Peter McKenzie Armstrong (born March 12, 1940) is an American composer and pianist. His forty-some works have drawn most strongly from sources not primarily associated with music -- integer sequences, Markov chains, axial rotation, tessellation structures, chemical element properties, Archimedes' Ostomachion, the Periodic Table, et al -- with the goal to convey their shapes and proportions persuasively in sound. Most of his works are scored in LilyPond for piano, either solo or in mixed duo. Other works include several for flute and earlier pieces for MIDI ensembles and Csound.
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Compositions Overview
Grouping by Materials & Process Opus
o All-interval 12-tone chords
o Axial rotation through all degrees
o Cellular automata (Conway "Life")
Markov Chains:
o Fibonacci family
o Others
o Ostomachion, o Phi, o Periodic Table
o Simplest Perfect Squared Square
o Synthetic & juxtaposed modes
o Variation/reconstruction
13 18-20 25-26 33
6a-d 7 9 28 36-38 39
21-22 27 30a-c
4-5 17 24
12 16a-b 35
15, 23, 31
10 34a-b
1-3 32
8 11 14 29
Generation Most of Armstrong's works are developed algorithmically (in APL/J), then scored in LilyPond. Extensive composer-edits to LilyPond's secondary MIDI output produce final demonstration audio. For solo piano works, this WAV result is then converted to MP3 and input to Pianoteq for realization on one of its "Bösendorfer" instruments.
Access
Scores, published by Edition Ottaviano Petrucci, may be accessed and downloaded at the International Music Score Library Project (IMSLP). The audio is similarly available at SoundCloud, and video (score page-turn-synced with audio) is online at the Internet Archive.
Piano Solo
o 12 Variations in S-Mode, Op. 1 (1971)
o Black & White: Voicing/Articulation/Pedal Study, Op. 2 (197_)
o Mini-Studies on my Surname, Op. 3 (1983)
o Katikaze: Study in Single Notes, Op. 4 (1984)
o Krikos Epilogue, Op. 7 (1993)
o Variations on "Rule, Brittania!", Op. 11 (2007)
o Syzygies: Two-Part Takes on Wythoff's Matrix, Vol. I, Op. 16a (2014)
o Syzygies: Two-Part Takes on Wythoff's Matrix, Vol. II, Op. 16b (2014)
o Takeoffs on "Katikaze": Interval Expansion Study, Revised, Op. 17 (2022)
o No!: A Trifle, Op. 21 (2016)
o Patterns from the Game of Life, Part I: 8th Notes for Toy Piano, Op. 27 (2018)
o JE: A Mural -- after John Elliot's "Yesteryear on the Hudson", Op. 29 (2019)
o Patterns from the Game of Life, Part III: Pairs & Singles, Op. 30b (2019)
o Trends from the Periodic Table of Elements, Op. 31 (2020)
o Bunny Victoria Watson, a Chihuahua Triptych [orig. for Music Box], Op. 32 (2021)
o Triptych: Riddle, Dance, Echo, Op. 33 (2021)
o In Modulo, Part I: Cycles from the Perfect Squared Square, Op. 34a (2022)
o In Modulo, Part II: Cycles from the P.S.Square Absentees, Op. 34b (2022)
o Whirly: Ostinato on a Subprime Fib, Op. 35 (2023)
o Circular Variations on a Name, Revised, Op. 36 (2023)
o Circular Variations on "F. J. E.", Op. 38 (2024)
o Pitch/Time Swaps as applied to J.S. Bach's WTC, Op. 39 (2025)
Piano 4 Hands
o Flipidodes: All-interval 12-tone Chords Voicing Study, Op. 18 (2015)
o Last Breath: Hexachordal Articulation Study, Op. 19 (2015)
o Flitter, Dither & Rant: Assorted Chordal Confusion, Op. 20 (2015)
o Thin Rake c/o "The Game of Life", Op. 22 (2016)
o 'Tis To Waft, Op. 26 (2017)
o Patterns from the Game of Life, Part II: Rondo Infernale, Op. 30a (2019)
o Patterns from the Game of Life, Part IV: Ostinato Polemico, Op. 30c (2019)
Piano 6 Hands
o Chord for Mr. Woodshed (Arr. PMA), Op. 25 (2017)
2 Pianos
o Krikos 1: Circular Variations on the Opening of Schoenberg's Opus 33a, Op. 6 (1991)
Autopiano
o Dapper '1' and Dreadful '0', Op. 12 (2011)
o Refractions: 12-Tone Chords on an All-Interval Row, Op. 13 (2012)
o Phigits: One-Part Takes on the Digits of Phi, Op. 23 (2016)
o 11/8, 2nd Edition, Op. 24 (2016)
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Flute Solo
o Partita Traverse for Flute Solo after J.S.Bach, Op. 8 (1993)
Flute & Guitar
o Stuckle: Takeoffs on a bar each from Schoenberg and French Folksong, Op. 9 (2012)
Flute & Mandolin
o Circular Variations on "M. C. J. A. F. P.", Op. 37 (2024)
Flute & Piano
o Stuckle2: Stuckle with a Between, Op. 28 (2018)
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Digital Ensemble
o Cycles for Synclavier, Op. 5 (1984)
o [CTT-95]: Bus Ride over a Bach Bass [2 xylophones, steel drum, cello pizz.], Op. 14 (2012)
o Ostomachion: Wind Chimes from Archimedes' Box [12 MIDI instruments], Op. 15 (2013)
Csound
o Noitnevni Trap-2 (1984)
Krikoi on the Opening of Schoenberg's Opus 33a, (1992)
o 1: Circular Variations, Op. 6a
o 2: Time^Space Vortex, Op. 6b
o 3: Prelude & Centrifugue, Op. 6c
o 4: Helix, Op. 6d
o Additudes: Fibonacci/Lucas Mod Cycles set in the Order-21 Perfect Square, Op. 10 (2005)
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