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\begin{abstract}
The use of electronic feedback as tools for musical composition has
featured in many composition, popular for it's volatile and
featured in many compositions, popular for it's complex, volatile and
indeterminate nature. Intrinsic to the use of feedback is the use of
amplification, capable of artificially altering an input's energy, as a
method for feedback control. This essay aims to provide a definition of
these tools in their different forms, and to analyse their use in a
range of prominent compositions. Forms of feedback will be defined,
followed by a discussion of the musical implications of their use,
including consideration for aspects such as process, indeterminacy,
including the consideration of aspects such as process, indeterminacy,
spectral implications and rhythmic implications. This will be related
to a number of compositions in order to provide an overall
understanding of their role in experimental music composition.
@@ -72,25 +72,24 @@
\section{Defining feedback and amplification}
A simple definition of feedback is the process of routing the output of a
system back to the input of that system.~\parencite[p.1]{weisert2010ioi}
This can take many form in the context of music, whether it is the acoustic
This can take many forms in the context of music. Whether it is the acoustic
feedback created by aiming a microphone to it's amplifier, or the digital
feedback present in an IIR filter, in all cases a loop is created from an
output point of a system, back to it's input.\\
The three types of feedback to be considered are:
The two types of electronic feedback are:
\begin{itemize}
\item{Acoustic Feedback}
\item{Electronic Feedback}
\item{Mathmatical Feedback}
\end{itemize}
In order to fully understand feedback, electronic amplification will also
be explored due to it's integral part in feedback system control.
\subsection{Acoustic Feedback}
Acoustic feedback occurs when a closed loop is created between an audio
transducer (such as a microphone or guitar pickup) and amplifier,
causing previously amplified audio to be reamplified continuously at an
transducer (such as a microphone or guitar pick-up) and amplifier,
causing previously amplified audio to be re-amplified continuously at an
exponential rate as illustrated in Figure~\ref{acoustic_feedback}.\\
\begin{figure}
\begin{figure}[H]
\makebox[\textwidth]{\includegraphics[width=\textwidth]{acoustic_feedback_diagram}}
\caption[Caption for LOF]{Acoustic Feedback Diagram\protect\footnotemark}
\label{acoustic_feedback}
@@ -99,18 +98,19 @@
\footnotetext{Diagram taken from:~\parencite[p.185]{holmes2012eaem}}
This is a common problem in the context of live audio, as the exponential
nature of the feedback causes a distinct "howling" sound that builds
rapidly and is commonly considered unplesant. As a result, a great deal of
nature of the feedback causes a distinct ``howling'' sound that builds
rapidly and is commonly considered unpleasant. As a result, a great deal of
research has been carried out into methods for attenuating and controlling
this effect.~\parencite[p.1]{waterschoot2010fyafc} However, the volatile
and unpredictable nature of acoustic feedback has been used to great effect
in both popular and avant-garde music.~\parencite[p.186]{holmes2012eaem}
Pioneering guitarists such as Jimi Hendrix have used the loop created
through placing an electric guitar pickup close to it's amplifier to
compliment virtuosic guitar solos in pieces such as Foxy
Lady~\citeyearpar{} This is taken one step further in avante-garde works
such as Steve Reich's Pendulum Music, where feedback becomes the focus of
the piece entirely. This is discussed further in section~\ref{pendulum}
compliment virtuosic guitar solos in pieces such as Foxey
Lady~\citeyearpar{hendrix1967fl}. This is taken one step further in
avant-garde works such as Steve Reich's Pendulum Music, where feedback
becomes the focus of the piece entirely. This is discussed further in
section~\ref{pendulum}
\subsection{Electronic Feedback}
Electronic feedback takes the principal of recursively feeding an output
@@ -125,36 +125,24 @@
of this effect.~\parencite[p.186, 390]{holmes2012eaem} A detailed analysis
of these techniques are presented in section~\ref{ElecFeed}\\
Although it is outside the scope of this essay, it is worth noting that
delay feedback forms the basis for electronic IIR filtering, both in the
analog and digital domain, and by extension is an integral part of almost
any composition that utilises audio
filters/equalizers.~\parencite[p.71-72]{zolzer2011dafx} This is an example
of how the precice control of electronic feedback can lead to a plethora of
creative musical possibilities.
\subsection{Amplification}
Amplification is the process of scaling a signal by a chosen factor.
