6L 16s: Difference between revisions

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This is the MOS where the pattern 3L 8s repeats at the half octave. However, it has a small major third as a generator instead of the medium to large major third which generates 3L 8s. With the half-octave equivalence, the third inverts to a 'diatonic' whole tone of no more than 4/22edo (218.182 cents).
{{Infobox MOS}}
{{MOS intro}}
 
It has a small major third as a generator instead of the medium to large major third which generates 3L 8s. With the half-octave equivalence, the third inverts to a "diatonic" whole tone of no more than 4/22edo (218.182{{c}}).
 
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum}}
 
{{todo|expand}}


{| class="wikitable"
|-
| | 4/22
| |
| |
| |
| |
| | 218.182
|-
| |
| |
| |
| |
| | 17/94
| | 217.021
|-
| |
| |
| |
| | 13/72
| |
| | 216.667
|-
| |
| |
| |
| |
| | 22/122
| | 216.393
|-
| |
| |
| | 9/50
| |
| |
| | 216
|-
| |
| |
| |
| |
| |
| | 215.733
|-
| |
| |
| |
| |
| | 23/128
| | 215.625
|-
| |
| |
| |
| |
| |
| | 215.559
|-
| |
| |
| |
| | 14/78
| |
| | 215.385
|-
| |
| |
| |
| |
| |
| | 215.156
|-
| |
| |
| |
| |
| | 19/106
| | 215.094
|-
| |
| | 5/28
| |
| |
| |
| | 214.286
|-
| |
| |
| |
| |
| | 16/90
| | 213.333
|-
| |
| |
| |
| | 11/62
| |
| | 212.903
|-
| |
| |
| |
| |
| |
| | 212.615
|-
| |
| |
| |
| |
| | 17/96
| | 212.5
|-
| |
| |
| |
| |
| |
| | 212.38
|-
| |
| |
| | 6/34
| |
| |
| | 211.765
|-
| |
| |
| |
| |
| |
| | 211.478
|-
| |
| |
| |
| |
| | 13/74
| | 210.811
|-
| |
| |
| |
| | 7/40
| |
| | 210
|-
| |
| |
| |
| |
| | 8/46
| | 208.696
|-
| | 1/6
| |
| |
| |
| |
| | 200
|}
[[Category:MOS scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Latest revision as of 13:58, 5 May 2025

↖ 5L 15s ↑ 6L 15s 7L 15s ↗
← 5L 16s 6L 16s 7L 16s →
↙ 5L 17s ↓ 6L 17s 7L 17s ↘
Scale structure
Step pattern LssLsssLsssLssLsssLsss
sssLsssLssLsssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 7\22 to 2\6 (381.8 ¢ to 400.0 ¢)
Dark 1\6 to 4\22 (200.0 ¢ to 218.2 ¢)
TAMNAMS information
Related to 6L 4s (lemon)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 6L 10s
Sister 16L 6s
Daughters 22L 6s, 6L 22s
Neutralized 12L 10s
2-Flought 28L 16s, 6L 38s
Equal tunings
Equalized (L:s = 1:1) 7\22 (381.8 ¢)
Supersoft (L:s = 4:3) 23\72 (383.3 ¢)
Soft (L:s = 3:2) 16\50 (384.0 ¢)
Semisoft (L:s = 5:3) 25\78 (384.6 ¢)
Basic (L:s = 2:1) 9\28 (385.7 ¢)
Semihard (L:s = 5:2) 20\62 (387.1 ¢)
Hard (L:s = 3:1) 11\34 (388.2 ¢)
Superhard (L:s = 4:1) 13\40 (390.0 ¢)
Collapsed (L:s = 1:0) 2\6 (400.0 ¢)
View • Talk • Edit

6L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 16 small steps, with a period of 3 large steps and 8 small steps that repeats every 600.0 ¢, or twice every octave. 6L 16s is a grandchild scale of 6L 4s, expanding it by 12 tones. Generators that produce this scale range from 381.8 ¢ to 400 ¢, or from 200 ¢ to 218.2 ¢.

It has a small major third as a generator instead of the medium to large major third which generates 3L 8s. With the half-octave equivalence, the third inverts to a "diatonic" whole tone of no more than 4/22edo (218.182 ¢).

