6L 19s: Difference between revisions

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== Scale tree ==
== Scale tree ==
{{MOS tuning spectrum}}
{{MOS tuning spectrum
| 7/4 = [[Hemithirds]]/[[luna]]
| 7/3 = [[Hemiwürschmidt]]
| 8/3 = [[Roulette]]
| 10/3 = [[Mediantone]]
}}


{{todo|expand}}
{{todo|expand}}
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Latest revision as of 23:04, 9 June 2025

↖ 5L 18s ↑ 6L 18s 7L 18s ↗
← 5L 19s 6L 19s 7L 19s →
↙ 5L 20s ↓ 6L 20s 7L 20s ↘
Scale structure
Step pattern LsssLsssLsssLsssLsssLssss
ssssLsssLsssLsssLsssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\25 to 1\6 (192.0 ¢ to 200.0 ¢)
Dark 5\6 to 21\25 (1000.0 ¢ to 1008.0 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 6L 13s
Sister 19L 6s
Daughters 25L 6s, 6L 25s
Neutralized 12L 13s
2-Flought 31L 19s, 6L 44s
Equal tunings
Equalized (L:s = 1:1) 4\25 (192.0 ¢)
Supersoft (L:s = 4:3) 13\81 (192.6 ¢)
Soft (L:s = 3:2) 9\56 (192.9 ¢)
Semisoft (L:s = 5:3) 14\87 (193.1 ¢)
Basic (L:s = 2:1) 5\31 (193.5 ¢)
Semihard (L:s = 5:2) 11\68 (194.1 ¢)
Hard (L:s = 3:1) 6\37 (194.6 ¢)
Superhard (L:s = 4:1) 7\43 (195.3 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
View • Talk • Edit

6L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 19 small steps, repeating every octave. 6L 19s is a great-grandchild scale of 6L 1s, expanding it by 18 tones. Generators that produce this scale range from 192 ¢ to 200 ¢, or from 1000 ¢ to 1008 ¢.

This is the MOS where the large steps divide the small steps into groups of 3-3-3-3-3-4. It is generated by a "neutral" whole tone of no less than 4\25 (192 ¢), which is most commonly taken to represent 28/25 and 19/17; interpreting it as Didacus[25], 2 generators reach 5/4 and 5 generators reach 7/4. Various extensions of didacus exist to find the 3rd harmonic within the MOS, most prominently hemithirds (-15 generators) and hemiwürschmidt (+16).

