14L 1s
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Scale structure
Step pattern
LLLLLLLLLLLLLLs
sLLLLLLLLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
1\15 to 1\14 (80.0¢ to 85.7¢)
Dark
13\14 to 14\15 (1114.3¢ to 1120.0¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
5:1 to 6:1
Related MOS scales
Parent
1L 13s
Sister
1L 14s
Daughters
15L 14s, 14L 15s
Neutralized
13L 2s
2-Flought
29L 1s, 14L 16s
Equal tunings
Equalized (L:s = 1:1)
1\15 (80.0¢)
Supersoft (L:s = 4:3)
4\59 (81.4¢)
Soft (L:s = 3:2)
3\44 (81.8¢)
Semisoft (L:s = 5:3)
5\73 (82.2¢)
Basic (L:s = 2:1)
2\29 (82.8¢)
Semihard (L:s = 5:2)
5\72 (83.3¢)
Hard (L:s = 3:1)
3\43 (83.7¢)
Superhard (L:s = 4:1)
4\57 (84.2¢)
Collapsed (L:s = 1:0)
1\14 (85.7¢)
| ← 13L 1s | 14L 1s | 15L 1s → |
| ↙ 13L 2s | ↓ 14L 2s | 15L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLLLLLLL
14L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 1 small step, repeating every octave. 14L 1s is related to 1L 9s, expanding it by 5 tones. Generators that produce this scale range from 80¢ to 85.7¢, or from 1114.3¢ to 1120¢. Scales of this form are always proper because there is only one small step.
This scale is notable for corresponding to 15-note scales of temperaments like nautilus and sextilififths. 6 steps of the scale cover a diatonic fourth, and they also go from the lower bound to upper bound of diatonic fourths (3\7 to 2\5) over the course of the entire step ratio spectrum, corresponding to going from 14edo perfect fourth to 15edo pefect fourth.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 14|0 | 1 | LLLLLLLLLLLLLLs |
| 13|1 | 2 | LLLLLLLLLLLLLsL |
| 12|2 | 3 | LLLLLLLLLLLLsLL |
| 11|3 | 4 | LLLLLLLLLLLsLLL |
| 10|4 | 5 | LLLLLLLLLLsLLLL |
| 9|5 | 6 | LLLLLLLLLsLLLLL |
| 8|6 | 7 | LLLLLLLLsLLLLLL |
| 7|7 | 8 | LLLLLLLsLLLLLLL |
| 6|8 | 9 | LLLLLLsLLLLLLLL |
| 5|9 | 10 | LLLLLsLLLLLLLLL |
| 4|10 | 11 | LLLLsLLLLLLLLLL |
| 3|11 | 12 | LLLsLLLLLLLLLLL |
| 2|12 | 13 | LLsLLLLLLLLLLLL |
| 1|13 | 14 | LsLLLLLLLLLLLLL |
| 0|14 | 15 | sLLLLLLLLLLLLLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0¢ to 80.0¢ |
| Perfect 1-mosstep | P1ms | L | 80.0¢ to 85.7¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 85.7¢ to 160.0¢ |
| Major 2-mosstep | M2ms | 2L | 160.0¢ to 171.4¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 171.4¢ to 240.0¢ |
| Major 3-mosstep | M3ms | 3L | 240.0¢ to 257.1¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 257.1¢ to 320.0¢ |
| Major 4-mosstep | M4ms | 4L | 320.0¢ to 342.9¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 342.9¢ to 400.0¢ |
| Major 5-mosstep | M5ms | 5L | 400.0¢ to 428.6¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 428.6¢ to 480.0¢ |
| Major 6-mosstep | M6ms | 6L | 480.0¢ to 514.3¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 514.3¢ to 560.0¢ |
