When I'm not geeking out about Bitcoin (a peer to peer electronic) Cash (system), I'm geeking out about music theory. Specifically, "microtonal music theory". I recently released this video giving an overview of a tuning system called "porcupine temperament", if you'd like to check it out:
Here's the script for reference, thanks for watching/reading!
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Most western musicians will be intimately familiar with the diatonic scale. It’s got 5 large steps and 2 small steps. It’s got 3 major chords, 3 minor chords, and a diminished chord. And there are various modifications of the scale arrived at via sharps and flats, like the harmonic scale, the melodic scale, or the double harmonic scale, all with their own modes, sets of chords, and melodic characteristics.
But the diatonic scale, with all of those details playing into the intricacies of using it to make music, is just one possible scale structure among many.
For example, consider a scale with 1 large step and 6 small steps. With a small step size of around 160 cents (or 1.6 semitones), we end up with a 7-note scale containing two major chords, two minor chords, and three diminished chords. We also end up with some intervals that are pretty far from anything we have access to in standard western tuning.
This 1 large 6 small scale can be derived from accurate tunings of what’s called Porcupine temperament. While in western music we have a circle of fifths (which can be flatted to give us better thirds), in Porcupine you have a circle of major-second-ish intervals that can be flatted to give us better… well, pretty much everything.
If you continue that chain of seconds beyond the 7 note scale, we get another melodically consistent scale right at 8 notes with a structure of 7 large steps and 1 small step, and then at 15 notes with a structure of 7 large steps and 8 small steps. These scales might be loosely analogous to our pentatonic, diatonic, and chromatic scales, though it’s especially interesting that two of these scales are just one note apart. Perhaps alternating between the two depending on the melodic needs of a given passage would be commonplace in porcupine temperament!
This “1L6s” scale can also be modified by a generalized sharp and flat, which is derived as the interval between large and small steps in the scale. These modifications can be used to gain access to combinations of major and minor chords that weren’t available before, and to create melodic interest, especially with small steps surrounding target notes. While this all may seem like relatively familiar territory, the actual function of each of large and small step, of each chord and harmony, is almost entirely unexplored territory, and still honestly feels pretty alien, even after having written some music in this system myself.
To hear a 4 part round I wrote using this 1L6s scale, check out this video:
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