The sketchbooks for Peter Maxwell Davies's Symphony No. 3 can be used to reconstruct the composer's precompositional workings. These sketchbooks illustrate the composer's use of sieving, pitch and durational matrices, and magic squares. The initial operation used is that of sieving, in which the pitch content of the borrowed material is reduced by selecting the portion to be used and omitting repeated pitches from the sieved set. A pitch matrix is a square in which each pitch of the sieved set is placed, much like a twelve-tone row matrix, horizontally across the top of the square. However, the set is also written vertically down the first column of the matrix. The square is then completed through transposition of each row in accordance with the first pitch of that row from the sieved set. To form the durational matrix, each note in the pitch matrix is numbered horizontally across each row, working left to right. Magic squares are mathematically generated squares which can correspond to celestial bodies; for example, Davies uses the Magic Square of Mercury in the Symphony No. 3. Each pitch from the pitch/durational matrix is transferred to the magic square according to its number. Davies subjects his borrowed material, a plainchant, to these manipulations to generate compositional material. Through abstract procedures, Davies creates a new musical work based on borrowed material, but without that material being evident.

Works: Davies: Symphony No. 3. (14-22).

Sources: Anonymous: Sancte Michael Archangele, defende nos in praelio (16, 18).

Index Classifications: 1900s

Contributed by: Christopher Holmes