5L 6s
↖ 4L 5s | ↑ 5L 5s | 6L 5s ↗ |
← 4L 6s | 5L 6s | 6L 6s → |
↙ 4L 7s | ↓ 5L 7s | 6L 7s ↘ |
┌╥┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║│││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLsLsLsL
5L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 6 small steps, repeating every octave. 5L 6s is a child scale of 5L 1s, expanding it by 5 tones. Generators that produce this scale range from 218.2 ¢ to 240 ¢, or from 960 ¢ to 981.8 ¢.
This pattern has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 ¢ flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root. The name for this MOS pattern is p-chro machinoid, although the alternative name mothroid was given by CompactStar as part of their temperament-centric MOS naming system (TCMNAMS). It has also been named slentonic by Inthar, after slendric temperament.
Scale properties
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 240.0 ¢ | |
2-mosstep | Diminished 2-mosstep | d2ms | 2s | 0.0 ¢ to 218.2 ¢ |
Perfect 2-mosstep | P2ms | L + s | 218.2 ¢ to 240.0 ¢ | |
3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 240.0 ¢ to 327.3 ¢ |
Major 3-mosstep | M3ms | 2L + s | 327.3 ¢ to 480.0 ¢ | |
4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 240.0 ¢ to 436.4 ¢ |
Major 4-mosstep | M4ms | 2L + 2s | 436.4 ¢ to 480.0 ¢ | |
5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 480.0 ¢ to 545.5 ¢ |
Major 5-mosstep | M5ms | 3L + 2s | 545.5 ¢ to 720.0 ¢ | |
6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 480.0 ¢ to 654.5 ¢ |
Major 6-mosstep | M6ms | 3L + 3s | 654.5 ¢ to 720.0 ¢ | |
7-mosstep | Minor 7-mosstep | m7ms | 3L + 4s | 720.0 ¢ to 763.6 ¢ |
Major 7-mosstep | M7ms | 4L + 3s | 763.6 ¢ to 960.0 ¢ | |
8-mosstep | Minor 8-mosstep | m8ms | 3L + 5s | 720.0 ¢ to 872.7 ¢ |
Major 8-mosstep | M8ms | 4L + 4s | 872.7 ¢ to 960.0 ¢ | |
9-mosstep | Perfect 9-mosstep | P9ms | 4L + 5s | 960.0 ¢ to 981.8 ¢ |
Augmented 9-mosstep | A9ms | 5L + 4s | 981.8 ¢ to 1200.0 ¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 4L + 6s | 960.0 ¢ to 1090.9 ¢ |
Major 10-mosstep | M10ms | 5L + 5s | 1090.9 ¢ to 1200.0 ¢ | |
11-mosstep | Perfect 11-mosstep | P11ms | 5L + 6s | 1200.0 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
15 | Augmented 8-mosdegree | A8md |
14 | Augmented 6-mosdegree | A6md |
13 | Augmented 4-mosdegree | A4md |
12 | Augmented 2-mosdegree | A2md |
11 | Augmented 0-mosdegree | A0md |
10 | Augmented 9-mosdegree | A9md |
9 | Major 7-mosdegree | M7md |
8 | Major 5-mosdegree | M5md |
7 | Major 3-mosdegree | M3md |
6 | Major 1-mosdegree | M1md |
5 | Major 10-mosdegree | M10md |
4 | Major 8-mosdegree | M8md |
3 | Major 6-mosdegree | M6md |
2 | Major 4-mosdegree | M4md |
1 | Perfect 2-mosdegree | P2md |
0 | Perfect 0-mosdegree Perfect 11-mosdegree |
P0md P11md |
−1 | Perfect 9-mosdegree | P9md |
−2 | Minor 7-mosdegree | m7md |
−3 | Minor 5-mosdegree | m5md |
−4 | Minor 3-mosdegree | m3md |
−5 | Minor 1-mosdegree | m1md |
−6 | Minor 10-mosdegree | m10md |
−7 | Minor 8-mosdegree | m8md |
−8 | Minor 6-mosdegree | m6md |
