Photo courtesy Joe Monzo
Ever since encountering Harry Partch‘s Genesis of a Music in the early 1980s, I’ve been most interested in just-intonation (JI) tuning systems. The initial reason for my interest was that I realized there were far more pitches available to composers than the usual 12, and that their relationships could be far more subtle, intricate, and complex than the limited set of 12 different intervals available in 12-tone equal-temperament (12-tET).
The desire to simplify Partch’s numerical (ratio-based) notation led to me create harmonic lattice-diagrams to represent the pitches in ‘ratio-space’. I have since discovered that many others before me (Tanaka, Fokker, Wilson, Johnston) have had the same idea.
Related to my lattice-diagrams is a method of notating rational (i.e., JI) pitches which utilizes prime-factorization. To me, this was a much simpler notation than using integer ratios. I came up with a name for this: JustMusic.
My original paper on this is at http://tonalsoft.com/monzo/article/article.htm
Stimulated by Partch’s short sketch of a ‘history of intonation’, I began constructing lattice-diagrams for many different historical tuning systems, which were gradually added to my paper until it became a book, JustMusic: A New Harmony.
At the same time (around 1984), I realized that the key to my being able to compose in the kind of complex JI tunings I wanted to use, would be to make use of computer software to handle the math calculations and produce aural output. My JustMusic software has been under development ever since, and hopefully will be ready for release within the next couple of years.
Along the way, I’ve become fascinated with the role that prime numbers seem to play in our perception of music. My most important contribution to theory so far seems to be my formulation of the concept of ‘finity‘, which is a generalization of Fokker’s ‘periodicity-block‘ concept.
I’m interested in studying the historical conceptions of various shapes and sizes of periodicity blocks in music all over the world. I believe that this ‘history of finity in tuning’ (which, I now realize, is what my book attempts to be) can enrich our knowledge of many other aspects of our lives and histories, especially ancient religious beliefs, possibly even extending to modern scientific theories about the universe.
Thanks to my interaction with other microtonal theorists on the internet Tuning List, I have become much more catholic in my tuning interests, so that even though I still prefer to use JI in my own compositions, I now also do a lot of research into other types of tuning systems, such as meantones, well-temperaments, and non-just non-equal tunings.
The content on my website leans pretty heavily toward tuning theory, and I’m most well know these days for my hyperlinked Encyclopaedia of Tuning.