11L 4s
Jump to navigation
Jump to search
Scale structure
Step pattern
LLLsLLLsLLLsLLs
sLLsLLLsLLLsLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
4\15 to 3\11 (320.0¢ to 327.3¢)
Dark
8\11 to 11\15 (872.7¢ to 880.0¢)
TAMNAMS information
Descends from
4L 3s (smitonic)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
4L 7s
Sister
4L 11s
Daughters
15L 11s, 11L 15s
Neutralized
7L 8s
2-Flought
26L 4s, 11L 19s
Equal tunings
Equalized (L:s = 1:1)
4\15 (320.0¢)
Supersoft (L:s = 4:3)
15\56 (321.4¢)
Soft (L:s = 3:2)
11\41 (322.0¢)
Semisoft (L:s = 5:3)
18\67 (322.4¢)
Basic (L:s = 2:1)
7\26 (323.1¢)
Semihard (L:s = 5:2)
17\63 (323.8¢)
Hard (L:s = 3:1)
10\37 (324.3¢)
Superhard (L:s = 4:1)
13\48 (325.0¢)
Collapsed (L:s = 1:0)
3\11 (327.3¢)
| ↖ 10L 3s | ↑ 11L 3s | 12L 3s ↗ |
| ← 10L 4s | 11L 4s | 12L 4s → |
| ↙ 10L 5s | ↓ 11L 5s | 12L 5s ↘ |
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥┬┐ │║║║│║║║│║║║│║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLLsLLLsLLL
11L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 4 small steps, repeating every octave. 11L 4s is a grandchild scale of 4L 3s, expanding it by 8 tones. Generators that produce this scale range from 320¢ to 327.3¢, or from 872.7¢ to 880¢. The bright generator represents a minor third slightly sharp of 6/5 (315.6¢), though this MOS is most reasonably interpreted in the 2.7.11 orgone temperament where it is identified as ~77/64. At its harmonic entropy minimum, the octave-reduced 7th harmonic (about 968¢) equals 3 of these generators.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 14|0 | 1 | LLLsLLLsLLLsLLs |
| 13|1 | 5 | LLLsLLLsLLsLLLs |
| 12|2 | 9 | LLLsLLsLLLsLLLs |
| 11|3 | 13 | LLsLLLsLLLsLLLs |
| 10|4 | 2 | LLsLLLsLLLsLLsL |
| 9|5 | 6 | LLsLLLsLLsLLLsL |
| 8|6 | 10 | LLsLLsLLLsLLLsL |
| 7|7 | 14 | LsLLLsLLLsLLLsL |
| 6|8 | 3 | LsLLLsLLLsLLsLL |
| 5|9 | 7 | LsLLLsLLsLLLsLL |
| 4|10 | 11 | LsLLsLLLsLLLsLL |
| 3|11 | 15 | sLLLsLLLsLLLsLL |
| 2|12 | 4 | sLLLsLLLsLLsLLL |
| 1|13 | 8 | sLLLsLLsLLLsLLL |
| 0|14 | 12 | sLLsLLLsLLLsLLL |
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 80.0¢ |
| Major 1-mosstep | M1ms | L | 80.0¢ to 109.1¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 109.1¢ to 160.0¢ |
| Major 2-mosstep | M2ms | 2L | 160.0¢ to 218.2¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 218.2¢ to 240.0¢ |
| Major 3-mosstep | M3ms | 3L | 240.0¢ to 327.3¢ | |
| 4-mosstep | Diminished 4-mosstep | d4ms | 2L + 2s | 218.2¢ to 320.0¢ |
| Perfect 4-mosstep | P4ms | 3L + s | 320.0¢ to 327.3¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 327.3¢ to 400.0¢ |
| Major 5-mosstep | M5ms | 4L + s | 400.0¢ to 436.4¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 436.4¢ to 480.0¢ |
| Major 6-mosstep | M6ms | 5L + s | 480.0¢ to 545.5¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 5L + 2s | 545.5¢ to 560.0¢ |
| Major 7-mosstep | M7ms | 6L + s | 560.0¢ to 654.5¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 5L + 3s | 545.5¢ to 640.0¢ |
