I first copied Ptolemy’s major scale. C=1/1, D=9/8, E=5/4, F=4/3, G=3/2, A=5/3, B=15/8, C=2/1 into Pd.
I then made the scale chromatic by adding C#=16/15, Eflat=6/5, F#=4/3, Aflat=8/5, and Bflat=9/5.
I also replicated a 16 pitch octave that Gioseffo Zarlino designed with the intent to allow a wide range of chords to be in tune.
These are all from the Just Intonation Explained page by Kyle Gann.
So after getting comfortable setting frequency values in Pd and listening to the results I experimented with one of my own.
My favorite was inspired by the number 11. I choose this # for a few of reasons. I have liked it aesthetically since I was a kid. Two 1’s side by side. It is also a prime number. Minimal and complex. And the last reason is an homage to Spinal Tap. “This one goes to Eleven”. It’s hard to take anything seriously unless it’s funny.
I started a progression keeping with the 64 Hz as a base to begin. This led to a series set between 192 and 384. Multiplying by the number 192 by 11 through 22 and dividing by eleven. I liked what I heard. Then I found the 3/2 within this series which is 288Hz. I then used 288 as the One, or base for the next series following the same “This One Goes to 11” method. I hope that made some sense.
The series sounds moderately dark. It has a focused intensity, modulating between a cerebral analysis of and a challenging emotional response to something. Of course that is subjective. I enjoyed exploring and letting the numbers and tones lead the process. I can now appreciate how individuals like La Monte Young, Terry Riley and others could feel limited by the concept of equal temperament.
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