| Major 7-mosstep | M7ms | 7L | 560.0¢ to 600.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 600.0¢ to 640.0¢ |
| Major 8-mosstep | M8ms | 8L | 640.0¢ to 685.7¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 685.7¢ to 720.0¢ |
| Major 9-mosstep | M9ms | 9L | 720.0¢ to 771.4¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 771.4¢ to 800.0¢ |
| Major 10-mosstep | M10ms | 10L | 800.0¢ to 857.1¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 10L + s | 857.1¢ to 880.0¢ |
| Major 11-mosstep | M11ms | 11L | 880.0¢ to 942.9¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 11L + s | 942.9¢ to 960.0¢ |
| Major 12-mosstep | M12ms | 12L | 960.0¢ to 1028.6¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 12L + s | 1028.6¢ to 1040.0¢ |
| Major 13-mosstep | M13ms | 13L | 1040.0¢ to 1114.3¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 13L + s | 1114.3¢ to 1120.0¢ |
| Augmented 14-mosstep | A14ms | 14L | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 14L + s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\15 | 80.000 | 1120.000 | 1:1 | 1.000 | Equalized 14L 1s | |||||
| 6\89 | 80.899 | 1119.101 | 6:5 | 1.200 | ||||||
| 5\74 | 81.081 | 1118.919 | 5:4 | 1.250 | ||||||
| 9\133 | 81.203 | 1118.797 | 9:7 | 1.286 | ||||||
| 4\59 | 81.356 | 1118.644 | 4:3 | 1.333 | Supersoft 14L 1s | |||||
| 11\162 | 81.481 | 1118.519 | 11:8 | 1.375 | ||||||
| 7\103 | 81.553 | 1118.447 | 7:5 | 1.400 | ||||||
| 10\147 | 81.633 | 1118.367 | 10:7 | 1.429 | ||||||
| 3\44 | 81.818 | 1118.182 | 3:2 | 1.500 | Soft 14L 1s Nautilus | |||||
| 11\161 | 81.988 | 1118.012 | 11:7 | 1.571 | ||||||
| 8\117 | 82.051 | 1117.949 | 8:5 | 1.600 | ||||||
| 13\190 | 82.105 | 1117.895 | 13:8 | 1.625 | ||||||
| 5\73 | 82.192 | 1117.808 | 5:3 | 1.667 | Semisoft 14L 1s | |||||
| 12\175 | 82.286 | 1117.714 | 12:7 | 1.714 | ||||||
| 7\102 | 82.353 | 1117.647 | 7:4 | 1.750 | ||||||
| 9\131 | 82.443 | 1117.557 | 9:5 | 1.800 | ||||||
| 2\29 | 82.759 | 1117.241 | 2:1 | 2.000 | Basic 14L 1s | |||||
| 9\130 | 83.077 | 1116.923 | 9:4 | 2.250 | ↕ Sextilififths | |||||
| 7\101 | 83.168 | 1116.832 | 7:3 | 2.333 | ||||||
| 12\173 | 83.237 | 1116.763 | 12:5 | 2.400 | ||||||
| 5\72 | 83.333 | 1116.667 | 5:2 | 2.500 | Semihard 14L 1s | |||||
| 13\187 | 83.422 | 1116.578 | 13:5 | 2.600 | ||||||
| 8\115 | 83.478 | 1116.522 | 8:3 | 2.667 | ||||||
| 11\158 | 83.544 | 1116.456 | 11:4 | 2.750 | ||||||
| 3\43 | 83.721 | 1116.279 | 3:1 | 3.000 | Hard 14L 1s | |||||
| 10\143 | 83.916 | 1116.084 | 10:3 | 3.333 | ||||||
| 7\100 | 84.000 | 1116.000 | 7:2 | 3.500 | ||||||
| 11\157 | 84.076 | 1115.924 | 11:3 | 3.667 | ||||||
| 4\57 | 84.211 | 1115.789 | 4:1 | 4.000 | Superhard 14L 1s | |||||
| 9\128 | 84.375 | 1115.625 | 9:2 | 4.500 | ||||||
| 5\71 | 84.507 | 1115.493 | 5:1 | 5.000 | ||||||
| 6\85 | 84.706 | 1115.294 | 6:1 | 6.000 | ||||||
| 1\14 | 85.714 | 1114.286 | 1:0 | → ∞ | Collapsed 14L 1s | |||||