Music Derived from Physical Processes

Sound (Art and Technology)

Lorenz Schwarz
Karlsruhe University of Arts and Design (HfG)

Summer Semester 2024
Course info

← Overview

The session can begin with a collaborative reconstruction of Steve Reich’s Pendulum Music (1968), or with a close reading of its written instructions.

A reconstruction uses:

  • dynamic microphones
  • active loudspeakers
  • a mixing desk

Either way, the piece provides the starting point for the subsequent analysis.

Music Derived from Physical Processes

Process Music and Minimalism

Steve Reich's Pendulum Music (1968) as a case study in:

  • Process-oriented composition
  • Physical systems as musical structures
  • Acoustic feedback as sonic material
  • Minimal music aesthetics
Music Derived from Physical Processes

PENDULUM MUSIC

FOR MICROPHONES, AMPLIFIERS SPEAKERS AND PERFORMERS

Three, four or more microphones are suspended from the ceiling or from microphone boom stands by their cables so that they all hang the same distance from the floor and are all free to swing with a pendular motion. Each microphone’s cable is plugged into an amplifier which is connected to a loudspeaker. Each microphone hangs a few inches directly above or next to its speaker.

Before the performance each amplifier is turned up just to the point where feedback occurs when a mike swings directly over or next to its speaker, but no feedback occurs as the mike swings to either side. This level on each amplifier is then marked for future reference and all amplifiers are turned down.

The performance begins with performers taking each mike, pulling it back like a swing, and then holding them while another performer turns up the amplifiers to their pre-marked levels. Performers then release all the microphones in unison. Thus, a series of feedback pulses are heard which will either be all in unison or not depending on the gradually changing phase relations of the different mike pendulums.

Performers then sit down to watch and listen to the process along with the rest of the audience.

The piece is ended sometime shortly after all mikes have come to rest and are feeding back a continuous tone by performers pulling out the power cords of the amplifiers.

— Steve Reich, Pendulum Music (1968, revised version), Universal Edition UE 16155

American composer Steve Reich

Considered one of the pioneers of minimalist music

  • Born 1936 in New York.
  • His parents divorced when he was one year old.
  • He made many train journeys from New York to Los Angeles to visit his mother (see Different Trains).
  • Graduated in philosophy in 1957.
  • Received master’s degree in music from Mills College in 1963.
  • Studied African drumming at the University of Ghana in Accra.

center Portrait of Steve Reich, photographed by Bernard Gotfryd, 1982–84

Steve Reich, 1982–84 · Photo: Bernard Gotfryd
no known restrictions
Music Derived from Physical Processes

Musical influences

  • Balinese gamelan, Indian music, and African drumming.
  • Tape and electronic music.
  • Chanting of the Hebrew scriptures.
  • Twelve-tone technique and serialism.
  • The music and playing of John Coltrane.
Music Derived from Physical Processes

Notable compositions (excerpt)

  • Come Out (1966)
  • Drumming (1971)
  • Music for 18 Musicians (1974–76)
  • Different Trains for string quartet and tape (1988)
  • City Life for amplified ensemble (1995)
  • Double Sextet (2007)
Audio example:

Steve Reich: Different Trains

Three-movement piece for string quartet and tape
(1988)

▶ Listen online (external link)

Music Derived from Physical Processes

Musical Minimalism

Different institutional contexts after World War II:

Postwar Europe (Boulez, Stockhausen)

  • serialism shaped festivals, broadcasting studios, and academies
  • systematic composition marked a break with inherited traditions

United States (Riley, Reich, Glass, Eastman)

  • a more decentralized experimental scene
  • repetition, open form, and audible processes
Audio example:

Pierre Boulez: Structures I

(1952)

▶ Listen online (external link)

Clapping music

center Opening rhythmic pattern of Steve Reich’s Clapping Music and its first displacement

First two bars show the fundamental rhythm in 12/8 time and its first variation cycle.

