2L 5s: Difference between revisions
→Scale tree: general improvement |
Should go for symmetric mode by default (it has a symmetric and the least tuning deviation from 12edo A440) |
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| Line 7: | Line 7: | ||
| Equalized = 3 | | Equalized = 3 | ||
| Paucitonic = 1 | | Paucitonic = 1 | ||
| Pattern = | | Pattern = sLsssLs | ||
| Neutral = 4L 3s | | Neutral = 4L 3s | ||
}} | }} | ||
| Line 14: | Line 14: | ||
While antidiatonic is closely associated with [[mavila]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not [[7L 2s]] mavila superdiatonic scales. | While antidiatonic is closely associated with [[mavila]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not [[7L 2s]] mavila superdiatonic scales. | ||
== Notation == | == Notation == | ||
Diamond MOS notation, &/@ = raise and lower by one chroma. We'll write this using | Diamond MOS notation, &/@ = raise and lower by one chroma. We'll write this using DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz. The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up ''flattens'' a note by a chroma, rather than sharpening it as in diatonic ([[5L 2s]]). | ||
== Scale tree == | == Scale tree == | ||
Revision as of 14:09, 11 April 2021
User:IlL/Template:RTT restriction
| ↖ 1L 4s | ↑ 2L 4s | 3L 4s ↗ |
| ← 1L 5s | 2L 5s | 3L 5s → |
| ↙ 1L 6s | ↓ 2L 6s | 3L 6s ↘ |
sssLssL
2L 5s or antidiatonic refers to the structure of octave-equivalent MOS scales with generators ranging from 3\7 (3 degrees of 7edo = 514.29¢) to 1\2 (one degree of 2edo = 600¢). In the case of 7edo, L and s are the same size; in the case of 2edo, s becomes so small it disappears (and all that remains are the two equal L's).
While antidiatonic is closely associated with mavila, not every 2L 5s scale is an instance of "mavila", since some of them extend to 2L 7s scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales.
Notation
Diamond MOS notation, &/@ = raise and lower by one chroma. We'll write this using DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz. The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up flattens a note by a chroma, rather than sharpening it as in diatonic (5L 2s).
Scale tree
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 3\7 | 514.286 | 1 | 1 | 1.000 | ||||||
| 16\37 | 518.919 | 6 | 5 | 1.200 | ||||||
| 13\30 | 520.000 | 5 | 4 | 1.250 | ||||||
| 23\53 | 520.755 | 9 | 7 | 1.286 | ||||||
| 10\23 | 521.739 | 4 | 3 | 1.333 | ||||||
| 27\62 | 522.581 | 11 | 8 | 1.375 | ||||||
| 17\39 | 523.077 | 7 | 5 | 1.400 | ||||||
| 24\55 | 523.636 | 10 | 7 | 1.428 | ||||||
| 7\16 | 525.000 | 3 | 2 | 1.500 | L/s = 3/2, mavila is in this region | |||||
| 25\57 | 526.316 | 11 | 7 | 1.571 | ||||||
| 18\41 | 526.829 | 8 | 5 | 1.600 | ||||||
| 29\66 | 527.273 | 13 | 8 | 1.625 | Golden mavila | |||||
| 11\25 | 528.000 | 5 | 3 | 1.667 | ||||||
| 26\59 | 528.814 | 12 | 7 | 1.714 | ||||||
| 15\34 | 529.412 | 7 | 4 | 1.750 | ||||||
| 19\43 | 530.233 | 9 | 5 | 1.800 | ||||||
| 4\9 | 533.333 | 2 | 1 | 2.000 | Basic antidiatonic (Generators smaller than this are proper) | |||||
| 17\38 | 536.842 | 9 | 4 | 2.250 | ||||||
| 13\29 | 537.931 | 7 | 3 | 2.333 | ||||||
| 22\49 | 538.776 | 12 | 5 | 2.400 | ||||||
| 9\20 | 540.000 | 5 | 2 | 2.500 | ||||||
| 23\51 | 541.176 | 13 | 5 | 2.600 | Unnamed golden tuning | |||||
| 14\31 | 541.935 | 8 | 3 | 2.667 | ||||||
| 19\42 | 542.857 | 11 | 4 | 2.750 | ||||||
| 5\11 | 545.455 | 3 | 1 | 3.000 | L/s = 3/1 | |||||
| 16\35 | 548.571 | 10 | 3 | 3.333 | ||||||
| 11\24 | 550.000 | 7 | 2 | 3.500 | ||||||
| 17\37 | 551.351 | 11 | 3 | 3.667 | ||||||
| 6\13 | 553.846 | 4 | 1 | 4.000 | ||||||
| 13\28 | 557.143 | 9 | 2 | 4.500 | ||||||
| 7\15 | 560.000 | 5 | 1 | 5.000 | ||||||
| 8\17 | 564.706 | 6 | 1 | 6.000 | Liese↓, triton↓ | |||||
| 1\2 | 600.000 | 1 | 0 | → inf | ||||||
Musical Examples
Mike Battaglia has "translated" several common practice pieces into mavila antidiatonic by using Graham Breed's Lilypond code to tune the generators flat. Musical examples are provided in 9-EDO, 16-EDO, 23-EDO, and 25-EDO, for comparison. Note that the melodic and/or intonational properties differ slightly for each tuning.
9-EDO:
16-EDO:
23-EDO:
25-EDO: