6L 5s
↖ 5L 4s | ↑ 6L 4s | 7L 4s ↗ |
← 5L 5s | 6L 5s | 7L 5s → |
↙ 5L 6s | ↓ 6L 6s | 7L 6s ↘ |
┌╥╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
sLsLsLsLsLL
6L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 5 small steps, repeating every octave. 6L 5s is a child scale of 5L 1s, expanding it by 5 tones. Generators that produce this scale range from 981.8 ¢ to 1000 ¢, or from 200 ¢ to 218.2 ¢. The name amsochromic has been proposed for this scale by Lériendil, originally assigned to 5L 6s by Praveen Venkataramana and standing for "acute major second chromatic"; the name was moved to 6L 5s due to the existing use of "slentonic" for the other MOS.
This MOS has a harmonic entropy minimum (Baldy) which is highly improper (L = 8, s = 1) in an optimal tuning, However, its saving grace is that it at least has index 2 in syntonic temperaments with wide fifths like superpyth (2.3.7) and pentacircle (2.3.11/7.13/11)[clarification needed].
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 diatonic interval categories.
Intervals
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 109.1 ¢ |
Major 1-mosstep | M1ms | L | 109.1 ¢ to 200.0 ¢ | |
2-mosstep | Perfect 2-mosstep | P2ms | L + s | 200.0 ¢ to 218.2 ¢ |
Augmented 2-mosstep | A2ms | 2L | 218.2 ¢ to 400.0 ¢ | |
3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 200.0 ¢ to 327.3 ¢ |
Major 3-mosstep | M3ms | 2L + s | 327.3 ¢ to 400.0 ¢ | |
4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 400.0 ¢ to 436.4 ¢ |
Major 4-mosstep | M4ms | 3L + s | 436.4 ¢ to 600.0 ¢ | |
5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 400.0 ¢ to 545.5 ¢ |
Major 5-mosstep | M5ms | 3L + 2s | 545.5 ¢ to 600.0 ¢ | |
6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 600.0 ¢ to 654.5 ¢ |
Major 6-mosstep | M6ms | 4L + 2s | 654.5 ¢ to 800.0 ¢ | |
7-mosstep | Minor 7-mosstep | m7ms | 3L + 4s | 600.0 ¢ to 763.6 ¢ |
Major 7-mosstep | M7ms | 4L + 3s | 763.6 ¢ to 800.0 ¢ | |
8-mosstep | Minor 8-mosstep | m8ms | 4L + 4s | 800.0 ¢ to 872.7 ¢ |
Major 8-mosstep | M8ms | 5L + 3s | 872.7 ¢ to 1000.0 ¢ | |
9-mosstep | Diminished 9-mosstep | d9ms | 4L + 5s | 800.0 ¢ to 981.8 ¢ |
Perfect 9-mosstep | P9ms | 5L + 4s | 981.8 ¢ to 1000.0 ¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 5L + 5s | 1000.0 ¢ to 1090.9 ¢ |
Major 10-mosstep | M10ms | 6L + 4s | 1090.9 ¢ to 1200.0 ¢ | |
11-mosstep | Perfect 11-mosstep | P11ms | 6L + 5s | 1200.0 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
16 | Augmented 1-mosdegree | A1md |
15 | Augmented 3-mosdegree | A3md |
14 | Augmented 5-mosdegree | A5md |
13 | Augmented 7-mosdegree | A7md |
12 | Augmented 9-mosdegree | A9md |
11 | Augmented 0-mosdegree | A0md |
10 | Augmented 2-mosdegree | A2md |
9 | Major 4-mosdegree | M4md |
8 | Major 6-mosdegree | M6md |
7 | Major 8-mosdegree | M8md |
6 | Major 10-mosdegree | M10md |
5 | Major 1-mosdegree | M1md |
4 | Major 3-mosdegree | M3md |
3 | Major 5-mosdegree | M5md |
2 | Major 7-mosdegree | M7md |
1 | Perfect 9-mosdegree | P9md |
0 | Perfect 0-mosdegree Perfect 11-mosdegree |
P0md P11md |
−1 | Perfect 2-mosdegree | P2md |
−2 | Minor 4-mosdegree | m4md |
−3 | Minor 6-mosdegree | m6md |
−4 | Minor 8-mosdegree | m8md |
