Fifteenth century fractals

Pardon the little joke at the end of this video.




Late Medieval to early Renaissance music yielded an efflorescence of brilliant process compositions. Ockeghem's Missa Prolationis intrigues me because of its relation to the modern concept of fractal mathematics. The example above is a nice taste of it, you watch the augmentation and diminution of the lines as they go by.




When my spare time permits at some point, I will make a thorough examination of this score. I am curious to know where Ockeghem distorted or altered the process, producing variants in the lines, and for what reasons. From what I can see at a glance, there are lots of instances to look at. Alas the score available from IMSLP is all in C clefs, which don't bother me in limited cases but, their exclusive use in the score is annoying.




Counterpoint is process/system composing, so the parameters of the system are crucially important. Where and why you 'tweak' your system to preserve some other element- rhythm, duration, musicality, adherence to formal design etc. etc. is where the artistry interacts with the science. It's like chess in that respect, it's all math and pattern except for the unpredictable human element. Computers may beat people, but they don't do it in elegant or interesting ways.




The real achievement in this work is not that it is designed and carried out in such a disciplined way, which is astonishing actually, but that he still made beauty out of it. There are lots of fractal canons and fugues people have composed and posted online. I have heard quite a few but found none that I felt aspired to a high artistic level. Ockeghem was native to prolational music, so his instincts were in line with the technique. It wasn't contrived for him.




I make some use of techniques like this in other ways, consistent with a modern aesthetic. I still have a lot to understand about this piece.