Kyle Gann: Solitaire (2009)

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Solitaire uses a just-intonation scale of 29 pitches; about 38 pitches are implied, but some of these are so close that substitutes are used instead. The piece is in E-flat, although no tonic chord ever appears. Harmonies are arranged around nine chords. Four of these are conventional IV, V, vi, and ii in E-flat major. Another is a major 7th on flat III. Three chords are built on the 7th, 11th, and 13th harmonics respectively, and a final on on the 7th subharmonic, 8/7. I made a chart of all possible chord successions and, upon listening over and over, characterized them as "piquant," "subtle," "eerie," "weak," "intense," and so on, following these moods as the progression seemed to require. The private game alluded to in the title was to meander among these nine chords (and eight rhythmic patterns) moving as little as possible in register; to find as much variety as possible within extreme limitations, going deeper into the existing framework rather than outward from it. This is an exploration of a true New Tonality, the tonality we could develop from including not only triads derived from the third and fifth harmonics, as has been done for centuries, but also the seventh, eleventh, and thirteenth.

The scale (given in Ben Johnston's notation) is given below. Notes with asterisks following the cents number are the ones subsumed into other ratios (in other words, the notes without such asterisks make up the basic 29-pitch scale):

Pitch:EbE13bEb^EL F7+FF+FLF^Gb G7b^G13bGGLG^A7b+AbAb^
Ratio:1/165/6433/3215/14 35/3210/99/88/755/48 6/577/6439/325/49/7165/12821/164/311/8
Cents:02753119 155182204231236* 316320*343386435440*471498551

B13b7bALB7bBbBb^ C13bC7+CC+CLC^ D7bDbD13bDDL-D^E7b+
91/6410/7 35/243/299/6413/8105/64 5/327/1612/755/327/49/5117/6415/840/21495/25663/32
609*618 653702755841857*884 906933938*96910181044108811161142*1173

(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, - lowers it by 80/81, # raises it by 25/24, 7 lowers it by 35/36, L raises it by 35/36, ^ raises it by 33/32, a 13 raises it by 65/64, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.

The piece is dedicated to Robert Ashley, and inspired by his comment: "Eventfulness is really boring."

Kyle Gann

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