Factors $>1.$ result in an increased overall amplitude (a regenerative
feedback system), whilst factors
$<1.$ result in an attenuated signal amplitude (a degenerative feedback
system)~\parencite[p.3-4]{kadis2012sosr}.
Amplification is the process of scaling a signal by a chosen factor.~\parencite[p.3-4]{kadis2012sosr}.
This artificial modification of amplitude has a number of interesting sonic
effects in itself, as it allows for the magnification of sounds that may not
naturally be perceivable and conversely, the reduction of extremely loud
sounds, to with a comfortable range for hearing. This explored through
works such as John Cage's Cartridge Music and Stockhausen's Mikrophonie as
discussed in section~\ref{amp}\\
sounds to a comfortable range for hearing. This is explored through
works such as John Cage's Cartridge Music as discussed in
section~\ref{amp}\\
It has been stated that feedback (particularly acoustic feedback) is
difficult to control. This is due to it's recursive nature and the tendancy
in many situations for output that exceeds unity gain (a state, whereby the
output amplitude of a feedback system is equal to that of it's input) to be
fed back into the system. Amplification is therefor a crucial element for
controlling the results of a feedback system. By attenuating an output
before feeding it back to a system, it is possible to ensure that outputs
do not grow at an exponential rate.~\parencite[p.71-72]{zolzer2011dafx}
\begin{figure}
It has been stated that feedback is difficult to control. This is due to
it's recursive nature and the tendency for output that exceeds unity gain
(a state, whereby the output amplitude of a feedback system is equal to
that of it's input) to be fed back into the system. Amplification is
therefore a crucial element for controlling the results of a feedback
system. By attenuating an output before feeding it back to a system, it is
possible to ensure that outputs do not grow at an exponential
rate.~\parencite[p.71-72]{zolzer2011dafx}
\begin{figure}[H]
\makebox[\textwidth]{\includegraphics[width=0.75\textwidth]{IIR_flow_diagram}}
\caption[Caption for LOF]{Basic Feedback Signal Flowchart\protect\footnotemark}
\label{feed_flowchart}
@@ -163,8 +151,8 @@
\footnotetext{Diagram adapted from:~\parencite[p.72]{zolzer2011dafx}}
\begin{figure}[H]
This can be demonstrated mathmatically using the following example equation
for a feedback system as illustrated in figure~\ref{feed_flowchart}:
This can be demonstrated mathematically using the following example equation
for a feedback system as illustrated in figure~\ref{feed_flowchart}~\parencite[p.70-72]{zolzer2011dafx}:
\begin{align*}
& y(n) = x(n) + gy(n-M)\\
& \text{where:}\\
@@ -175,43 +163,12 @@
& g\text{ is the feedback coefficient}\\
\end{align*}
\end{figure}
It is clear that $|g|$ dictates the stability of the signal, as values
$>1.$ increase exponentially as stated above.~\parencite[p.70-72]{zolzer2011dafx}
For example, in the case of acoustic feedback, $g$ is dictated by the
amount of signal that passes from the amplifier back to the microphone.
Placing the microphone close will result in a large amount of the amplified
signal returning to the amplifier, causing further amplification. When the
system reaches it's limit (which it will do very quickly) the signal
distorts, causing the typical "howling" effect.
\subsection{Mathmatical Feedback}
Mathmatical feedback is not technically a form of electronic feedback and
so will not be discussed in detail, however it does provide a good example
of the extent to which the concepts of feedback are used for creative
purposes in the context of experimental music.
Previously discussed feedback methods operate directly on a signal.
However, mathmatical feedback differs, in that it applies the mathmatical
principals of feedback to influence musical parameters of the composition.
