I have always found it a special challenge to compose music in the equal-
tempered system, in which I do not customarily hear or think. If I am to
restrict myself to such a small set of intervals, and forgo the essential
distinctions between pairs of intervals that are "enharmonically equivalent"
(e.g. that between a major third and a diminished fourth), then
either the music must be diatonic or atonal, or there must be some kind of
pitch-class game going on. Pitch-class games tend to wear out their welcome
very, very quickly, which makes it hard to write "big" piano
music. Accordingly, all of my piano works are comparatively brief; the second
movement of this Sonata is much the largest single form that I have ever
composed for piano.
The pitch-class game in this Sonata is that only nine pitch-classes are used: B, C, D, D#, E, F#, G, G#, A#. This is the residue of the equal-tempered collection after the augmented triad A C# F is taken away. The set of nine is therefore symmetric around a triple axis, which is an academic way of saying that anything it can do on or around B, it can just as easily do on or around G, or D-sharp. This permits just enough of a range of "modulations" to develop the forms of this work without plunging into monotony (at least, it is my judgment that I have not plunged into monotony).
The first movement ("Prelude") must be played as slowly as possible, given the acoustics of the instrument and the space. How slow is too slow? When the continuity of the softest passages threatens to dissolve.
The second movement ("Toccata") bears much the same kind of oblique relation to sonata form as the Sonata's pitch-class set does to the diatonic collection. The "first theme" is a pair of tiny motives that are foreshadowed in the introduction and stated explicitly in bars 13 and 14. The "second theme" grows from a four-note motive first stated in the left hand in bars 53 -- 55. A codetta element appears first at bar 76 and in an expanded form at bars 82 and 83. Something recapitulatory starts happening at bar 147, although the development and recapitulation cannot be usefully distinguished. The "second theme" returns at bar 184 and the coda begins at bar 200.
The third movement is a travesty waltz, owing much to Shostakovich's affectionate (but very sharp-edged) parodies of Chopin. Its ending makes no sense, nor is it intended to; that is one way to define the difference between a parody and a travesty.
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