Musica battuta : double toy piano étude for one soloist
by Andrián Pertout (2016)
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Musica battuta or 'Beaten Music' was especially composed
for Antonietta Loffredo (Como, Italy) for the 2016 'Multiple
Keyboards' Project (Sydney, Australia) curated by Australian
composer, pianist, harpsichordist and writer Diana Blom in
association with Australian composer, keyboardist and music
researcher Michael Hannan. The work serves as an exploration of
the musical implications of combinatoriality as an organizational
determinant via the utilization of mathematician Joel Haak's
combinatorial analysis of American composer Steve Reich's
rhythmic pattern from Clapping Music (1972), while
additionally adopting the novel harmonic concept of 'All-Interval
Tetrachords and Other Homometries' from American minimalist
composer and music theorist (also former student of Morton
Feldman) Tom Johnson, eloquently presented in his publication
Other Harmony: Beyond Tonal and Atonal (2014).
In The Geometry of Music Rhythm: What Makes a 'Good' Rhythm Good? (2013) Godfried T. Toussaint presents the back ground to a combinatorial analysis by mathematician Joel Haak of American composer Steve Reich's rhythmic pattern from Clapping Music (1972) [x x x . x x . x . x x .], which states that because there are "eight claps per cycle of 12 pulses in Clapping Music" means that the combinatorial possibilities (or "ways one can select 8 out of 12 pulses") may be mathematically represented by the equation (12!)/(8!)(4!)=495. This figure, the result of an adherence to two separate conditions: (1) that the pattern begins with a note and not a rest, and (2), that the pattern does not contain a rest larger than one pulse between two consecutive onsets (or sounded pulses). Toussaint explains that with "these two constraints, the original 12 units, composed of eight claps and four rests, are reduced to eight units made up of four clap-rest patterns [x .] and four solitary claps [.]," adding that "in this setting, there are now only eight two-valued elements taken four at a time, and thus the formula for the total number of possible patterns becomes 8!/((4!)(4!))=70." Hack then introduces a third condition into his analysis: that the pattern should not be a cyclic permutation of another pattern (i.e. a clockwise or anti-clockwise rotation), which effectively reduces the total number of admissible patterns from 70 to 10. A fourth condition is then introduced: that the "combined 12-pulse clapping patterns made by both performers should not repeat themselves before the ending of the piece." In other words, as one player in Clapping Music systematically rotates the rhythmic pattern by a pulse (or the incremental rhythmic displacement of the pattern against a static version of the pattern), no combination of these two patterns results in repetition of canonic materials. A fifth condition then eliminates the possibility of consecutive repeats of any particular rhythmic cell, which finally results in the reduction from 495 possible patterns to 2: Reich's Clapping Music pattern and [x x x x . x . x x . x .]; the latter, or alternative pattern being the pattern adopted in Musica battuta.
Instrumentation: Schoenhut concert grand (Model 379B, 37-key toy piano) and Schoenhut traditional spinet (Model 6625B, 25-key toy piano).
Duration: 7 min.
Difficulty: Advanced — Professional
Written for: Antonietta Loffredo
First performance: at Multiple Keyboards - new works for piano duet & 2-4 pianos/toy pianos (Theme and Variations (Willoughby)) on 8 Dec 2016
The composer notes the following styles, genres, influences, etc associated with this work:
Godfried T. Toussaint’s The Geometry of Music Rhythm: What Makes a ‘Good’ Rhythm Good? (2013) ; Steve Reich’s Clapping Music (1972) ; Tom Johnson’s Other Harmony: Beyond Tonal and Atonal (2014) ; Combinatoriality
Performances of this work
8 Dec 2016: at Multiple Keyboards - new works for piano duet & 2-4 pianos/toy pianos (Theme and Variations (Willoughby)).
8 Dec 16: Theme and Variations Showroom, Willoughby, Sydney
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