4L 21s: Difference between revisions

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{{MOS intro}}
{{MOS intro}}
This scale is associated with [[moulin]] temperament, which includes a very precise 8:11:13 triad. [[Eliora]] proposes the name ''moulinoid'' for this pattern.
 
This scale is associated with [[moulin]] temperament, which includes a very precise 8:11:13 [[triad]]. [[Eliora]] proposes the name ''moulinoid'' for this pattern.
 
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum}}
 
{{stub}}
{{stub}}

Latest revision as of 14:20, 5 May 2025

↖ 3L 20s ↑ 4L 20s 5L 20s ↗
← 3L 21s 4L 21s 5L 21s →
↙ 3L 22s ↓ 4L 22s 5L 22s ↘
Scale structure
Step pattern LsssssLsssssLsssssLssssss
ssssssLsssssLsssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 6\25 to 1\4 (288.0 ¢ to 300.0 ¢)
Dark 3\4 to 19\25 (900.0 ¢ to 912.0 ¢)
TAMNAMS information
Related to 4L 5s (gramitonic)
With tunings 5:1 to 1:0
Related MOS scales
Parent 4L 17s
Sister 21L 4s
Daughters 25L 4s, 4L 25s
Neutralized 8L 17s
2-Flought 29L 21s, 4L 46s
Equal tunings
Equalized (L:s = 1:1) 6\25 (288.0 ¢)
Supersoft (L:s = 4:3) 19\79 (288.6 ¢)
Soft (L:s = 3:2) 13\54 (288.9 ¢)
Semisoft (L:s = 5:3) 20\83 (289.2 ¢)
Basic (L:s = 2:1) 7\29 (289.7 ¢)
Semihard (L:s = 5:2) 15\62 (290.3 ¢)
Hard (L:s = 3:1) 8\33 (290.9 ¢)
Superhard (L:s = 4:1) 9\37 (291.9 ¢)
Collapsed (L:s = 1:0) 1\4 (300.0 ¢)
View • Talk • Edit

4L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 21 small steps, repeating every octave. 4L 21s is related to 4L 5s, expanding it by 16 tones. Generators that produce this scale range from 288 ¢ to 300 ¢, or from 900 ¢ to 912 ¢.

This scale is associated with moulin temperament, which includes a very precise 8:11:13 triad. Eliora proposes the name moulinoid for this pattern.

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 4L 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 48.0 ¢
Major 1-mosstep M1ms L 48.0 ¢ to 300.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 96.0 ¢
Major 2-mosstep M2ms L + s 96.0 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 144.0 ¢
Major 3-mosstep M3ms L + 2s 144.0 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 192.0 ¢
Major 4-mosstep M4ms L + 3s 192.0 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 240.0 ¢
Major 5-mosstep M5ms L + 4s 240.0 ¢ to 300.0 ¢
6-mosstep Diminished 6-mosstep d6ms 6s 0.0 ¢ to 288.0 ¢
Perfect 6-mosstep P6ms L + 5s 288.0 ¢ to 300.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 300.0 ¢ to 336.0 ¢
Major 7-mosstep M7ms 2L + 5s 336.0 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 300.0 ¢ to 384.0 ¢
Major 8-mosstep M8ms 2L + 6s 384.0 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 300.0 ¢ to 432.0 ¢
Major 9-mosstep M9ms 2L + 7s 432.0 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 300.0 ¢ to 480.0 ¢
Major 10-mosstep M10ms 2L + 8s 480.0 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 300.0 ¢ to 528.0 ¢
Major 11-mosstep M11ms 2L + 9s 528.0 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 300.0 ¢ to 576.0 ¢
Major 12-mosstep M12ms 2L + 10s 576.0 ¢ to 600.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 600.0 ¢ to 624.0 ¢
Major 13-mosstep M13ms 3L + 10s 624.0 ¢ to 900.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 600.0 ¢ to 672.0 ¢
Major 14-mosstep M14ms 3L + 11s 672.0 ¢ to 900.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 600.0 ¢ to 720.0 ¢
Major 15-mosstep M15ms 3L + 12s 720.0 ¢ to 900.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 600.0 ¢ to 768.0 ¢
Major 16-mosstep M16ms 3L + 13s 768.0 ¢ to 900.0 ¢
17-mosstep Minor 17-mosstep m17ms 2L + 15s 600.0 ¢ to 816.0 ¢
Major 17-mosstep M17ms 3L + 14s 816.0 ¢ to 900.0 ¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 600.0 ¢ to 864.0 ¢
Major 18-mosstep M18ms 3L + 15s 864.0 ¢ to 900.0 ¢
19-mosstep Perfect 19-mosstep P19ms 3L + 16s 900.0 ¢ to 912.0 ¢
Augmented 19-mosstep A19ms 4L + 15s 912.0 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms 3L + 17s 900.0 ¢ to 960.0 ¢
Major 20-mosstep M20ms 4L + 16s 960.0 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms 3L + 18s 900.0 ¢ to 1008.0 ¢
Major 21-mosstep M21ms 4L + 17s 1008.0 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 3L + 19s 900.0 ¢ to 1056.0 ¢
Major 22-mosstep M22ms 4L + 18s 1056.0 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 3L + 20s 900.0 ¢ to 1104.0 ¢
Major 23-mosstep M23ms 4L + 19s 1104.0 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 3L + 21s 900.0 ¢ to 1152.0 ¢
Major 24-mosstep M24ms 4L + 20s 1152.0 ¢ to 1200.0 ¢
25-mosstep Perfect 25-mosstep P25ms 4L + 21s 1200.0 ¢

Generator chain

Generator chain of 4L 21s
Bright gens Scale degree Abbrev.
28 Augmented 18-mosdegree A18md
27 Augmented 12-mosdegree A12md
26 Augmented 6-mosdegree A6md
25 Augmented 0-mosdegree A0md
24 Augmented 19-mosdegree A19md
23 Major 13-mosdegree M13md
22 Major 7-mosdegree M7md
21 Major 1-mosdegree M1md
20 Major 20-mosdegree M20md
19 Major 14-mosdegree M14md
18 Major 8-mosdegree M8md
17 Major 2-mosdegree M2md
16 Major 21-mosdegree M21md
15 Major 15-mosdegree M15md
14 Major 9-mosdegree M9md
13 Major 3-mosdegree M3md
12 Major 22-mosdegree M22md
11 Major 16-mosdegree M16md
10 Major 10-mosdegree M10md
9 Major 4-mosdegree M4md
8 Major 23-mosdegree M23md
7 Major 17-mosdegree M17md
6 Major 11-mosdegree M11md
5 Major 5-mosdegree M5md
4 Major 24-mosdegree M24md
3 Major 18-mosdegree M18md
2 Major 12-mosdegree M12md
1 Perfect 6-mosdegree P6md
0 Perfect 0-mosdegree
Perfect 25-mosdegree		 P0md
P25md
−1 Perfect 19-mosdegree P19md
−2 Minor 13-mosdegree m13md
−3 Minor 7-mosdegree m7md
−4 Minor 1-mosdegree m1md
−5 Minor 20-mosdegree m20md
−6 Minor 14-mosdegree m14md
−7 Minor 8-mosdegree m8md
−8 Minor 2-mosdegree m2md
−9 Minor 21-mosdegree m21md
−10 Minor 15-mosdegree m15md
−11 Minor 9-mosdegree m9md
−12 Minor 3-mosdegree m3md
−13 Minor 22-mosdegree m22md
−14 Minor 16-mosdegree m16md
−15 Minor 10-mosdegree m10md
−16 Minor 4-mosdegree m4md
−17 Minor 23-mosdegree m23md
−18 Minor 17-mosdegree m17md
−19 Minor 11-mosdegree m11md
−20 Minor 5-mosdegree m5md
−21 Minor 24-mosdegree m24md
−22 Minor 18-mosdegree m18md
−23 Minor 12-mosdegree m12md
−24 Diminished 6-mosdegree d6md
−25 Diminished 25-mosdegree d25md
−26 Diminished 19-mosdegree d19md
−27 Diminished 13-mosdegree d13md
−28 Diminished 7-mosdegree d7md

