I've taken one of Vi's challenges and begun hashing out the mechanics behind writing a piece of music based on pi - I decided to take a stab at the first 16 digits, which gives me a nice multiple of 4 to work with (useful in a common time piece). However, in her video, she used whole steps, which is certainly interesting enough to write a piece of music on... instead of whole steps, I decided to use half steps.
What I've got so far is quite an odd chord progression based on a very chromatic melody. "592" outlines a Neapolitan chord, so that was a no-brainer; the rest had a ton of flexibility. It switches a lot between major and minor chords - going straight from tonic to major submediant, which could also technically be called a secondary dominant of supertonic. Then the Neapolitan, and I started out just going from the minor Neapolitan to the parallel major, but dominant 7th of the leading-tone proved to be a little more interesting, and led naturally into subdominant 7th followed by supertonic 13th... if you're not completely lost by now, maybe it will help that my melodic rhythm is straight quarter notes and my harmonic rhythm is straight half notes.
The ending can go a number of ways... supertonic 13th branches naturally into either borrowed major submediant or dominant of submediant, and each of those has a fairly good progression into fully diminished leading tone OR dominant 7th of submediant. Not a traditional cadence, but I'm still making decisions, and I may use several of these at different points in the piece depending on context. Hopefully I'll be able to write some interesting development, pi sets the bar pretty darn nosebleed-high in terms of chromaticism!
I guess stay tuned... maybe. Not sure if I'll finish this or not, but I plan to experiment more tomorrow.