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 6L 19s
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 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 96.0 ¢
Major 2-mosstep M2ms L + s 96.0 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 144.0 ¢
Major 3-mosstep M3ms L + 2s 144.0 ¢ to 200.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 192.0 ¢
Perfect 4-mosstep P4ms L + 3s 192.0 ¢ to 200.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0 ¢ to 240.0 ¢
Major 5-mosstep M5ms 2L + 3s 240.0 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0 ¢ to 288.0 ¢
Major 6-mosstep M6ms 2L + 4s 288.0 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 200.0 ¢ to 336.0 ¢
Major 7-mosstep M7ms 2L + 5s 336.0 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 200.0 ¢ to 384.0 ¢
Major 8-mosstep M8ms 2L + 6s 384.0 ¢ to 400.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0 ¢ to 432.0 ¢
Major 9-mosstep M9ms 3L + 6s 432.0 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 400.0 ¢ to 480.0 ¢
Major 10-mosstep M10ms 3L + 7s 480.0 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 400.0 ¢ to 528.0 ¢
Major 11-mosstep M11ms 3L + 8s 528.0 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 400.0 ¢ to 576.0 ¢
Major 12-mosstep M12ms 3L + 9s 576.0 ¢ to 600.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 600.0 ¢ to 624.0 ¢
Major 13-mosstep M13ms 4L + 9s 624.0 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 600.0 ¢ to 672.0 ¢
Major 14-mosstep M14ms 4L + 10s 672.0 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 600.0 ¢ to 720.0 ¢
Major 15-mosstep M15ms 4L + 11s 720.0 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 600.0 ¢ to 768.0 ¢
Major 16-mosstep M16ms 4L + 12s 768.0 ¢ to 800.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 800.0 ¢ to 816.0 ¢
Major 17-mosstep M17ms 5L + 12s 816.0 ¢ to 1000.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 800.0 ¢ to 864.0 ¢
Major 18-mosstep M18ms 5L + 13s 864.0 ¢ to 1000.0 ¢
19-mosstep Minor 19-mosstep m19ms 4L + 15s 800.0 ¢ to 912.0 ¢
Major 19-mosstep M19ms 5L + 14s 912.0 ¢ to 1000.0 ¢
20-mosstep Minor 20-mosstep m20ms 4L + 16s 800.0 ¢ to 960.0 ¢
Major 20-mosstep M20ms 5L + 15s 960.0 ¢ to 1000.0 ¢
21-mosstep Perfect 21-mosstep P21ms 5L + 16s 1000.0 ¢ to 1008.0 ¢
Augmented 21-mosstep A21ms 6L + 15s 1008.0 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 5L + 17s 1000.0 ¢ to 1056.0 ¢
Major 22-mosstep M22ms 6L + 16s 1056.0 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 5L + 18s 1000.0 ¢ to 1104.0 ¢
Major 23-mosstep M23ms 6L + 17s 1104.0 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 5L + 19s 1000.0 ¢ to 1152.0 ¢
Major 24-mosstep M24ms 6L + 18s 1152.0 ¢ to 1200.0 ¢
25-mosstep Perfect 25-mosstep P25ms 6L + 19s 1200.0 ¢

Generator chain

Generator chain of 6L 19s
Bright gens Scale degree Abbrev.
30 Augmented 20-mosdegree A20md
29 Augmented 16-mosdegree A16md
28 Augmented 12-mosdegree A12md
27 Augmented 8-mosdegree A8md
26 Augmented 4-mosdegree A4md
25 Augmented 0-mosdegree A0md
24 Augmented 21-mosdegree A21md
23 Major 17-mosdegree M17md
22 Major 13-mosdegree M13md
21 Major 9-mosdegree M9md
20 Major 5-mosdegree M5md
19 Major 1-mosdegree M1md
18 Major 22-mosdegree M22md
17 Major 18-mosdegree M18md
16 Major 14-mosdegree M14md
15 Major 10-mosdegree M10md
14 Major 6-mosdegree M6md
13 Major 2-mosdegree M2md
12 Major 23-mosdegree M23md
11 Major 19-mosdegree M19md
10 Major 15-mosdegree M15md
9 Major 11-mosdegree M11md
8 Major 7-mosdegree M7md
7 Major 3-mosdegree M3md
6 Major 24-mosdegree M24md
5 Major 20-mosdegree M20md
4 Major 16-mosdegree M16md
3 Major 12-mosdegree M12md
2 Major 8-mosdegree M8md
1 Perfect 4-mosdegree P4md
0 Perfect 0-mosdegree
Perfect 25-mosdegree		 P0md
P25md
−1 Perfect 21-mosdegree P21md
−2 Minor 17-mosdegree m17md
−3 Minor 13-mosdegree m13md
−4 Minor 9-mosdegree m9md
−5 Minor 5-mosdegree m5md
−6 Minor 1-mosdegree m1md
−7 Minor 22-mosdegree m22md
−8 Minor 18-mosdegree m18md
−9 Minor 14-mosdegree m14md
−10 Minor 10-mosdegree m10md
−11 Minor 6-mosdegree m6md
−12 Minor 2-mosdegree m2md
−13 Minor 23-mosdegree m23md
−14 Minor 19-mosdegree m19md
−15 Minor 15-mosdegree m15md
−16 Minor 11-mosdegree m11md
−17 Minor 7-mosdegree m7md
−18 Minor 3-mosdegree m3md
−19 Minor 24-mosdegree m24md
−20 Minor 20-mosdegree m20md
−21 Minor 16-mosdegree m16md
−22 Minor 12-mosdegree m12md
−23 Minor 8-mosdegree m8md
−24 Diminished 4-mosdegree d4md
−25 Diminished 25-mosdegree d25md
−26 Diminished 21-mosdegree d21md
−27 Diminished 17-mosdegree d17md
−28 Diminished 13-mosdegree d13md
−29 Diminished 9-mosdegree d9md
−30 Diminished 5-mosdegree d5md

