3L 16s: Difference between revisions
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro}} | {{MOS intro}} | ||
This scale is associated with [[magic]] temperament, where 5 bright generators maps to [[3/1]] and the generator is a flat [[5/4]], and [[würschmidt]] temperament, where 8 bright generators map to [[6/1]] and the generator is a slightly sharp [[5/4]]. | This scale is associated with [[magic]] temperament, where 5 bright generators maps to [[3/1]] and the generator is a flat [[5/4]], and [[würschmidt]] temperament, where 8 bright generators map to [[6/1]] and the generator is a slightly sharp [[5/4]]. | ||
== Modes == | == Modes == | ||
{{MOS modes}} | {{MOS modes}} | ||
== Intervals == | |||
{{MOS intervals}} | |||
== Scale tree == | == Scale tree == | ||
{{Todo|review|inline=1|text=Review entries from past page revision and enter them into the scale tree.}}{{Scale tree|depth=5|Comments=11/8:[[Witchcraft]]; 3/2:[[Magic]] is around here; 13/8:[[Necromancy]]<br>Golden magic (380.8191¢); 12/5:[[Marveltri]] is around here; 13/5:Unnamed golden tuning (383.2314¢); 9/2:[[Sulis]]; 5/1:[[Grendel]]/[[Würschmidt]]}} | {{Todo|review|inline=1|text=Review entries from past page revision and enter them into the scale tree.}}{{Scale tree|depth=5|Comments=11/8:[[Witchcraft]]; 3/2:[[Magic]] is around here; 13/8:[[Necromancy]]<br>Golden magic (380.8191¢); 12/5:[[Marveltri]] is around here; 13/5:Unnamed golden tuning (383.2314¢); 9/2:[[Sulis]]; 5/1:[[Grendel]]/[[Würschmidt]]}} | ||
{{todo|expand}} | |||
[[Category:19-tone scales]] | [[Category:19-tone scales]] | ||
[[Category:Magic]] | [[Category:Magic]] | ||
Revision as of 23:49, 15 December 2024
| ↖ 2L 15s | ↑ 3L 15s | 4L 15s ↗ |
| ← 2L 16s | 3L 16s | 4L 16s → |
| ↙ 2L 17s | ↓ 3L 17s | 4L 17s ↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║│││││║│││││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssssLsssssLsssssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9 ¢ to 400 ¢, or from 800 ¢ to 821.1 ¢.
This scale is associated with magic temperament, where 5 bright generators maps to 3/1 and the generator is a flat 5/4, and würschmidt temperament, where 8 bright generators map to 6/1 and the generator is a slightly sharp 5/4.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 18|0 | 1 | LsssssLsssssLssssss |
| 17|1 | 7 | LsssssLssssssLsssss |
| 16|2 | 13 | LssssssLsssssLsssss |
| 15|3 | 19 | sLsssssLsssssLsssss |
| 14|4 | 6 | sLsssssLssssssLssss |
| 13|5 | 12 | sLssssssLsssssLssss |
| 12|6 | 18 | ssLsssssLsssssLssss |
| 11|7 | 5 | ssLsssssLssssssLsss |
| 10|8 | 11 | ssLssssssLsssssLsss |
| 9|9 | 17 | sssLsssssLsssssLsss |
| 8|10 | 4 | sssLsssssLssssssLss |
| 7|11 | 10 | sssLssssssLsssssLss |
| 6|12 | 16 | ssssLsssssLsssssLss |
| 5|13 | 3 | ssssLsssssLssssssLs |
| 4|14 | 9 | ssssLssssssLsssssLs |
| 3|15 | 15 | sssssLsssssLsssssLs |
| 2|16 | 2 | sssssLsssssLssssssL |
| 1|17 | 8 | sssssLssssssLsssssL |
| 0|18 | 14 | ssssssLsssssLsssssL |
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 63.2 ¢ |
| Major 1-mosstep | M1ms | L | 63.2 ¢ to 400.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 126.3 ¢ |
| Major 2-mosstep | M2ms | L + s | 126.3 ¢ to 400.0 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0 ¢ to 189.5 ¢ |
| Major 3-mosstep | M3ms | L + 2s | 189.5 ¢ to 400.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0 ¢ to 252.6 ¢ |
| Major 4-mosstep | M4ms | L + 3s | 252.6 ¢ to 400.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 5s | 0.0 ¢ to 315.8 ¢ |
| Major 5-mosstep | M5ms | L + 4s | 315.8 ¢ to 400.0 ¢ | |
| 6-mosstep | Diminished 6-mosstep | d6ms | 6s | 0.0 ¢ to 378.9 ¢ |
| Perfect 6-mosstep | P6ms | L + 5s | 378.9 ¢ to 400.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 400.0 ¢ to 442.1 ¢ |
| Major 7-mosstep | M7ms | 2L + 5s | 442.1 ¢ to 800.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 400.0 ¢ to 505.3 ¢ |
| Major 8-mosstep | M8ms | 2L + 6s | 505.3 ¢ to 800.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 400.0 ¢ to 568.4 ¢ |
| Major 9-mosstep | M9ms | 2L + 7s | 568.4 ¢ to 800.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | L + 9s | 400.0 ¢ to 631.6 ¢ |
| Major 10-mosstep | M10ms | 2L + 8s | 631.6 ¢ to 800.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | L + 10s | 400.0 ¢ to 694.7 ¢ |
| Major 11-mosstep | M11ms | 2L + 9s | 694.7 ¢ to 800.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | L + 11s | 400.0 ¢ to 757.9 ¢ |
| Major 12-mosstep | M12ms | 2L + 10s | 757.9 ¢ to 800.0 ¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 2L + 11s | 800.0 ¢ to 821.1 ¢ |
| Augmented 13-mosstep | A13ms | 3L + 10s | 821.1 ¢ to 1200.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 2L + 12s | 800.0 ¢ to 884.2 ¢ |
| Major 14-mosstep | M14ms | 3L + 11s | 884.2 ¢ to 1200.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 2L + 13s | 800.0 ¢ to 947.4 ¢ |
| Major 15-mosstep | M15ms | 3L + 12s | 947.4 ¢ to 1200.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 2L + 14s | 800.0 ¢ to 1010.5 ¢ |
| Major 16-mosstep | M16ms | 3L + 13s | 1010.5 ¢ to 1200.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 2L + 15s | 800.0 ¢ to 1073.7 ¢ |
| Major 17-mosstep | M17ms | 3L + 14s | 1073.7 ¢ to 1200.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 2L + 16s | 800.0 ¢ to 1136.8 ¢ |
| Major 18-mosstep | M18ms | 3L + 15s | 1136.8 ¢ to 1200.0 ¢ | |
| 19-mosstep | Perfect 19-mosstep | P19ms | 3L + 16s | 1200.0 ¢ |
Scale tree
|
Todo: review Review entries from past page revision and enter them into the scale tree. |