This is demonstarted in Tom Johnson's Rational Melody XXI, where Johnson
specifies each subsequent bar as a retrograde of the previous bar, thus
causing the composition of each bar to rely on it's
predecessor.~\parencite[p.72]{weisert2010ioi} This follows the same
principles as stated in the equation with minor changes:
\begin{align*}
& y(n) = x(n) + g \cdot \text{ret}(y(n-M))\\
& \text{where:}\\
& \text{ret is a retrograde function}\\
& g = 1\\
& n_0 = \text{the initial musical phrase}\\
& n_{n\neq0} = \text{an empty phrase}
\end{align*}
\section{Musical Aspects and Implications of Feedback Systems}
There are a number of interesting musical implications when using feedback
and amplitude ajustment as a compositional tools. Features, such as it's
indeterministic nature and rhythmic characteristics, inherent to the nature
of feedback make it an interesting technique for musical exploration and
and amplitude adjustment as a compositional tools. Features such as
indeterministic and rhythmic characteristics, inherent to the nature
of feedback, make it an interesting technique for musical exploration and
there are many examples of artists exploiting these qualities in
experimental compositions. Likewise, amplitude modification offers a number
of compositional possibilities for both the control of feedback and for
@@ -221,83 +178,84 @@
\subsection{Indeterminacy}\label{indeterminate}
Indeterminacy is related to the use of chance operations in music
composition and performance. techniques that involve a degree of
composition and performance. Techniques that involve a degree of
uncertainty, where external variables or unpredictable factors affect the
outcome, are defined as indeterminate. Simms describes indeterminacy as
"Any part of a musical work is indeterminate if it is chosen by chance, or
outcome, are defined as indeterminate. Simms uses the following definition
for indeterminacy:
``Any part of a musical work is indeterminate if it is chosen by chance, or
if its performance is not precisely
specified."~\parencite[p.357]{simms1986mtc} It is a topic of interest for
specified.''~\parencite[p.357]{simms1986mtc} It is a topic of interest for
experimental composers for a number of reasons.
\subsubsection{Variation in Performance}\label{variance}
Using indeterministic processes as part of a composition allows for
variation in the performance of said composition on a case by case basis.
Through the addition of random factors to a composition, far greater
degrees of variance are created in the performance of a peice, allowing for
degrees of variance are created in the performance of a piece, allowing for
an infinite number of possible versions as opposed to the comparatively
limited interpretation of static compositions where all elements are
controlled directly by the composer.~\parencite[p.97-98, 381]{jc2009co,
holmes2012eaem}
This variance can take many forms dependant on the indeterministic factor.
An example might be the performer, which is demonstarted well through
An example might be the performer, which is demonstrated well through
Cornelius Cardew and Christian Wolff's compositions for the Fluxorchestra.
By composing "unambiguous, concrete proposals (which still left room for
personal idiosyncrasies in realization)", indeterminicity was created
By composing ``unambiguous, concrete proposals (which still left room for
personal idiosyncrasies in realization)'', indeterminicity was created
through the skill and interpretation of the performers in pieces such as
"Stones" by Wolff or "The Great Learning" by
``Stones'' by Wolff or ``The Great Learning'' by
Cardew~\parencite[110]{nyman1999em}\\
In terms of feedback, variance in feedback will depend primarily on the
variance of the input to the system and the variance of control. due to the
variance of the input to the system and the variance of control. Due to the
non-linear fashion in which feedback effects input to produce an output,
subtle changes in these may resut in significant changes to the output. An
subtle changes in these may result in significant changes to the output. An
example of this is a guitarist using an amplifier to produce feedback from
his guitar. In each performance, the subtle changes in distance between the
guitar and amplifier may result in significant differences to feedback
tone. This property of feedback applies to compositions such as Steve
Reich's Pendulum Music, aswell as Gordon Mumma's Hornpipe, discussed in
Reich's Pendulum Music and Gordon Mumma's Hornpipe, discussed in
section~\ref{pendulum} and section~\ref{hornpipe}.
\subsubsection{Bias Removal}
Indeterminacy is able to remove personal bias and ego involved in decision
making from a composition or performance. By leaving compositional
decisions to chance, it is ensured that the music produced is not created
with intent and is seperated from the composer's personal taste, as stated
with intent and is separated from the composer's personal taste, as stated
by John Cage~\parencite[p.381]{holmes2012eaem}. This technique is used in
his composition "Music of Changes", where chance operations are used for
the organisation of material in such a way that "bypassed a reliance on his
aesthetic judgment". By combining this relinquished control with the
precise control of other aspects of the peice, Cage was able to create a
"balance between rational and irrational" through the combination of
his composition ``Music of Changes'', where chance operations are used for
the organisation of material in such a way that ``bypassed a reliance on his
aesthetic judgement''. By combining this relinquished control with the
precise control of other aspects of the piece, Cage was able to create a
``balance between rational and irrational'' through the combination of
control and total removal of control over compositional
elements~\parencite[p.97-98]{jc2009co}.\\
In relation to feedback directly, the ability for feedback to create
exponentially complex output from relatively simple feedback systems
create clear elements of indeterminacy through the unpredictability of
their output. This is demonstrated in Steve Reich's "Pendulum Music" as
discussed in section ~\ref{pendulum}. Parallels can be drawn between John
Cage's use of indeterminacy to dictate organizational aspects of "Music of
Changes" with Steve Reich's use of feedback to dictate sonic events in
"Pendulum Music".
their output. This is demonstrated in Steve Reich's ``Pendulum Music'' as
discussed in section~\ref{pendulum}. Parallels can be drawn between John
Cage's use of indeterminacy to dictate organizational aspects of ``Music of
Changes'' with Steve Reich's use of feedback to dictate sonic events in
``Pendulum Music''.
