Composed for dancer Louise Lippold, as were In a Landscape (1948) and A Flower (1950). The pitches are again derived from paper imperfections, but this time a predefined rhythmic controls the density of notes. Chance operations (with the I Ching) are used to determine methods of sound production (on the keyboard, muting [string muted with fingers or hand and played on the keyboard] or plucked.) Tempo and dynamics are left to the performer. The score is four pages long. Music for Piano 3 (1953) Dedicated to Morton Feldman. Starting with this piece, all subsequent entries in the series are exactly one page long, and the number of notes and/or sounds is determined by the I Ching chance operations. In this and subsequent pieces dynamics and durations are free. Music for Piano 4–19 (for any number of pianos) (1953) Composed for Merce Cunningham's choreography titled Solo Suite in Space and Time. Starting with these sixteen pieces, all subsequent entries in the series may be performed together, either in sequence or simultaneously, by any number of pianists. Overlapping of and silences between pieces are allowed. Music for Piano 20, for piano (1953) Composed for the same Cunningham choreography as in Music for Piano 4-19. Music for Piano 21–36, Music for Piano 37-52 (for piano solo or in an ensemble) (1955) Composed for the same Cunningham choreography as in Music for Piano 4-19 and Music for Piano 20. This time methods of sound production include noises produced by playing on the body of the piano in various places. In the versions recorded by Steffen Schleiermacher (see below) he employs a "superball" which he rubs on exterior parts of the piano, creating various groaning or moaning sounds. The two groups of sixteen pieces are different in that the limits for chance operations using the I Ching are 1–127 for the first group and 1-32 for the second group, numbers corresponding to relative difficulty of performance. Cage described the compositional process in full in a 1957 article, which was later reprinted in his first book, Silence. Music for Piano 53–68 (for piano solo or in an ensemble) (1956) Dedicated to Grete Sultan. Music for Piano 69–84 (for piano solo or in an ensemble) (1956) Both collections were composed for the same Cunningham choreography, Solo Suite in Space and Time. Music for Piano 53–68 is dedicated to, and was first performed by, Grete Sultan. Music for