First 605 words of the document:
1.Nested structure as "micromacrocosmic" (the smallscale reflected in the large
scale). Selfsimilar formation known as a fractal in which each subdivision of
the structure resembles a miniature version of the whole. All 3 sonatas are
2.In Sonata 1Piece starts with 5 phrases forming a unit of 4+3+2+3+4 bars
3.The microstructure 1 7Pattern for 17:4+1+3+4+1+3+4+2+4+2crotchets. The
entre pattern of 28 crotchets equates to double dotted semibreve=semibreve +
minim + crotchet=7 crotchets. Uses it as a multiplayer from which Cage
constructs the entire sonata (macro structure)
4.Microstructure is not clearly articulated in bars 812
5.Bar 3 is a restatement of bar 1, while the 2 chords in bar 5 are repeated in
compressed form in the first half of bar 6 which are followed by 2 more
appearances of the 1st chord from bar 5.
6.Bar 1819 include a reference to the opening chords of sonata
7.The end is confirmed by the tiny coda, in which the right hand of bar 24 is
subjected to varied repetition in bars 2526.
8.In Sonata 2, the material in the first 9 bars is from bars 12
9.31 crotchets=7¾ bars of 4/4. Cage forms his macro structure from 7¾
permutations of the micro structure in pattern 1½:I + 2 3/8:I for rhythmic
tidiness, he settles for a close approximant of 11 ½ crotchet beats rather than
mathematically exact 11/8 crotchet beats. Micro Structure 19: 1 ½, 1 ½, 2 3/8,
2 3/8 bars.
10. A new idea appears with the start of 2 part writing in bar 10 and Cage
adapts this to announce the beginning of section 2 (bars 15)
11. The ostinato (A sharpB) starting at bar 17³ derives from the rising
semitone at the start of the left hand figure in bar 2 and the flurry of highregister
ostinato in bar 28 seems to derive from bar 5.
12. First section consists of 3 statements of the opening righthand figure, in
the 2 of which the final note is truncated to a crotchet.
13. In Sonata 3, macro structure based on micro structure 18:1,1,3 1/4, 3 ¼
14. The left hand of bars 1415 repeats the ostinato accompaniment first
heard in bars 1112 but in bar 14 only it is transposed up a semitone.
1.The rhythm of the melody in the final bars is a reminder of the rhythm in bar 4.
2.Opening of sonata 2 starts with a sixbeat idea in the right hand. When this is
answered by a new idea in the left hand, Cage substitutes a rest for the
crotchet in the middle of the rhythm. Bar 3¹ the rest falls on a strong beat and so
launches the syncopation that dominates this sonata.
3.The crotchet rest also causes the 4quaver figure that started on a weak beat in
bar 3(metric displacement)
4.Jazzlike rhythms permeate much of this sonata. E.g. metrical displacement of
the repeated figure in bars 78 is essentially the early jazz device of secondary
rag in which 3 beat figures is repeated across the 4fold beat of quadruple
time. A cascade of ragtimelike syncopation follows in the rhythmic repetitions
5.While all of this is going on in the left hand, the 1st 3 demisemiquavers of the
motif from bar 2 remain in bar 13, augmented to 8 times their original value.
6.Left hand part looks like a pedal but preparation leaves the pitch unclear and
so it sounds more like a percussive reference point (momentarily shifting off
the beat in bar 6) for the irregular note lengths in the melody. The latter sounds
even more irregular than they look because the recurring G sharp is heavily
muted and so seems percussive rather than pitched.
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1.In bar 13, the sustained B (left hand) in the next bar sounds like a semitone
because both notes are only partially muted, but when the semitone is inverted
in bar 15 ( E flatD), it sounds like a distorted echo, because E flat is fully
2.The entire progression of parallel chords creates a cadential effect, despite the
fact that many of the notes are of indeterminate pitch.
3.In sonata 3 2nd sections opens with a new idea in bar 9(left hand).…read more