Mavila
- This page is about the regular temperament. For the scale structures sometimes associated with it, see 7L 2s and 2L 5s.
Mavila is a temperament where the major chroma, 135/128, is tempered out. Like meantone, mavila is based on the chain of fifths, but as a result of tempering out 135/128 rather than 81/80, the fifths are supposedly very flat (~670 – 680 ¢ or so), flatter than even that of 7edo (4\7). Consequently, stacking 7 of these fifths gives you an antidiatonic mos scale, where in a certain sense, major and minor intervals get reversed. For example, stacking four fifths and octave-reducing now gets you a 6/5 minor third, whereas stacking three fourths and octave-reducing now gets you a 5/4 major third. Note that since we have a heptatonic scale, terms like fifths, thirds, etc. make perfect sense and really are the fifth, third, etc. steps in the antidiatonic scale.
This has some very strange implications for music. The mavila antidiatonic scale is similar to the normal diatonic scale, except interval classes are flipped. Wherever there was a major third, you will find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major – instead of a diminished triad in the major scale, there is now an augmented triad.
As an example, the anti-Ionian scale has steps of ssLsssL, which looks like the regular Ionian scale except the "L" intervals are now "s" and vice versa.
Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in antidiatonic. That is, with Beethoven's Für Elise, there are actually two compositions – the one that you know, and the antidiatonic equivalent that has never been heard before until now. Examples of this are provided in the #Music section.
Mavila tunings range from 9edo to 7edo, with 16edo, 23edo, and 25edo being typical. These tunings detune 5/4 and 3/2 by significant amounts; it is thus reasonable to call mavila an exotemperament, though it is certainly more accurate than the archetypal exotemperaments such as father.
Mavila's antidiatonic scale is similar to Pelog scales used in Indonesian gamelan music. While Pelog's exact tuning is subject to significant regional variation and usually has unequal intervals throughout the scale (as opposed to having exactly two interval sizes), it can be well approximated by the antidiatonic scales of 9edo and 16edo.
Mavila was first discovered by Erv Wilson, possibly in 1989[1], after studying the tuning of the timbila music of the Chopi tribe in Mozambique.
See Mavila family #Mavila for more technical data.
Interval chain
In the following table, odd harmonics 1–11 and their inverses are in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 679.0 | 3/2, 16/11, 22/15 |
| 2 | 158.0 | 9/8, 11/10, 12/11, 16/15 |
| 3 | 836.9 | 8/5, 18/11 |
| 4 | 315.9 | 6/5 |
| 5 | 994.9 | 9/5 |
| 6 | 473.9 | 27/20, 32/25 |
| 7 | 1152.8 | 48/25, 108/55 |
* In 2.3.5.11-subgroup CWE tuning, octave reduced
Modal harmony
Scales
- Mavila-eb – 12-tone chromatic scale, equal-beating tuning
MOS tree
In addition to the 7-note anti-diatonic scale described, Mavila also has a 9 note "superdiatonic" mos, the "super-Ionian" mode of which looks LLLsLLLLs. This is the basis for the Armodue theory.
Mavila generates a 16-tone "chromatic" mos. In a certain sense, much of mavila makes sense if viewed within the lens of a 16-tone chromatic gamut, similarly to how much of meantone is thought of in the setting of a 12-tone chromatic gamut.
After the 16-tone "chromatic" scale is the 23-tone or 25-tone "enharmonic" mos (depending on the tuning of the fifth), which can be thought of as an "extended mavila" analogous to the "extended meantone" 19-tone enharmonic scale. The two alternative enharmonic scales are similar to how if the fifth is tuned sharper than 12edo, it will generate a 17-tone mos rather than a 19-tone one.
Tunings
The fifths of mavila are very flat – 16edo (675.0 ¢) and 23edo (678.3 ¢) are typical tunings. As a result, mavila is best played with stretched octaves and/or specialized timbres: either timbres with high rolloff (e.g. sine waves, marimba, and ocarina) or high inharmonicity (i.e. detuned partials, such as Gamelans, bells, or Timbila instruments).
As with meantone, mavila has its own tuning spectrum. 7edo, with its 685.714 ¢ fifth, is often thought of as an informal dividing line between meantone and mavila, in which case it forms the sharpmost endpoint on the mavila tuning spectrum and the flatmost endpoint of the meantone spectrum: if the fifth is flatter than this, it will generate anti-diatonic scales, and if it is sharper than this, it will generate diatonic scales. The fifth of 9edo is also often thought of as the other (flatmost) endpoint on the mavila spectrum.