Modes

Scale degrees of the modes of 6L 19s
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 LsssLsssLsssLsssLsssLssss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Perf.
23|1 5 LsssLsssLsssLsssLssssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
22|2 9 LsssLsssLsssLssssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
21|3 13 LsssLsssLssssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
20|4 17 LsssLssssLsssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
19|5 21 LssssLsssLsssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
18|6 25 sLsssLsssLsssLsssLsssLsss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
17|7 4 sLsssLsssLsssLsssLssssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf.
16|8 8 sLsssLsssLsssLssssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
15|9 12 sLsssLsssLssssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
14|10 16 sLsssLssssLsssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
13|11 20 sLssssLsssLsssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
12|12 24 ssLsssLsssLsssLsssLsssLss Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
11|13 3 ssLsssLsssLsssLsssLssssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Perf.
10|14 7 ssLsssLsssLsssLssssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
9|15 11 ssLsssLsssLssssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
8|16 15 ssLsssLssssLsssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
7|17 19 ssLssssLsssLsssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
6|18 23 sssLsssLsssLsssLsssLsssLs Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
5|19 2 sssLsssLsssLsssLsssLssssL Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Min. Perf.
4|20 6 sssLsssLsssLsssLssssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
3|21 10 sssLsssLsssLssssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
2|22 14 sssLsssLssssLsssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
1|23 18 sssLssssLsssLsssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
0|24 22 ssssLsssLsssLsssLsssLsssL Perf. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 19s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\25 192.000 1008.000 1:1 1.000 Equalized 6L 19s
21\131 192.366 1007.634 6:5 1.200
17\106 192.453 1007.547 5:4 1.250
30\187 192.513 1007.487 9:7 1.286
13\81 192.593 1007.407 4:3 1.333 Supersoft 6L 19s
35\218 192.661 1007.339 11:8 1.375
22\137 192.701 1007.299 7:5 1.400
31\193 192.746 1007.254 10:7 1.429
9\56 192.857 1007.143 3:2 1.500 Soft 6L 19s
32\199 192.965 1007.035 11:7 1.571
23\143 193.007 1006.993 8:5 1.600
37\230 193.043 1006.957 13:8 1.625
14\87 193.103 1006.897 5:3 1.667 Semisoft 6L 19s
33\205 193.171 1006.829 12:7 1.714
19\118 193.220 1006.780 7:4 1.750 Hemithirds/luna
24\149 193.289 1006.711 9:5 1.800
5\31 193.548 1006.452 2:1 2.000 Basic 6L 19s
Scales with tunings softer than this are proper
21\130 193.846 1006.154 9:4 2.250
16\99 193.939 1006.061 7:3 2.333 Hemiwürschmidt
27\167 194.012 1005.988 12:5 2.400
11\68 194.118 1005.882 5:2 2.500 Semihard 6L 19s
28\173 194.220 1005.780 13:5 2.600
17\105 194.286 1005.714 8:3 2.667 Roulette
23\142 194.366 1005.634 11:4 2.750
6\37 194.595 1005.405 3:1 3.000 Hard 6L 19s
19\117 194.872 1005.128 10:3 3.333 Mediantone
13\80 195.000 1005.000 7:2 3.500
20\123 195.122 1004.878 11:3 3.667
7\43 195.349 1004.651 4:1 4.000 Superhard 6L 19s
15\92 195.652 1004.348 9:2 4.500
8\49 195.918 1004.082 5:1 5.000
9\55 196.364 1003.636 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 19s
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