6L 5s
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Scale structure
Step pattern
LLsLsLsLsLs
sLsLsLsLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
9\11 to 5\6 (981.8¢ to 1000.0¢)
Dark
1\6 to 2\11 (200.0¢ to 218.2¢)
TAMNAMS information
Descends from
5L 1s
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
5L 1s
Sister
5L 6s
Daughters
11L 6s, 6L 11s
Neutralized
1L 10s
2-Flought
17L 5s, 6L 16s
Equal tunings
Equalized (L:s = 1:1)
9\11 (981.8¢)
Supersoft (L:s = 4:3)
32\39 (984.6¢)
Soft (L:s = 3:2)
23\28 (985.7¢)
Semisoft (L:s = 5:3)
37\45 (986.7¢)
Basic (L:s = 2:1)
14\17 (988.2¢)
Semihard (L:s = 5:2)
33\40 (990.0¢)
Hard (L:s = 3:1)
19\23 (991.3¢)
Superhard (L:s = 4:1)
24\29 (993.1¢)
Collapsed (L:s = 1:0)
5\6 (1000.0¢)
| ↖ 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¢.
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 ].
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 10|0 | 1 | LLsLsLsLsLs |
| 9|1 | 10 | LsLLsLsLsLs |
| 8|2 | 8 | LsLsLLsLsLs |
| 7|3 | 6 | LsLsLsLLsLs |
| 6|4 | 4 | LsLsLsLsLLs |
| 5|5 | 2 | LsLsLsLsLsL |
| 4|6 | 11 | sLLsLsLsLsL |
| 3|7 | 9 | sLsLLsLsLsL |
| 2|8 | 7 | sLsLsLLsLsL |
| 1|9 | 5 | sLsLsLsLLsL |
| 0|10 | 3 | sLsLsLsLsLL |
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¢ |
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 | |||||