If you’ve heard me talk about anything at all in the last four years I have probably brought up the fact that I always write in A. Of course this is not entirely true – any feedback/noise music I write is not in anything. However when it comes to pitched music this is basically true. Before I get into my reasoning, I’ll start by saying how I came to it.
When I was doing my Masters at Mills College, I had a seminar with professor Chris Brown which focused on alternate tunings. We looked at Harry Partch’s Genesis of a Music, the Just Intonation Network’s Just Intonation Primer, went to meet Ellen Fullman and see her “Long String Instrument” while she was in residence at the Marin Headlands Center for the Arts. Additionally I was studying Javanese Gamelan with Daniel Schmidt, one of the pioneers in bring Gamelan music to the west, instrument builder, and a composer who works extensively with tunings. This perfect storm of influences propelled me into the world of alternate tunings.
My first real venture in Just Intonation was my thesis at Mills Pulses (an acoustic work even though my degree was in Electronic Music, which I still find funny) which was premiered on the Signal Flow concert series. Due to working with Daniel, I decided to use the Bonang from the Mills Gamelan as well as building an instrument of my own which I called the Pentachord: a 6′ long five stringed instrument for playing natural harmonics. The ensemble was filled out with electric guitar and contrabass which would also only play natural harmonics. In this instance the Bonang tuning happened to be based on A 440Hz so that decision was made for me (although given the choice I probably would have stuck with A anyway). The piece was a success and won me the Paul Merritt Henry Prize for new works for string instruments that year but, more importantly, gave me a taste of working in Just Intonation, and once you’ve had Just you don’t go back!
During that same Signal Flow, my friend Chuck Johnson was also having a work for strings and Gamelan instrument in Just Intonation called Meet me by the pleroma. His piece however was based on 60Hz and centered around amplifying the difference tones produced by various just intervals. This was fascinating because it not only automatically produced a bass voice but also informs the performers when they are tuned correctly. I found this so compelling that ever since then all of my pitched music has also focused on difference tones (but based on 55Hz of course).
So that’s how I got started down this road. Now for some theory:
Just Intonation is all about breaking down the octave into smaller and smaller pieces. Rather than there being an arbitrary 12 tones, there are an infinite number restricted only by how far you want to take it. There are of course practical limits such as how precisely one can tune by ear, how in tune a particular instrument can play, how precise a floating point number on a computer can be, but barring that the sky is the limit. The way I look at it, if I have so many choices available based on one pitch, why would I need to go elsewhere?
Just Intonation is also all about the overtone series (by definition actually), and thus so are its difference tones. Anytime you have a justly tuned interval, when you subtract the two pitches you produce a difference tone that always falls within the overtone series of those pitches. Take the just perfect fifth. If I base it on a the overtone series of 100Hz, the first fifth I get is between 200Hz and 300Hz. Since 300-200 = 100, you can see that they are all part of the same series.
Difference tones dictate which octave you need. If I take that same example but make it 300Hz – 290Hz, you get 10Hz as the difference. Although 300Hz and 200Hz are both justly in tune with a fundamental of 10Hz, since this is below the threshold of pitch (somewhere around 25Hz), most people would perceive this interval as just being out of tune. If you however take the same ratio (30:29) and move it up, say to 3000Hz and 2900Hz, the difference tone is then in a range we can hear as a pitch (100Hz) and it sounds in-tune. The exact same interval has a different in-tuneness (because I hate the outdated term dissonance) solely due to a change in register.
Putting this all together:
Since Just Intonation can produce basically an unlimited number of relationships (individual pitches and difference tones) all from a single fundamental pitch (in my case A 55Hz), I have no need to go elsewhere.
If I write something tuned to any other pitch what would I gain? Nothing that I couldn’t achieve by using higher register ratios.
Why don’t I ever modulate?
– that would make things far more difficult on performers since all tuning relationships would change
– I have more than enough pitches right here in A
– modulation is a device for tonality and I am not writing tonal music
Don’t I ever get tired of hearing A all the time? Not at all! Since difference tones centered around 55Hz tend to be pretty close to the lowest pitches we can perceive I always get some killer bass. Going much lower pushes things towards the out of tune threshold and higher is, well, not low enough for me.
So to sum up: 55Hz rocks!