\subsection{Process and Control}
The term "process" refers to the situation outlined by a composer, designed
for the creation of sound. Where popular music focuses on creating pre-defined
musical content and structure, experimental musicians focus on the creation
of a process through which sound may be generated. This may involve the
creation of rules or instructions that outline the conditions that are
needed in order to create an outcome, the content of which may differ on
each performance based on any indeterministic factors (see
section~\ref{indeterminate})~\parencite[p.4]{nyman1999em}
There are many forms of process used for the composition of experimental
music. These are observed in detail in \textit{Experimental Music - Cage
and Beyond}~\parencite[p.4-14]{nyman1999em}
The term ``process'' refers to the situation outlined by a composer,
designed for the creation of sound. Where popular music focuses on creating
pre-defined musical content and structure, experimental musicians focus on
the creation of a process through which sound may be generated. This may
involve the creation of rules or instructions that outline the conditions
that are needed in order to create an outcome, the content of which may
differ on each performance based on any indeterministic factors (see
section~\ref{indeterminate}) There are many forms of process used for the
composition of experimental music. These are observed in detail in
\textit{Experimental Music - Cage and
Beyond}~\parencite[p.4-14]{nyman1999em}
\subsubsection{Feedback Process}
Feedback is concerned mainly with electronic process, where an electronic
system is defined/set up in order to facilitate the creation of sound. The
specified set-up will therefor have a direct impact on the outcome of the
peice, combined with factors such as the methods for control other
processes involved in the peices realisation. This is true of Gordon
specified setup will therefore have a direct impact on the outcome of the
piece, combined with other factors such as the methods used for control of other
processes involved in the piece's realisation. This is true of Gordon
Mumma's Hornpipe~\citeyearpar{mumma2002lem} (as detailed in
section~\ref{hornpipe}) where electronic circuitry is designed specifically
to explore the effects of custom electronic circuitry used to produce
@@ -320,21 +278,21 @@
as, for example, providing an electronic feedback circuit with a louder
input will most likely result in a louder output. This relationship may not
be linear and depends on the design of the feedback system, which in turn
determines the indeterministic nature of these
dictates the indeterministic nature of these
systems~\parencite[p.19-27]{weisert2010ioi}. However, it still provides a
method for control over the output of the system. This is apparent in
Mumma's Hornpipe~\citeyearpar{mumma2002lem} where the performer must adapt
the input to the system (in this case the sound produced by the french
the input to the system (in this case the sound produced by the French
horn) in reaction to the electronic sound produced by the ``cybersonic
console''.