| Major 8-mosstep | M8ms | 6L + 2s | 640.0¢ to 654.5¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 6L + 3s | 654.5¢ to 720.0¢ |
| Major 9-mosstep | M9ms | 7L + 2s | 720.0¢ to 763.6¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 7L + 3s | 763.6¢ to 800.0¢ |
| Major 10-mosstep | M10ms | 8L + 2s | 800.0¢ to 872.7¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 8L + 3s | 872.7¢ to 880.0¢ |
| Augmented 11-mosstep | A11ms | 9L + 2s | 880.0¢ to 981.8¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 8L + 4s | 872.7¢ to 960.0¢ |
| Major 12-mosstep | M12ms | 9L + 3s | 960.0¢ to 981.8¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 9L + 4s | 981.8¢ to 1040.0¢ |
| Major 13-mosstep | M13ms | 10L + 3s | 1040.0¢ to 1090.9¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 10L + 4s | 1090.9¢ to 1120.0¢ |
| Major 14-mosstep | M14ms | 11L + 3s | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 11L + 4s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 4\15 | 320.000 | 880.000 | 1:1 | 1.000 | Equalized 11L 4s | |||||
| 23\86 | 320.930 | 879.070 | 6:5 | 1.200 | ||||||
| 19\71 | 321.127 | 878.873 | 5:4 | 1.250 | ||||||
| 34\127 | 321.260 | 878.740 | 9:7 | 1.286 | ||||||
| 15\56 | 321.429 | 878.571 | 4:3 | 1.333 | Supersoft 11L 4s | |||||
| 41\153 | 321.569 | 878.431 | 11:8 | 1.375 | ||||||
| 26\97 | 321.649 | 878.351 | 7:5 | 1.400 | ||||||
| 37\138 | 321.739 | 878.261 | 10:7 | 1.429 | ||||||
| 11\41 | 321.951 | 878.049 | 3:2 | 1.500 | Soft 11L 4s | |||||
| 40\149 | 322.148 | 877.852 | 11:7 | 1.571 | ||||||
| 29\108 | 322.222 | 877.778 | 8:5 | 1.600 | ||||||
| 47\175 | 322.286 | 877.714 | 13:8 | 1.625 | ||||||
| 18\67 | 322.388 | 877.612 | 5:3 | 1.667 | Semisoft 11L 4s | |||||
| 43\160 | 322.500 | 877.500 | 12:7 | 1.714 | ||||||
| 25\93 | 322.581 | 877.419 | 7:4 | 1.750 | ||||||
| 32\119 | 322.689 | 877.311 | 9:5 | 1.800 | ||||||
| 7\26 | 323.077 | 876.923 | 2:1 | 2.000 | Basic 11L 4s Scales with tunings softer than this are proper | |||||
| 31\115 | 323.478 | 876.522 | 9:4 | 2.250 | ||||||
| 24\89 | 323.596 | 876.404 | 7:3 | 2.333 | ||||||
| 41\152 | 323.684 | 876.316 | 12:5 | 2.400 | ||||||
| 17\63 | 323.810 | 876.190 | 5:2 | 2.500 | Semihard 11L 4s | |||||
| 44\163 | 323.926 | 876.074 | 13:5 | 2.600 | ||||||
| 27\100 | 324.000 | 876.000 | 8:3 | 2.667 | ||||||
| 37\137 | 324.088 | 875.912 | 11:4 | 2.750 | ||||||
| 10\37 | 324.324 | 875.676 | 3:1 | 3.000 | Hard 11L 4s | |||||
| 33\122 | 324.590 | 875.410 | 10:3 | 3.333 | ||||||
| 23\85 | 324.706 | 875.294 | 7:2 | 3.500 | ||||||
| 36\133 | 324.812 | 875.188 | 11:3 | 3.667 | ||||||
| 13\48 | 325.000 | 875.000 | 4:1 | 4.000 | Superhard 11L 4s | |||||
| 29\107 | 325.234 | 874.766 | 9:2 | 4.500 | ||||||
| 16\59 | 325.424 | 874.576 | 5:1 | 5.000 | ||||||
| 19\70 | 325.714 | 874.286 | 6:1 | 6.000 | ||||||
| 3\11 | 327.273 | 872.727 | 1:0 | → ∞ | Collapsed 11L 4s | |||||