Electrifying some Bohlen-Pierce

The first four days of pomodoro composing I devoted to finding some melodies that could go over a Bohlen-Pierce bassline. For those who don't know, Bohlen-Pierce is a scale that has its "semitones" be roughly the size of 1.46 regular semitones.

That's a weird number, you may think, and it sort of is. Bohlen-Pierce has a slightly interesting history - it was invented thrice separately, each time by microwave engineers. Your regular scale - the twelve tone equal scale - divides the octave into twelve equal steps. The octave is a doubling in frequency. Step size is measured logarithmically, though, so it's not just 2/12 - it's 2^1/12. The reasons for this are simple in some ways, but require some maths to explain; historically, it's the result of several different developments in music, and it turns out it's really the result of quite a long chain of adjustments. In a way, the 12 tone scale is a lot like certain technological standards: a good compromise between several desired qualities. It is also a lot like technological standards in that they may be somewhat arbitrary
Now, Bohlen-Pierce does not divide the octave, it divides the fifth of the octave - the ratio 3/1 - instead. By dividing 3/1 into 13, it produces a fairly interesting set of intervals, all pretty close to certain just-intonation intervals such as 5/3, 7/5, 7/3, 15/7, etc. Basically, any combination of 3^x * 5^y * 7^z where x, y, z ∈ Z and |x|, |y|, |z| are fairly low will be fairly accurately approximated by Bohlen-Pierce. 

Thus, we get fairly good approximations of chords where the series of frequencies involved are close to 3:5:7 or 5:7:9 (or their minor chord versions 7/7 : 7/5 : 7/3 and 9/9 : 9/7 : 9/3, from now on 9/(9:7:3)). Since we assume the tritave - the fancy name given to the octave's fifth - is sort of like an octave, note names repeat at the tritave and chord inversions are inverted by the tritave rather than the octave.

Now, this is theory I've known for years, and been mucking around with a lot. I have always found composing melodies in Bohlen-Pierce a challenge, but in two 25-minute periods I managed to compose the melody lines (except for the bits that follow the bass in almost parallel, those are old; the bass and drums and whatnot are about a year old) in this little ditty. It's not a good composition- but I am surprisingly content with the quality of the melodies, it's the first time I've managed to pull off something this passable in Bohlen-Pierce in such a short time. Still, an early draft, but with the melodies in there it's about ten times closer to being an actual thing than before. I did more in 50 minutes than I've done in ten hours before.

I think this relative success is due to approaching it way more goal-oriented now than before, when I've merely been content to play around and happen upon stuff earlier.