Solitaire is one of my favorites among my works, but I feel it is generally misunderstood. On the surface it seems very "normal," but the peculiar elements are in the background. It is superficially simple: a free-flowing melody, vernacular-tinged yet non-repeating, inscribed over a series of harmonies. The piece's oddness and originality stem from its harmonic structure, which combines the exotic and the familiar. Some of the chords are perfectly familiar ones in E-flat, others are based on the 7th, 11th, and 13th harmonics of that pitch. For me, the piece is like a casual conversation with a stranger - a stranger who knows more than you suspect, and whose words mean more than you think - and you slowly realize it's not what it seems. In fact, the piece reflects experiences I had talking with Robert Ashley, to whom it is dedicated, as inspired by his comment, "Eventfulness is really boring." Or as Charles Ives wrote, "What music sounds like may not be what it is."

While everything in the piece is scored, the sonic realization is by the great Canadian composer and my sometimes collaborator M.C. Maguire.

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:	Eb	E13b	Eb^	EL	F7+	F	F+	FL	F^	Gb	G7b^	G13b	G	GL	G^	A7b+	Ab	Ab^
Ratio:	1/1	65/64	33/32	15/14	35/32	10/9	9/8	8/7	55/48	6/5	77/64	39/32	5/4	9/7	165/128	21/16	4/3	11/8
Cents:	0	27	53	119	155	182	204	231	236*	316	320*	343	386	435	440*	471	498	551

B13b7b

AL

B7b

Bb

Bb^

C13b

C7+

C

C+

CL

C^

D7b

Db

D13b

D

DL-

D^

E7b+

91/64

10/7

35/24

3/2

99/64

13/8

105/64

5/3

27/16

12/7

55/32

7/4

9/5

117/64

15/8

40/21

495/256

63/32

609*

618

653

702

755

841

857*

884

906

933

938*

969

1018

1044

1088

1116

1142*

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.

Kyle Gann

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