−9 | Minor 4-mosdegree | m4md |
−10 | Diminished 2-mosdegree | d2md |
−11 | Diminished 11-mosdegree | d11md |
−12 | Diminished 9-mosdegree | d9md |
−13 | Diminished 7-mosdegree | d7md |
−14 | Diminished 5-mosdegree | d5md |
−15 | Diminished 3-mosdegree | d3md |
Modes
UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||
10|0 | 1 | LsLsLsLsLss | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Perf. |
9|1 | 3 | LsLsLsLssLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
8|2 | 5 | LsLsLssLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
7|3 | 7 | LsLssLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
6|4 | 9 | LssLsLsLsLs | Perf. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
5|5 | 11 | sLsLsLsLsLs | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
4|6 | 2 | sLsLsLsLssL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Perf. |
3|7 | 4 | sLsLsLssLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Min. | Perf. | Min. | Perf. |
2|8 | 6 | sLsLssLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
1|9 | 8 | sLssLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
0|10 | 10 | ssLsLsLsLsL | Perf. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
2\11 | 218.182 | 981.818 | 1:1 | 1.000 | Equalized 5L 6s | |||||
11\60 | 220.000 | 980.000 | 6:5 | 1.200 | ||||||
9\49 | 220.408 | 979.592 | 5:4 | 1.250 | ||||||
16\87 | 220.690 | 979.310 | 9:7 | 1.286 | ||||||
7\38 | 221.053 | 978.947 | 4:3 | 1.333 | Supersoft 5L 6s | |||||
19\103 | 221.359 | 978.641 | 11:8 | 1.375 | ||||||
12\65 | 221.538 | 978.462 | 7:5 | 1.400 | ||||||
17\92 | 221.739 | 978.261 | 10:7 | 1.429 | ||||||
5\27 | 222.222 | 977.778 | 3:2 | 1.500 | Soft 5L 6s | |||||
18\97 | 222.680 | 977.320 | 11:7 | 1.571 | ||||||
13\70 | 222.857 | 977.143 | 8:5 | 1.600 | ||||||
21\113 | 223.009 | 976.991 | 13:8 | 1.625 | ||||||
8\43 | 223.256 | 976.744 | 5:3 | 1.667 | Semisoft 5L 6s | |||||
19\102 | 223.529 | 976.471 | 12:7 | 1.714 | ||||||
11\59 | 223.729 | 976.271 | 7:4 | 1.750 | ||||||
14\75 | 224.000 | 976.000 | 9:5 | 1.800 | ||||||
3\16 | 225.000 | 975.000 | 2:1 | 2.000 | Basic 5L 6s Scales with tunings softer than this are proper | |||||
13\69 | 226.087 | 973.913 | 9:4 | 2.250 | ||||||
10\53 | 226.415 | 973.585 | 7:3 | 2.333 | ||||||
17\90 | 226.667 | 973.333 | 12:5 | 2.400 | ||||||
7\37 | 227.027 | 972.973 | 5:2 | 2.500 | Semihard 5L 6s Shoe | |||||
18\95 | 227.368 | 972.632 | 13:5 | 2.600 | ||||||
11\58 | 227.586 | 972.414 | 8:3 | 2.667 | ||||||
15\79 | 227.848 | 972.152 | 11:4 | 2.750 | ||||||
4\21 | 228.571 | 971.429 | 3:1 | 3.000 | Hard 5L 6s | |||||
13\68 | 229.412 | 970.588 | 10:3 | 3.333 | ||||||
9\47 | 229.787 | 970.213 | 7:2 | 3.500 | ||||||
14\73 | 230.137 | 969.863 | 11:3 | 3.667 | ||||||
5\26 | 230.769 | 969.231 | 4:1 | 4.000 | Superhard 5L 6s | |||||
11\57 | 231.579 | 968.421 | 9:2 | 4.500 | Cynder | |||||
6\31 | 232.258 | 967.742 | 5:1 | 5.000 | Mothra | |||||
7\36 | 233.333 | 966.667 | 6:1 | 6.000 | Slendric, Rodan ↓ | |||||
1\5 | 240.000 | 960.000 | 1:0 | → ∞ | Collapsed 5L 6s |