==CRAZY 9-EDO VERSION - FOR USE ONLY IF YOU'RE TRAPPED ON A DESERT ISLAND WITH ONLY ONE INSTRUMENT IN 9-EDO==
These musical examples are tuned to what is known as "mavila" temperament. It is named after the Mavila village of the Chopi people in southern Mozambique, where this tuning system was first discovered by Kraig Grady.
Because of the structure of this unique tuning, it is true that every existing piece of common practice music has a "shadow" version in mavila temperament. That is, when Beethoven wrote Fur Elise, he actually wrote two compositions - the one that you know, and the anti-diatonic equivalent in mavila temperament. It's only that the anti-diatonic versions have never been heard before.
Mavila is a tuning system whereby four stacked perfect fifths, rather than getting you to a major third, gets you to a minor third - meaning that the fifths are flat. Conversely, four stacked perfect fourths gets you to a major third, rather than a minor third. This has some very strange implications for music. The mavila diatonic scale is similar to the normal diatonic scale - except interval classes are flipped. Wherever there was a major third, you'll 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 - you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad.
In these examples, the chosen mavila temperament is 9-equal, which was chosen because there are only 9 notes to the octave. It's an odd tuning, in that although it has comparatively awful harmonic properties, and its melodic properties are a mixed bag, it does "work" in a sense: it's a rare novelty that allows you to set up tonality with only 9 notes to the octave. If you plan on getting stuck on a desert island sometime soon, and you only have 9 pieces of wood with which to construct a 9-tone wooden xylophone, it would be worthwhile to know how to use this tuning.
A special thanks goes out to Graham Breed; his custom Lilypond code and several weeks worth of gchat discussion are what made all of this possible.
of , which is