Many of you know that I’m a fan of Tom Johnson’s music. I’ve reviewed his CDs (Questions and The Chord Catalogue) and Narayana’s Cows is a work that I end up showing all of my composition students at some point (just ask them). I have a copy of Self-Similar Melodies and I worked through the first few chapters of it (and that book typically gets loaned out to students, too). I can only hang with the first few chapters of Self-Similar Melodies because my math isn’t all that strong and my own music isn’t as inspired by process as Johnson’s. Still, I constantly admire Johnson’s ability to make rather direct numerical/musical ideas into compelling pieces and to explain those processes in prose form. When asked if I’d look at Johnson’s new book Looking at Numbers I jumped at the chance. I wasn’t entirely sure if I’d understand it (again, my math is not so advanced) but I was game to try it out.
The text of each article is terse and pointed, as one would expect from Johnson’s music. The star of the book is not so much the text but the charts/graphs/maps which Johnson uses to elucidate various mathematical patterns, hence the title Looking at Numbers. Right away, on pages 2 and 3, there are four charts which show radically different ways of walking through the permutations of the set [1,2,3,4]. Where Self-Similar would give me a paragraph describing how these permutations could be mapped, Looking at Numbers truly shows variety.
I can’t speak directly to the appropriateness of the number theories described in the book but Johnson’s description of his applications of said relationships is always compelling. I never really “got” the relationships in Twelve, for example, and now I feel like I have a much better handle on them. And, maybe because my math skills are lacking, I feel like I can use these maps for inspiration more readily than anything I read in Self-Similar Melodies. Reading through the various articles in Looking at Numbers (with copious notes, references, and places to learn more) I came away with not only a deeper understanding of specific pieces but also a more accessible practical model of how I could use these techniques and make them my own. Published by Birkhäuser, this book is equal parts number theory and musical inspiration. Not too many people can pull that off but Tom Johnson can, of course.