\paragraph{System Parameters}\mbox{}\\
As stated above, the design of the feedback system will determine it's
reponse to a given input. A common method for controlling the design of a
feedback system is through the implementation of variable nodes, for the
dynamic ajustment of parameters.~\parencite[p.19-27]{weisert2010ioi}
response to a given input. A common method for controlling the design of a
feedback system is through the implementation of variable nodes for the
dynamic adjustment of parameters.~\parencite[p.19-27]{weisert2010ioi}
A clear example of this is the use of a scaling factor in the feedback loop
to paraemtize the regenerative/degenerative nature of the system. By
to parametrize the regenerative/degenerative nature of the system. By
altering this parameter, the degree to which a signal is
amplified/attenuated on each recursion can be modified dynamically during
performance. This would be attributed to the guitar-amplifier distance in
@@ -343,11 +301,11 @@
\subsection{Rhythmic/Temporal Implications of Feedback}
The process of feeding a signal back through a system has consequences in
terms of a subsequent iteration's rhythms. The superposition of signals
causes alterations in the temporal content of the subsequenct signals,
causes alterations in the temporal content of the subsequent signals,
resulting in the removal and addition of temporal peaks to the signal (a
signal's peaks are linked to the perceived characteristic of the signal's
rhythm). The effects of feedback are discussed at length with regards to
Alvin Lucier's "I am sitting in a room" by
Alvin Lucier's ``I am sitting in a room'' by
Weisert~\parencite[p.64-68]{weisert2010ioi}. The rhythmic impact of a
feedback system is complex. However, at a basic level, it should be
understood that feedback causes a shift in rhythmic content over time. The
@@ -360,40 +318,54 @@
As with rhythmic content, feedback has a complex effect on the spectral
content of a signal. As with the rhythmic content, the effect of
superposition on the original signal emphasizes and reduces spectral
content. This is again, examined at length in Weisert's analysis of "I am
sitting in a room" and a similar shift in spectral content can be observed
content. This is again, examined at length in Weisert's analysis of ``I am
sitting in a room'' and a similar shift in spectral content can be observed
to that of the rhythmic content over
time.~\parencite[p.60-64]{weisert2010ioi}
\subsection{Dynamic Implications of Artificial Amplitude Adjustment}
The artificial ajustment of audio amplitude is an important technique as it
The artificial adjustment of audio amplitude is an important technique as it
allows for the alteration of a signal's energy. This acts as a form of
sonic magnifier, able to make inaudibley small sounds audible, as
demonstrated in pieces such as John Cage's "Cartridge
Music"~\citeyearpar{cage2013cm} and Stockhausen's "Mikrophonie"
sonic magnifier, able to make inaudibly small sounds audible, as
demonstrated in pieces such as John Cage's ``Cartridge
Music''~\citeyearpar{cage2013cm} and Stockhausen's ``Mikrophonie''
collection~\citeyearpar{stockhausen1995mmt}. This technique was instrumental in the
development of electroacoustic music by artists such as cage and
stockhausen as it allowed the details of quiet sounds to be amplified
artificially in a live environment.~\cite[p.351-352]{holmes2012eaem}
development of electroacoustic music by artists such as Cage and
Stockhausen as it allowed the details of quiet sounds to be amplified
artificially in a live environment.~\parencite[p.351-352]{holmes2012eaem}
This process is combined with the principals of a feedback system in order
to provide control to a feedback system. By altering the amplification of
signals in a feedback system, dynamic control of feedback properties is
possible. This is clearly used in works such as Robert Ashley's "The
Wolfman" in order to tune the feedback in an appropriate
fashion.~\cite[p.186]{holmes2012eaem}
possible. This is clearly used in works such as Robert Ashley's ``The
Wolfman'' in order to tune the feedback in an appropriate
fashion.~\parencite[p.186]{holmes2012eaem}
\section{Composition Analysis}
There are a large number of peices that utilise electronic feedback
creatively. This section analyses some of the most prominent peices in
order to present some explorations and useages of feedback in experimental
music.
There are a large number of pieces that utilise electronic feedback and
amplification creatively. This section analyses some of the most prominent
pieces in order to present some explorations and usages of feedback in
experimental music.
\subsection{Amplification}\label{amp}
\subsubsection{John Cage's Cartridge Music~\citeyearpar{cage2013cm}}
Cartridge music explores the amplification of small sounds through the use
of phonograph cartridges and a range of object in order to create amplified
audio based on the performer's interactions with these objects. By
inserting the object in place of the phonograph's needle, a performer is
able to create amplified sounds that vary based on the type of object used.
This piece was created to explore the possibilities of amplifying small
sounds to within an audible range and the chance sounds that are created as
a result. The piece focuses on the aesthetics of different mediums of
object, and does not concern itself with player improvisation as do other
examples. This reflects Cage's attitude towards the process and openness to
chance events by allowing the unexpected to form part of the piece, without
intervention of the performer.~\parencite[p.56-61]{lucier2012m109}
\subsection{Acoustic Feedback}
\subsubsection{Steve Reich's Pendulum Music~\parencite[p.31]{reich2002wom}}\label{pendulum}
This piece is possibly one of the most direct explorations of acoustic
feedback. Where other pieces the effects of feedback on an external source,
feedback. Where other pieces explore the effects of feedback on/with an external source,
Pendulum Music focuses directly on the sonic phenomena generated purely by
the feedback system and the acoustics of the space~\parencite[p.50-51]{weisert2010ioi}.
