The idea behind Fractured Paradise (Tuning Study No. 3) was very simple. I wanted to see what would happen if you took a typical country & western idiom and tuned it perfectly. I stole a bass line from a country song (never mind which one - its own author wouldn't recognize it), and used enough pitches so that every chord would be exactly in tune. The result was a non-chromatic scale with 16 pitches to the octave, even though there are only eight scale steps represented. The scale (given in Ben Johnston's notation) is as follows:
Pitch: B B+ C#+ D7 D7+ D E E+ F7+ F#+ F#++ G7+ G G+ A7+ A+ Ratio: 1/1 81/80 9/8 7/6 189/160 6/5 4/3 27/20 7/5 3/2 243/160 63/40 8/5 81/50 7/4 9/5 Cents: 0 22 204 267 288 316 498 520 583 702 723 786 814 835 969 1018
(If you don't have enough experience with just intonation to make sense of this chart, try reading the step-by-step Just Intonation Explained section.) In Johnston's notation, + raises a pitch by 81/80, # by 25/24, 7 lowers it by 35/36, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.
In addition, I was determined to bypass my usual rhythmic complexity for once and remain in 2/4 meter all the way through. I succeeded - even though the groups of 11, 7, or 5 16th-notes make the rhythms difficult to count in spots even for me.
February 13, 1999 at the Ussachevsky Memorial Festival, Pomona College, by Genevieve Lee
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