Modes

Scale degrees of the modes of 4L 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
24|0 1 LsssssLsssssLsssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Perf.
23|1 7 LsssssLsssssLssssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
22|2 13 LsssssLssssssLsssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
21|3 19 LssssssLsssssLsssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
20|4 25 sLsssssLsssssLsssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
19|5 6 sLsssssLsssssLssssssLssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
18|6 12 sLsssssLssssssLsssssLssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
17|7 18 sLssssssLsssssLsssssLssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
16|8 24 ssLsssssLsssssLsssssLssss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
15|9 5 ssLsssssLsssssLssssssLsss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
14|10 11 ssLsssssLssssssLsssssLsss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
13|11 17 ssLssssssLsssssLsssssLsss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
12|12 23 sssLsssssLsssssLsssssLsss Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
11|13 4 sssLsssssLsssssLssssssLss Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
10|14 10 sssLsssssLssssssLsssssLss Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
9|15 16 sssLssssssLsssssLsssssLss Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
8|16 22 ssssLsssssLsssssLsssssLss Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
7|17 3 ssssLsssssLsssssLssssssLs Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Perf.
6|18 9 ssssLsssssLssssssLsssssLs Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Perf.
5|19 15 ssssLssssssLsssssLsssssLs Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Perf.
4|20 21 sssssLsssssLsssssLsssssLs Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Perf.
3|21 2 sssssLsssssLsssssLssssssL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Perf.
2|22 8 sssssLsssssLssssssLsssssL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
1|23 14 sssssLssssssLsssssLsssssL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
0|24 20 ssssssLsssssLsssssLsssssL Perf. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 4L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
6\25 288.000 912.000 1:1 1.000 Equalized 4L 21s
31\129 288.372 911.628 6:5 1.200
25\104 288.462 911.538 5:4 1.250
44\183 288.525 911.475 9:7 1.286
19\79 288.608 911.392 4:3 1.333 Supersoft 4L 21s
51\212 288.679 911.321 11:8 1.375
32\133 288.722 911.278 7:5 1.400
45\187 288.770 911.230 10:7 1.429
13\54 288.889 911.111 3:2 1.500 Soft 4L 21s
46\191 289.005 910.995 11:7 1.571
33\137 289.051 910.949 8:5 1.600
53\220 289.091 910.909 13:8 1.625
20\83 289.157 910.843 5:3 1.667 Semisoft 4L 21s
47\195 289.231 910.769 12:7 1.714
27\112 289.286 910.714 7:4 1.750
34\141 289.362 910.638 9:5 1.800
7\29 289.655 910.345 2:1 2.000 Basic 4L 21s
Scales with tunings softer than this are proper
29\120 290.000 910.000 9:4 2.250
22\91 290.110 909.890 7:3 2.333
37\153 290.196 909.804 12:5 2.400
15\62 290.323 909.677 5:2 2.500 Semihard 4L 21s
38\157 290.446 909.554 13:5 2.600
23\95 290.526 909.474 8:3 2.667
31\128 290.625 909.375 11:4 2.750
8\33 290.909 909.091 3:1 3.000 Hard 4L 21s
25\103 291.262 908.738 10:3 3.333
17\70 291.429 908.571 7:2 3.500
26\107 291.589 908.411 11:3 3.667
9\37 291.892 908.108 4:1 4.000 Superhard 4L 21s
19\78 292.308 907.692 9:2 4.500
10\41 292.683 907.317 5:1 5.000
11\45 293.333 906.667 6:1 6.000
1\4 300.000 900.000 1:0 → ∞ Collapsed 4L 21s
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