@@ -405,8 +377,8 @@
microphones as the piece progresses, which is in keeping with Reichs works
such as Come Out~\citeyearpar{reich1966comeout}
This piece has a clear focus on process and was described as "the ultimate
process piece" by Reich. Designed as an "audible scupture", the piece is
This piece has a clear focus on process and was described as ``the ultimate
process piece'' by Reich. Designed as an ``audible sculpture'', the piece is
designed to limit human interaction in order to focus on the natural
interaction of acoustic feedback. Control of aesthetics is determined by
the semi-indeterministic method of releasing the suspended microphones,
@@ -426,14 +398,14 @@
creating even small vocal sounds, the performer is able to control the
aesthetics of the feedback loop demonstrating the exponentially complex
impact of even the simplest inputs to a feedback system, as described
previously. Ashley commented that "the vocal sounds used to induce the
feedback have to be extremely soft so as not to block it" and he regretted
previously. Ashley commented that ``the vocal sounds used to induce the
feedback have to be extremely soft so as not to block it'' and he regretted
that the piece was believed to be generated by screams, which was far from
true~\parencite[p.37]{gann2012ra}. The result is a massive build up of
distortion and noise that develops as more vocalisms are supplied to the
feedback loop. It has also been observed that the piece's spectral content
is largely dictated by the room acoustics, tending towards a build up of
high pitched, shrill tones in smalled rooms. This shows the general focus
high pitched, shrill tones in smaller rooms. This shows the general focus
on the concept of process in experimental
compositions~\parencite[p.18]{cage2011silence} as the piece may differ
dramatically based on the conditions of the performance.
@@ -445,36 +417,36 @@
by creating custom electronic circuitry for the generation, manipulation
and feedback of audio. This was then controlled through the live filtering
and amplification of the feedback circuits to alter the output over
time~\parencite[p.187]{holmes2012eaem}.\\
time~\parencite[p.187]{holmes2012eaem}.
\paragraph{Pulsers}\mbox{}\\
Pulsers aimed to explore the temporal and rhythmic effect of feedback and
live elctronics by using extensive electronic feedback/amplification
live electronics by using extensive electronic feedback/amplification
networks to modify the sound of various materials such as a tape recording
of an electronic violin~\parencite{tudor1984twle}. By altering the amplification and filtering of the
circuit live, the performer is given control over the rhythmic aspects of
the output. This results in the controlled use of the complex rhythms
possible with feedback.\\
possible with feedback.
\paragraph{Untitled}\mbox{}\\
Untitled was created as an exploration of the use of "no-input" live
electrnics. The electronic setup consisted of a complicated feedback setup
Untitled was created as an exploration of the use of ``no-input'' live
electronics. The electronic setup consisted of a complicated feedback setup
designed to manipulate the characteristics of sounds created purely through
the electronics (without any external input from microphones or
recordings).
The live ajustment of electronic parameters created an interesting
The live adjustment of electronic parameters created an interesting
improvisational element in Untitled, as the complex nature of the
circuitry created an interplay between performer and the system. The
performer would ajust parameters, the system would respond, and subsequent
performer would adjust parameters, the system would respond, and subsequent
alterations would be made as a result~\parencite{tudor1984twle}.
However, the tendancy for feedback to become uncontrollable and the
extermely complex signal path resulted in a piece too complex to be
However, the tendency for feedback to become uncontrollable and the
extremely complex signal path resulted in a piece too complex to be
manageable in terms of live performance. This is a good example of the
indeterminate, complex nature of
feedback.~\parencite[p.83-85]{weisert2010ioi}
\subsubsection{Gordon Mumma's Hornpipe~\citeyearpar{mumma2002lem}}\label{hornpipe}
Hornpipe is a composition that combines the input from a french horn with
Hornpipe is a composition that combines the input from a French horn with
custom electronic circuitry created by Mumma, in order to transform the input by
monitoring and altering output based on input resonance.
The piece aims to explore electronic circuitry as a form of extension to
@@ -488,10 +460,14 @@
unpredictability of the electronic circuitry based on the number of factors
that determine it's output.
\subsection{Amplification}\label{amp}
\subsubsection{John Cage's Cartridge Music~\citeyearpar{cage2013cm}}
\section{Conclusion}
It is clear that feedback provides enormous potential for creative
possibilities in music, as demonstrated by the wide variety of
experimental compositions detailed. This is far from an exhaustive set of
examples and many more examples explore the unique properties of feedback.
Overall, feedback's indeterministic nature, spectral/temporal impact, and
range of possibilities for control make it a unique and interesting area
for musical experimentation.
\printbibliography