Much like meantone, mavila is supported by several low-numbered edos, which will basically be the same size as the mosses listed above.
7edo can be thought of as a primitive tuning, yielding a completely equal heptatonic scale that is equally diatonic and anti-diatonic.
The next edo supporting mavila is 9edo, which has a fifth of 666.67 ¢ and approximates the Pelog tuning commonly found in Indonesian gamelan music. 9edo can be thought of as the first mavila edo (and the first edo in general) differentiating between 4:5:6 major and 10:12:15 minor chords. This is fairly interesting, as there is no real equivalent in meantone terms. It is larger than the "diatonic" sized mos, but smaller than the 16-tone "chromatic" mos. It is best thought of as a "superdiatonic" scale.
It is also supported by 16edo, which is probably the most common tuning for mavila temperament. This can be thought of as the first edo offering the potential for chromatic mavila harmony, similar to 12edo for meantone. This is also the usual setting for the aforementioned Armodue theory, although the Armodue theory can easily be extended to larger mavila scales such as Mavila[23].
The next edo supporting mavila is 23edo, which is the second-most common tuning for mavila temperament, used frequently by Igliashon Jones in his Cryptic Ruse albums. The fifth is in the sharper range for a mavila fifth at 678 ¢, and is consequently closer to 3/2 than in 16edo, although still fairly inharmonic compared to meantone. The anti-diatonic scale is more "quasi-equal" in this tuning than in 16edo.
25edo also supports mavila. The tuning is 672 ¢ and hence very flat, even flatter than 16edo, but not as flat as 9edo. This is 25edo's second-best 3/2; the alternate fifth generates 5edo.
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~3/2 = 677.145 ¢ | CWE: ~3/2 = 679.111 ¢ | POTE: ~3/2 = 679.806 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~3/2 = 676.039 ¢ | CWE: ~3/2 = 678.978 ¢ | POTE: ~3/2 = 679.788 ¢ |
Tuning spectrum
| Edo Generator |
Eigenmonzo (Unchanged interval)* |
Generator (¢) | Comments |
|---|---|---|---|
| 1\2 | 600.000 | Lower bound of 5-odd-limit diamond monotone | |
| 15/8 | 655.866 | ||
| 5\9 | 666.667 | ||
| 5/4 | 671.229 | ||
| 9\16 | 675.000 | ||
| 25/24 | 675.618 | ||
| 676.337 | octave mirror to Wilson's 523.662 meta-mavila | ||
| 13\23 | 678.261 | ||
| 5/3 | 678.910 | 5-odd-limit minimax | |
| 9/5 | 683.519 | 5-limit 9-odd-limit minimax | |
| 4\7 | 685.714 | Upper bound of 5-odd-limit diamond monotone 5-limit 9-odd-limit diamond monotone (singleton) | |
| 3/2 | 701.955 | Pythagorean tuning |
* Besides the octave
Other tunings
- DKW (2.3.5): ~2 = 1200.000 ¢, ~3/2 = 675.456 ¢
Music
- from Map of an Internal Landscape (Reissue) (2007)
- Illegible Red Ink – in 16edo tuning
- Run Run Red Robot – in 9edo tuning
- Court Music of the Mesa (fifth-transcription) (1989) – first piece written in meta-mavila
- Our Rainy Season (2011)
- Wallowing in Madness (2020) – in 16edo tuning
- Mavila Jazz Rhodes 1 (archived 2014)
- Kôsma jumiś lul (2017)
- Netbeans (2019)
- from Sean but not Heard (2012)
- Undercity ft. Hatsune Miku (2020) – in 16edo tuning
Experiments
Mike Battaglia has "translated" several common practice pieces into mavila by using Graham Breed's Lilypond code to tune the generators flat. Musical examples are provided in 9edo, 16edo, 23edo, and 25edo, for comparison. Note that the melodic and/or intonational properties differ slightly for each tuning.
- 9edo: Provided ID could not be validated.
- 16edo: Provided ID could not be validated.
- 23edo: Provided ID could not be validated.
- 25edo: Provided ID could not be validated.
See also
- African music – contains a discussion about the original tuning that inspired the discovery of this temperament
- Pitch set harmonization – includes instructions for applying pitch set harmonization to mavila
External links
- Meta Meantone & Meta Mavila by Erv Wilson
References
- ↑ A Linear Tuning of 4-"5"-"6" Artihmetic Mean (−3=5) paper from 1989 was referenced in Erv Wilson's Meta Meantone & Meta Mavila paper.