After Steve Reich, Clapping Music (1972) · underlying composition excluded from CC BY 4.0
Audio example:

Steve Reich: Clapping music

(1972)

▶ Listen online (external link)

Music Derived from Physical Processes

Minimalist processes

  • restricted musical material and persistent repetition
  • steady pulse, drones, or cyclical rhythms
  • gradual change through addition, subtraction, or phase shifting
  • often tonal or modal pitch organization
  • extended duration and focused listening
Music Derived from Physical Processes

Julius Eastman

Composer, pianist, and vocalist (1940–1990). A minimalist outside the familiar canon, whose additive process carries the music's own history forward:

  • additive "organic music": each new section carries the previous ones within it
  • open scores and collective, unspecified ensembles
  • Stay On It (1973), Femenine (1974), Gay Guerrilla (1979)
  • nearly lost after his death; recovered through Mary Jane Leach's archival work

▶ Listen online (external link)

Pendulum Music

“a piece that runs on its own once you set it up” — Steve Reich, 2000

  • Sound art installation and composition.

  • Written playing instruction instead of musical notation.

  • Series of feedback pulses moving in and out of phase.

▶ Listen online (external link)

center Suspended microphones swinging above loudspeakers in the setup for Pendulum Music

Music Derived from Physical Processes

Form and structure of Pendulum Music

  • the sound is generated solely through acoustic feedback
  • the temporal structure derives from the damped mechanical oscillation of the pendulums
  • slight physical differences between the pendulums create shifting phase relationships between the feedback pulses
Music Derived from Physical Processes

Process as musical form

Pendulum Music exhibits a gradual transformation of a simple musical idea:

  • the underlying physical and acoustic processes are made audible
  • the compositional process and sounding result coincide
  • acoustic and psychoacoustic effects emerge from the feedback system
Music Derived from Physical Processes

Process music

Process music involves compositions where a simple musical idea undergoes gradual transformation or variation over time:

Placing your feet in the sand by the ocean's edge and watching, feeling, and listening to the waves gradually bury them.

Steve Reich in "Writings about Music"

Music Derived from Physical Processes

Musical phasing

Musical phasing is a compositional technique in which two identical repeating patterns begin together and gradually move out of synchronization because one repeats at a slightly different speed.

Interactive demonstration: tape-loop phasing ↗

Audio example (excerpt):

Steve Reich: Come Out

(1966)

▶ Listen online (external link)

Music Derived from Physical Processes

Signal phase difference

Phase difference describes the angular relationship between two sinusoidal signals of the same frequency.

  • measured relative to a reference signal
  • expressed as an angle within one period

Phase angle and unit circle

center Unit circle relating phase angle to one period of a sinusoidal signal

Music Derived from Physical Processes

Swinging motion of a simple pendulum

The length of a pendulum determines its period :

gravitational acceleration
length

(Small angle approximation)


center Diagram of a simple pendulum showing its length, swing angle, and equilibrium position

center Damped oscillations of two pendulums with slightly different periods and an increasing phase difference

Oscillation amplitudes of two pendulums as a function of time with friction damping.

Music Derived from Physical Processes

Feedback

The return to the input of a part of the output of a machine, system, or process:

  • Circular causality.
  • Used in cybernetics and system theory.
Music Derived from Physical Processes

Acoustic feedback

Iterated amplification of a looped audio signal. Sound loop of an acoustic feedback system includes a circular connection between:

  • Microphone
  • Preamp
  • Power amp
  • Loudspeaker

Acoustic feedback in a sound-reinforcement system

center Signal-flow diagram of an acoustic feedback loop between microphone, amplifier, loudspeaker, and room

Music Derived from Physical Processes

Larsen tone

Named after Søren Absalon Larsen, the Larsen tone results from positive feedback within an acoustic system:

  • Resonant ringing, squealing, or howling.
  • It occurs when the loop gain is high enough to sustain oscillation at one or more frequencies.
Music Derived from Physical Processes

Barkhausen criterion

Necessary but not sufficient condition for an electronic circuit to produce oscillations:

Loop gain:
Phase delay: (n = integer)


Open graphing calculator

Music Derived from Physical Processes

Positive feedback

The returned signal reinforces the input and may produce oscillation or instability.

  • In a simplified sinusoidal model, constructive feedback corresponds to a loop phase of 0° or an integer multiple of 360°.

Negative feedback

The returned signal opposes changes in the system and tends to reduce deviations.

  • In a simplified sinusoidal model, this corresponds to a phase difference of 180°.
Music Derived from Physical Processes

Pitch of the feedback

Larsen tone depends on:

  • Time delay between the microphone and the loudspeaker.
  • Frequency response of the microphone and amplifier.
  • Room acoustics (resonance).

Karplus–Strong string synthesis


center Block diagram of Karplus–Strong synthesis with excitation, delay, filtering, output, and a feedback path

Feedback-based synthesis algorithm using a short delay and filtering to create plucked and percussive sounds.

