WINGATE: PIANO SONATA No. 1
“The Transcendental”
or
The First 3000 Digits of Euler’s Number for Piano Solo

(THIS PROJECT IS A WORK IN PROGRESS)

Movements:
I. Allegro (Digits 1-1000)
II. Adagio (Digits 1001-1500)
III. Scherzo (Digits 1501-2000)
IV. Allegro (Digits 2001-3000)

Duration:
20'

Notes:
Part of Wingate’s ‘Irrationals Trilogy’ (including the Symphony No. 3 ‘Pi’ and the String Quartet No. 2 ‘Phi’), his Piano Sonata No. 1 was composed using the first 3000 digits of Euler’s number as pitch class integers, and the work constitutes the third musical exploration in the composer’s oeuvre of what an irrational number ‘sounds like’. The subtitle is inspired by the mathematical status of Euler’s number as both an irrational number and a transcendental one (i.e. that it is not a root of any non-zero polynomial with rational coefficients), but also serves to invoke (via mathematics rather than Romanticism) Liszt’s famous ‘Transcendental Études’ (or Études d'exécution transcendante, S.139) for piano, published in 1852.

 

The procedure used to create this piano sonata yielded a particular and pervasive type of sonority throughout the piece’s four movements, often creating soundscapes of an open, welcoming character due to ubiquitous presence of open octaves as the only possible chords. The piece is often, in effect, a de facto octave étude for the piano, as the pianists hands are almost always spread into this open formation, and must accomplish many dramatic leaps to accommodate the multiple voicing across the keyboard. Quickly-sounded conglomerates of pedaled successive tones create the only sense of chordal effects, these agglomerate entities often serving as melodic units or thematic fragments, as for example the opening D-G-C#-G# motive.

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The score cover image is a visual representation of Euler’s number  by Franch-Canadian mathematician Simon Plouffe.