−5 | Minor 10-mosdegree | m10md |
−6 | Minor 1-mosdegree | m1md |
−7 | Minor 3-mosdegree | m3md |
−8 | Minor 5-mosdegree | m5md |
−9 | Minor 7-mosdegree | m7md |
−10 | Diminished 9-mosdegree | d9md |
−11 | Diminished 11-mosdegree | d11md |
−12 | Diminished 2-mosdegree | d2md |
−13 | Diminished 4-mosdegree | d4md |
−14 | Diminished 6-mosdegree | d6md |
−15 | Diminished 8-mosdegree | d8md |
−16 | Diminished 10-mosdegree | d10md |
Modes
UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||
10|0 | 1 | LLsLsLsLsLs | Perf. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
9|1 | 10 | LsLLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
8|2 | 8 | LsLsLLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
7|3 | 6 | LsLsLsLLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Perf. |
6|4 | 4 | LsLsLsLsLLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Perf. |
5|5 | 2 | LsLsLsLsLsL | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
4|6 | 11 | sLLsLsLsLsL | Perf. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
3|7 | 9 | sLsLLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
2|8 | 7 | sLsLsLLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
1|9 | 5 | sLsLsLsLLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
0|10 | 3 | sLsLsLsLsLL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Perf. |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
9\11 | 981.818 | 218.182 | 1:1 | 1.000 | Equalized 6L 5s | |||||
50\61 | 983.607 | 216.393 | 6:5 | 1.200 | ||||||
41\50 | 984.000 | 216.000 | 5:4 | 1.250 | ||||||
73\89 | 984.270 | 215.730 | 9:7 | 1.286 | ||||||
32\39 | 984.615 | 215.385 | 4:3 | 1.333 | Supersoft 6L 5s | |||||
87\106 | 984.906 | 215.094 | 11:8 | 1.375 | ||||||
55\67 | 985.075 | 214.925 | 7:5 | 1.400 | ||||||
78\95 | 985.263 | 214.737 | 10:7 | 1.429 | ||||||
23\28 | 985.714 | 214.286 | 3:2 | 1.500 | Soft 6L 5s | |||||
83\101 | 986.139 | 213.861 | 11:7 | 1.571 | ||||||
60\73 | 986.301 | 213.699 | 8:5 | 1.600 | ||||||
97\118 | 986.441 | 213.559 | 13:8 | 1.625 | ||||||
37\45 | 986.667 | 213.333 | 5:3 | 1.667 | Semisoft 6L 5s | |||||
88\107 | 986.916 | 213.084 | 12:7 | 1.714 | ||||||
51\62 | 987.097 | 212.903 | 7:4 | 1.750 | ||||||
65\79 | 987.342 | 212.658 | 9:5 | 1.800 | ||||||
14\17 | 988.235 | 211.765 | 2:1 | 2.000 | Basic 6L 5s Scales with tunings softer than this are proper | |||||
61\74 | 989.189 | 210.811 | 9:4 | 2.250 | ||||||
47\57 | 989.474 | 210.526 | 7:3 | 2.333 | ||||||
80\97 | 989.691 | 210.309 | 12:5 | 2.400 | ||||||
33\40 | 990.000 | 210.000 | 5:2 | 2.500 | Semihard 6L 5s | |||||
85\103 | 990.291 | 209.709 | 13:5 | 2.600 | ||||||
52\63 | 990.476 | 209.524 | 8:3 | 2.667 | ||||||
71\86 | 990.698 | 209.302 | 11:4 | 2.750 | ||||||
19\23 | 991.304 | 208.696 | 3:1 | 3.000 | Hard 6L 5s | |||||
62\75 | 992.000 | 208.000 | 10:3 | 3.333 | ||||||
43\52 | 992.308 | 207.692 | 7:2 | 3.500 | ||||||
67\81 | 992.593 | 207.407 | 11:3 | 3.667 | ||||||
24\29 | 993.103 | 206.897 | 4:1 | 4.000 | Superhard 6L 5s | |||||
53\64 | 993.750 | 206.250 | 9:2 | 4.500 | ||||||
29\35 | 994.286 | 205.714 | 5:1 | 5.000 | ||||||
34\41 | 995.122 | 204.878 | 6:1 | 6.000 | ||||||
5\6 | 1000.000 | 200.000 | 1:0 | → ∞ | Collapsed 6L 5s |