finished section on acoustic feedback definition

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\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}
\subsection{Electronic Feedback}
\subsection{Mathmatical FeedbacK}
Rational Melody XXI - Tom Johnson
Not electronic feedback, but serves as an example that feedback is not
limited to electronics.
IIR filter example?
\subsection{Amplification}
\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
exponential rate as illustrated in Figure~\ref{acoustic_feedback}.\\
\begin{figure}[H]
\makebox[\textwidth]{\includegraphics[width=0.75\textwidth]{acoustic_feedback_diagram}}
\caption[Caption for LOF]{Acoustic Feedback Diagram\protect\footnotemark}
\label{acoustic_feedback}
\end{figure}
\footnotetext{Diagram taken from:
\url{http://www.mediacollege.com/audio/howto/feedback.html}}
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 research has been carried out into methods for
attenuating and controlling this effect.~\parencite[p.1]{}
However, the volatile and unpredictable nature of acoustic feedback has
been used to great effect in both popular and avant-garde music.
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 works such as Steve Reich's Pendulum
Music, where feedback becomes the focus of the piece entirely. This is
discussed further in section~\ref{wolfman}
\subsection{Electronic Feedback}
\subsection{Mathmatical Feedback}
Rational Melody XXI - Tom Johnson
Not electronic feedback, but serves as an example that feedback is not
limited to electronics.
IIR filter example?
\subsection{Amplification}
\section{Musical Aspects and Implications of Feedback Systems}
\subsection{Indeterminacy}
\subsection{Process and Control}
\subsection{Rhythmic/Temporal Implications of Feedback}
\subsection{Spectral Implications of Feedback}
\subsection{Dynamic Implications of Artificial Amplitude Adjustment}
\subsection{Indeterminacy}
\subsection{Process and Control}
\subsection{Rhythmic/Temporal Implications of Feedback}
\subsection{Spectral Implications of Feedback}
\subsection{Dynamic Implications of Artificial Amplitude Adjustment}
\section{Composition Analysis}
\subsection{Acoustic Feedback}
Steve Reich's Pendulum Music
Robert Ashley's The Wolfman - ref: kyle gann - robert ashley
\subsection{Acoustic Feedback}
\subsubsection{Steve Reich's Pendulum Music}
\subsubsection{Robert Ashley's The Wolfman}\label{wolfman}
- ref: kyle gann - robert ashley
\subsection{Electronic Feedback}
David Tutor's Untitled (1996), Toneburst (2004), and Pulsers (1996)
Gordon Mumma's Hornpipe
\subsection{Electronic Feedback}
David Tutor's Untitled (1996), Toneburst (2004), and Pulsers (1996)
Gordon Mumma's Hornpipe
\subsection{Amplification}
John Cage's Cartridge Music
Stockhausen's Mikrophonie
\subsection{Amplification}
John Cage's Cartridge Music
Stockhausen's Mikrophonie
\printbibliography