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 16s
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 54.5 ¢
Major 1-mosstep M1ms L 54.5 ¢ to 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 109.1 ¢
Major 2-mosstep M2ms L + s 109.1 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 163.6 ¢
Major 3-mosstep M3ms L + 2s 163.6 ¢ to 200.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 200.0 ¢ to 218.2 ¢
Augmented 4-mosstep A4ms 2L + 2s 218.2 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0 ¢ to 272.7 ¢
Major 5-mosstep M5ms 2L + 3s 272.7 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0 ¢ to 327.3 ¢
Major 6-mosstep M6ms 2L + 4s 327.3 ¢ to 400.0 ¢
7-mosstep Diminished 7-mosstep d7ms L + 6s 200.0 ¢ to 381.8 ¢
Perfect 7-mosstep P7ms 2L + 5s 381.8 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 400.0 ¢ to 436.4 ¢
Major 8-mosstep M8ms 3L + 5s 436.4 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0 ¢ to 490.9 ¢
Major 9-mosstep M9ms 3L + 6s 490.9 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 400.0 ¢ to 545.5 ¢
Major 10-mosstep M10ms 3L + 7s 545.5 ¢ to 600.0 ¢
11-mosstep Perfect 11-mosstep P11ms 3L + 8s 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 600.0 ¢ to 654.5 ¢
Major 12-mosstep M12ms 4L + 8s 654.5 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 600.0 ¢ to 709.1 ¢
Major 13-mosstep M13ms 4L + 9s 709.1 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 600.0 ¢ to 763.6 ¢
Major 14-mosstep M14ms 4L + 10s 763.6 ¢ to 800.0 ¢
15-mosstep Perfect 15-mosstep P15ms 4L + 11s 800.0 ¢ to 818.2 ¢
Augmented 15-mosstep A15ms 5L + 10s 818.2 ¢ to 1000.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 800.0 ¢ to 872.7 ¢
Major 16-mosstep M16ms 5L + 11s 872.7 ¢ to 1000.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 800.0 ¢ to 927.3 ¢
Major 17-mosstep M17ms 5L + 12s 927.3 ¢ to 1000.0 ¢
18-mosstep Diminished 18-mosstep d18ms 4L + 14s 800.0 ¢ to 981.8 ¢
Perfect 18-mosstep P18ms 5L + 13s 981.8 ¢ to 1000.0 ¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 1000.0 ¢ to 1036.4 ¢
Major 19-mosstep M19ms 6L + 13s 1036.4 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 1000.0 ¢ to 1090.9 ¢
Major 20-mosstep M20ms 6L + 14s 1090.9 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms 5L + 16s 1000.0 ¢ to 1145.5 ¢
Major 21-mosstep M21ms 6L + 15s 1145.5 ¢ to 1200.0 ¢
22-mosstep Perfect 22-mosstep P22ms 6L + 16s 1200.0 ¢

Generator chain

Generator chain of 6L 16s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
13 Augmented 3-mosdegree A3md Augmented 14-mosdegree A14md
12 Augmented 7-mosdegree A7md Augmented 18-mosdegree A18md
11 Augmented 0-mosdegree A0md Augmented 11-mosdegree A11md
10 Augmented 4-mosdegree A4md Augmented 15-mosdegree A15md
9 Major 8-mosdegree M8md Major 19-mosdegree M19md
8 Major 1-mosdegree M1md Major 12-mosdegree M12md
7 Major 5-mosdegree M5md Major 16-mosdegree M16md
6 Major 9-mosdegree M9md Major 20-mosdegree M20md
5 Major 2-mosdegree M2md Major 13-mosdegree M13md
4 Major 6-mosdegree M6md Major 17-mosdegree M17md
3 Major 10-mosdegree M10md Major 21-mosdegree M21md
2 Major 3-mosdegree M3md Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md Perfect 18-mosdegree P18md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md		 Perfect 11-mosdegree
Perfect 22-mosdegree		 P11md
P22md
−1 Perfect 4-mosdegree P4md Perfect 15-mosdegree P15md
−2 Minor 8-mosdegree m8md Minor 19-mosdegree m19md
−3 Minor 1-mosdegree m1md Minor 12-mosdegree m12md
−4 Minor 5-mosdegree m5md Minor 16-mosdegree m16md
−5 Minor 9-mosdegree m9md Minor 20-mosdegree m20md
−6 Minor 2-mosdegree m2md Minor 13-mosdegree m13md
−7 Minor 6-mosdegree m6md Minor 17-mosdegree m17md
−8 Minor 10-mosdegree m10md Minor 21-mosdegree m21md
−9 Minor 3-mosdegree m3md Minor 14-mosdegree m14md
−10 Diminished 7-mosdegree d7md Diminished 18-mosdegree d18md
−11 Diminished 11-mosdegree d11md Diminished 22-mosdegree d22md
−12 Diminished 4-mosdegree d4md Diminished 15-mosdegree d15md
−13 Diminished 8-mosdegree d8md Diminished 19-mosdegree d19md

