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Performance by Antonietta Loffredo from the CD New Music for Multiple Keyboards |
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Work Overview
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.
Work Details
Year: 2016
Duration: 7-9 min.
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
4 Dec 20: Musikene (Euskal Herriko goi-mailako musika ikastegia/Centro Superior de Música del País Vasco), San Sebastián, Spain
2 Dec 20: 2020 Festival Kuraia: 27º Encuentros de Música Contemporánea, Centro Cultural Galileo, Madrid, Spain
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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