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:

(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.

Kyle Gann

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