Modes

Scale degrees of the modes of 6L 16s
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
20|0(2) 1 LssLsssLsssLssLsssLsss Perf. Maj. Maj. Maj. Aug. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Aug. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
18|2(2) 8 LsssLssLsssLsssLssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
16|4(2) 4 LsssLsssLssLsssLsssLss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Min. Maj. Maj. Perf.
14|6(2) 11 sLssLsssLsssLssLsssLss Perf. Min. Maj. Maj. Perf. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Perf. Min. Maj. Maj. Perf.
12|8(2) 7 sLsssLssLsssLsssLssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Perf. Min. Maj. Maj. Perf.
10|10(2) 3 sLsssLsssLssLsssLsssLs Perf. Min. Maj. Maj. Perf. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Perf. Min. Min. Maj. Perf.
8|12(2) 10 ssLssLsssLsssLssLsssLs Perf. Min. Min. Maj. Perf. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Perf. Min. Min. Maj. Perf.
6|14(2) 6 ssLsssLssLsssLsssLssLs Perf. Min. Min. Maj. Perf. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Perf. Min. Min. Maj. Perf.
4|16(2) 2 ssLsssLsssLssLsssLsssL Perf. Min. Min. Maj. Perf. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Perf. Min. Min. Min. Perf.
2|18(2) 9 sssLssLsssLsssLssLsssL Perf. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Perf.
0|20(2) 5 sssLsssLssLsssLsssLssL Perf. Min. Min. Min. Perf. Min. Min. Dim. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Dim. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 16s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\22 381.818 218.182 1:1 1.000 Equalized 6L 16s
37\116 382.759 217.241 6:5 1.200
30\94 382.979 217.021 5:4 1.250
53\166 383.133 216.867 9:7 1.286
23\72 383.333 216.667 4:3 1.333 Supersoft 6L 16s
62\194 383.505 216.495 11:8 1.375
39\122 383.607 216.393 7:5 1.400
55\172 383.721 216.279 10:7 1.429
16\50 384.000 216.000 3:2 1.500 Soft 6L 16s
57\178 384.270 215.730 11:7 1.571
41\128 384.375 215.625 8:5 1.600
66\206 384.466 215.534 13:8 1.625
25\78 384.615 215.385 5:3 1.667 Semisoft 6L 16s
59\184 384.783 215.217 12:7 1.714
34\106 384.906 215.094 7:4 1.750
43\134 385.075 214.925 9:5 1.800
9\28 385.714 214.286 2:1 2.000 Basic 6L 16s
Scales with tunings softer than this are proper
38\118 386.441 213.559 9:4 2.250
29\90 386.667 213.333 7:3 2.333
49\152 386.842 213.158 12:5 2.400
20\62 387.097 212.903 5:2 2.500 Semihard 6L 16s
51\158 387.342 212.658 13:5 2.600
31\96 387.500 212.500 8:3 2.667
42\130 387.692 212.308 11:4 2.750
11\34 388.235 211.765 3:1 3.000 Hard 6L 16s
35\108 388.889 211.111 10:3 3.333
24\74 389.189 210.811 7:2 3.500
37\114 389.474 210.526 11:3 3.667
13\40 390.000 210.000 4:1 4.000 Superhard 6L 16s
28\86 390.698 209.302 9:2 4.500
15\46 391.304 208.696 5:1 5.000
17\52 392.308 207.692 6:1 6.000
2\6 400.000 200.000 1:0 → ∞ Collapsed 6L 16s
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