Music Derived from Physical Processes

The artistic utilization of feedback

Feedback is a simple system that can generate complex and unexpected results.

  • Alvin Lucier - I Am Sitting in a Room (1969)
  • Peter Weibel - The Endless Sandwich (1970)
  • Nicolas Collins - Pea Soup (1974)
  • Toshimaru Nakamura – No-Input Mixing Board (2000)
  • Agostino Di Scipio - Untitled, Ecosystemic - Sound Installation in a Small Reverberant Space (2005)
  • Halldór Úlfarsson - Halldorophone (since 2008)
Music Derived from Physical Processes

Intentional feedback is an important element of the electric guitar sound. It can range from subtle atmospheric textures to loud, distorted wails.

Examples:

Music Derived from Physical Processes

Optical feedback

Video feedback is created when a video camera captures its own display output, resulting in cascaded images.

Artistic utilization of video feedback:

  • Nam June Paik
  • Steina and Woody Vasulka
  • Bill Viola
Music Derived from Physical Processes

Critical discussion

"About one minute of minimalism is a lot, because it is all the same. [Minimalists] are not aware of the larger dimensions of life. One also hears constant repetition in the speeches of Hitler, and in advertising. It has its dangerous aspects."

— Elliott Carter, quoted in Michael Walsh, "The Heart Is Back in the Game," Time, 20 Sept. 1982

Music Derived from Physical Processes

Legacy of Pendulum Music

Physical processes can generate musical structure.

Connections to:

  • sound installation and spatial practice
  • feedback-based electronic music
  • process-based and algorithmic composition
  • interactive and self-organizing systems

“The compositional process and the sounding music are one and the same thing.”
— Steve Reich, “Music as a Gradual Process” (1968)

Literature

  • Fink, Robert. Repeating Ourselves: American Minimal Music as Cultural Practice. University of California Press, 2009.
  • Kim, Seunghun, et al. “Augmenting environmental interaction in audio feedback systems.” Applied Sciences, vol. 6, no. 5, 28 Apr. 2016, p. 125, https://doi.org/10.3390/app6050125.
  • LaBelle, Brandon. Background Noise: Perspectives on Sound Art. Bloomsbury, 2012.
  • Lindberg, Erik. "The Barkhausen Criterion (Observation ?)." 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems 2010, pp. 15-18.
  • Magnusson, Thor, et al. “Reflexions upon feedback.” NIME 2022, https://doi.org/10.21428/92fbeb44.aa7de712.

Literature

  • Nyman, Michael. Experimental Music: Cage and Beyond. Cambridge University Press, 2012.
  • Ross, Alex. The Rest Is Noise: Listening to the Twentieth Century. Harper Perennial, 2009.
  • Reich, Steve. “On ‘Pendulum Music.’” Interview by Jason Gross. Perfect Sound Forever, April 2000. https://www.furious.com/perfect/ohm/reich.html
  • Reich, Steve. Writings about Music. Halifax: Press of the Nova Scotia College of Art and Design; New York: New York University Press, 1974.
  • Sanfilippo, Dario, and Andrea Valle. “Feedback systems: An analytical framework.” Computer Music Journal, vol. 37, no. 2, June 2013, pp. 12–27, https://doi.org/10.1162/comj_a_00176.

Literature

Websites

Third-party materials

These notices cover third-party assets reproduced locally in this slide deck. Concise rights information appears at the point of use; complete attribution, source and license information is provided here.

Quoted material

  • Steve Reich, Pendulum Music (1968, revised version) — complete text score quoted for analysis and practical reconstruction; Universal Edition, UE 16155; official work page; excluded from the course CC BY 4.0 license

Third-party materials (continued)

Material with a separate rights status

  • Steve Reich portrait — Bernard Gotfryd, 1982–84; Library of Congress, via Wikimedia Commons; no known restrictions on publication
  • Steve Reich, Clapping Music (1972) — analytical visualization by Lorenz Schwarz after the opening rhythm and first displacement; Universal Edition, UE16182; underlying composition excluded from the course CC BY 4.0 license

© 2026 Lorenz Schwarz

Original text, diagrams, illustrations, photographs, audio, and video are licensed under CC BY 4.0, except where otherwise noted.

Third-party material: See the preceding rights notices.

Contact: lschwarz@hfg-karlsruhe.de

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