf.
6|19 18 sssLsssssLssssLssssLssssLs Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf.
5|20 23 ssssLssssLssssLssssLssssLs Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf.
4|21 2 ssssLssssLssssLssssLsssssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Perf.
3|22 7 ssssLssssLssssLsssssLssssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
2|23 12 ssssLssssLsssssLssssLssssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|24 17 ssssLsssssLssssLssssLssssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|25 22 sssssLssssLssssLssssLssssL Perf. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 5L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\26 230.769 969.231 1:1 1.000 Equalized 5L 21s
26\135 231.111 968.889 6:5 1.200 Amaranthine/Chrysanthemum
21\109 231.193 968.807 5:4 1.250 Nearly pure 8/7
37\192 231.250 968.750 9:7 1.286
16\83 231.325 968.675 4:3 1.333 Supersoft 5L 21s
43\223 231.390 968.610 11:8 1.375
27\140 231.429 968.571 7:5 1.400
38\197 231.472 968.528 10:7 1.429
11\57 231.579 968.421 3:2 1.500 Soft 5L 21s
39\202 231.683 968.317 11:7 1.571
28\145 231.724 968.276 8:5 1.600
45\233 231.760 968.240 13:8 1.625
17\88 231.818 968.182 5:3 1.667 Semisoft 5L 21s
40\207 231.884 968.116 12:7 1.714
23\119 231.933 968.067 7:4 1.750
29\150 232.000 968.000 9:5 1.800 Mothra
6\31 232.258 967.742 2:1 2.000 Basic 5L 21s
Scales with tunings softer than this are proper
25\129 232.558 967.442 9:4 2.250
19\98 232.653 967.347 7:3 2.333 Mosura
32\165 232.727 967.273 12:5 2.400
13\67 232.836 967.164 5:2 2.500 Semihard 5L 21s
33\170 232.941 967.059 13:5 2.600
20\103 233.010 966.990 8:3 2.667
27\139 233.094 966.906 11:4 2.750
7\36 233.333 966.667 3:1 3.000 Hard 5L 21s
22\113 233.628 966.372 10:3 3.333 Euslendric, near 2.3.7 optimum
15\77 233.766 966.234 7:2 3.500
23\118 233.898 966.102 11:3 3.667 Guiron
8\41 234.146 965.854 4:1 4.000 Superhard 5L 21s
17\87 234.483 965.517 9:2 4.500 Rodan
9\46 234.783 965.217 5:1 5.000
10\51 235.294 964.706 6:1 6.000
1\5 240.000 960.000 1:0 → ∞ Collapsed 5L 21s
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