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Work Overview
Arithmós = Analogía = Armonía (αριθμός = αναλογία = αρμονία), or 'Number = Proportion = Harmony' was commissioned by American Saxophonist Noah Getz (Washington, DC, USA), and is dedicated to Andrew Clarke and Martin 'Chip' Sherrill II. The work pays tribute to Ionian Greek philosopher Pythagoras of Samos (570-495 BC), the "eponymous founder of Pythagoreanism," and additionally serves as an exploration of the musical implications of combinatoriality as an organizational determinant, adopting the novel harmonic concepts of 'heights and sums' and 'advancing chords' 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). Philosophically, 'Arithmós = Analogía = Armonía' attempts to embody the conceptual notions of numeral, or number (arithmós), mathematical proportion (analogía), and harmony, or concordance (armonía) in relation to Pythagoreanism - the "early Pre-Socratic Greek school of philosophy based around the metaphysical beliefs of Pythagoras and his followers." In Pythagoreanism: Number, Cosmos, and Harmony David Fideler explains that in "Pythagorean thought, number gives rise to proportion, and proportion gives rise to harmony. The Greek word armonía means 'fitting together' or 'joining together.' Harmony and justice is the result of good proportion made manifest, and the kosmos itself is a harmony in which all of the parts are proportionally bound together." The structural form of the work includes 18 distinct proportions, based on 7 distinct metric modulations. Magic Squares of orders 3, 4, 5 and 6 with magic constants of 15=Saturn, 34=Jupiter, 65=Mars and 111=the Sun (each row, column and diagonal adding up to 15, 34, 65 and 111 respectively) also feature in the work as rhythmic durational schemes. These four magic squares are reduced to modulo 3, 4, 5 and 6 respectively in 3x3, 4x4, 5x5 and 6x6 matrices in order to accommodate the musical intentions of the compositional process.
Work Details
Year: 2018
Instrumentation: There are 2 versions: Tenor saxophone ; Alto saxophone.
Duration: 9 min.
Difficulty: Advanced
Dedication note: Dedicated to Andrew Clarke and Martin ‘Chip’ Sherrill II
Commission note: Commissioned by Noah Getz.. Commissioned by Noah Getz. Version for alto saxophone written for James Nightingale
First performance: by Noah Getz — 11 Mar 18. Andrew Clarke and Martin ‘Chip’ Sherrill II Residence, Washington, DC, USA
The composer has noted the following styles, genres, influences, etc. associated with this work:
Pythagoras of Samos (570-495 BC) ; Tom Johnson, Other Harmony: Beyond Tonal and Atonal (2014) ; David Fideler, Pythagoreanism: Number, Cosmos, and Harmony Magic Squares.
Performances of this work
30 Jun 19: Hanson Dyer Hall, The Ian Potter Southbank Centre, Melbourne Conservatorium of Music, University of Melbourne, Melbourne International Saxophone Festival, Southbank, Melbourne, Australia. Featuring James Nightingale.
14 Apr 18: Watters Gallery, Sydney, Australia. Featuring James Nightingale.
11 Mar 18: Andrew Clarke and Martin ‘Chip’ Sherrill II Residence, Washington, DC, USA. Featuring Noah Getz.
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