Over the next series of posts, I’m going to explain how the lattice in the Flying Dream video works. Before I do, I want to take time to mention a terrific book.
I started investigating just intonation in earnest in early 2011. A couple of months in, my friend Kay Ashley loaned me her copy of Harmonic Experience, by W. A. Mathieu. Thank you so much, Kay!
I spent a few weeks with Kay’s copy and very soon knew I had to have my own. I devoured the book almost daily for at least a year. I still pull it out often, lug it to a cafe for browsing over breakfast, do bibliomancy with it if I’m stuck creatively, take it on vacations.
Harmonic Experience is the only music theory book I’ve read so far that actually increases my understanding of music, rather than obfuscating it. It’s huge, which could be intimidating. But I found it to be immediately accessible and entertaining. Mathieu has a great, light sense of humor. The concepts are introduced at a beautiful pace. And the ideas he presents are enlightening. “Aha” experiences abound.
Much of what I’ll present in this blog is heavily influenced and inspired by Mathieu. The lattice itself goes back to Euler in the 1700’s, but Mathieu expands on the idea enormously, arranging it so it corresponds to traditional musical staff notation, using it as a means to understand equal temperament, harmony, melody, chord progressions, world music, and much more.
Mathieu uses the term “positional analysis” to describe his system. For me, positional analysis opens the black box. It shows what’s happening in there. When my music is informed by the lattice, it makes more sense. I have more control over the effect it has on me and my audience. And it’s way more fun, because I know more about what I’m doing and why, rather than flailing around finding good sounds by instinct. And when I do compose by instinct (which is essential), I understand better why it sounds good, and can expand on my inspirations in a rewarding way.
‘Nuff said! If music theory has been frustrating for you in the past, as it has been for me, I can’t recommend this book highly enough.
Next: Between the Keys
Hi Gary, very interesting articles!
I love the feeling of just intonation and you explain some very complex physical properties of harmony very well (way beyond my understanding mostly. The lattice as a tool is fantastic.
What do you use to generate your drones and tones? Are you tuning them all yourself as well? I am a trombonist and love practising to drones for tuning but would like to be able to make chords and tune them for my practise for harmonic context and to feel the polarity of various intervals in relation to a chord or implied harmony.
I use Logic Pro, and at W.A. Mathieu’s suggestion, I mostly use a clarinet patch. The odd-harmonic quality of the clarinet really brings out the character of each interval.
Logic allows custom tunings in the Project Settings. With drones that just involve fifths and roots, ET is close enough. But tuning settings allow more complex chords to be right in tune, which I imagine would be pretty exciting to improvise over on trombone!