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Applications of the Discrete Fourier Transform to Music Analysis.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Applications of the Discrete Fourier Transform to Music Analysis./
Author:	Harding, Jennifer Diane.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	149 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-12, Section: A.
Contained By:	Dissertations Abstracts International82-12A.
Subject:	Music theory. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28320770
ISBN:	9798515282042

Applications of the Discrete Fourier Transform to Music Analysis.
Harding, Jennifer Diane.

Applications of the Discrete Fourier Transform to Music Analysis. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 149 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: A.

Thesis (Ph.D.)--The Florida State University, 2021.

This item must not be sold to any third party vendors.

The discrete Fourier transform (DFT) has recently gained traction as a music-theoretic and music analytical tool, providing a mathematically robust way of modeling various musical phenomena. I examine both local and large-scale harmonic structures by using computational methods to interpret the pitch classes of a digitally encoded musical score through the discrete Fourier transform. On the small scale, my methodology shows relationships between sonorities within Fourier space, and aids in making statements about proximity, similarity, and distance between individual harmonic structures. On the larger scale, my methodology offers a broad view of the backgrounded scales and pitch-class collections of a piece: the "macroharmony." The DFT has the distinct analyticaladvantage of being stylistically and historically neutral. This allows a single methodology to apply to music from a wide variety of genres, time periods, and styles.In Chapter 1, I present the conversations scholars have had thus far pertaining to the DFT and its applications to harmony and pitch classes. I focus particularly on the contributions of David Lewin, Ian Quinn, and Jason Yust as three of the most influential people in promoting the DFT asa viable music-theoretical tool. Chapter 2 contains an overview of how the DFT applies to pitch classes in 12-tone equal temperament, along with a tutorial on its application. I then discuss some of the challenges of computational approaches to music analysis.In Chapter 3, I focus on simultaneities--the amalgamation of pitch classes sounding in a particular moment in time--and the distances traveled in Fourier space when moving from one to another. My approach is an expansion of Justin Hoffman's cartographies of multisets in Fourier space, which I apply to a chorale by J. S. Bach and a passage from a string quartet by Thomas Ades. In Chapter 4I expand the span of musical time used to define the multiset. Instead of a single moment in time defined by a discrete harmonic event, I use the technique of overlapping windowing to examine the macroharmony of musical excerpts by W. A. Mozart and Olivier Messiaen. Chapter 5 expands the applications of the DFT even further, now to quarter-tone and other microtonal systems. I apply the techniques from previous chapters to works by Charles Ives and Alois Haba. Finally, Chapter 6provides a short summary of the project, and includes ideas for future research endeavors.

ISBN: 9798515282042Subjects--Topical Terms:

547155
Music theory.
Subjects--Index Terms:

Discrete Fourier transform

Applications of the Discrete Fourier Transform to Music Analysis.
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520 $a The discrete Fourier transform (DFT) has recently gained traction as a music-theoretic and music analytical tool, providing a mathematically robust way of modeling various musical phenomena. I examine both local and large-scale harmonic structures by using computational methods to interpret the pitch classes of a digitally encoded musical score through the discrete Fourier transform. On the small scale, my methodology shows relationships between sonorities within Fourier space, and aids in making statements about proximity, similarity, and distance between individual harmonic structures. On the larger scale, my methodology offers a broad view of the backgrounded scales and pitch-class collections of a piece: the "macroharmony." The DFT has the distinct analyticaladvantage of being stylistically and historically neutral. This allows a single methodology to apply to music from a wide variety of genres, time periods, and styles.In Chapter 1, I present the conversations scholars have had thus far pertaining to the DFT and its applications to harmony and pitch classes. I focus particularly on the contributions of David Lewin, Ian Quinn, and Jason Yust as three of the most influential people in promoting the DFT asa viable music-theoretical tool. Chapter 2 contains an overview of how the DFT applies to pitch classes in 12-tone equal temperament, along with a tutorial on its application. I then discuss some of the challenges of computational approaches to music analysis.In Chapter 3, I focus on simultaneities--the amalgamation of pitch classes sounding in a particular moment in time--and the distances traveled in Fourier space when moving from one to another. My approach is an expansion of Justin Hoffman's cartographies of multisets in Fourier space, which I apply to a chorale by J. S. Bach and a passage from a string quartet by Thomas Ades. In Chapter 4I expand the span of musical time used to define the multiset. Instead of a single moment in time defined by a discrete harmonic event, I use the technique of overlapping windowing to examine the macroharmony of musical excerpts by W. A. Mozart and Olivier Messiaen. Chapter 5 expands the applications of the DFT even further, now to quarter-tone and other microtonal systems. I apply the techniques from previous chapters to works by Charles Ives and Alois Haba. Finally, Chapter 6provides a short summary of the project, and includes ideas for future research endeavors.
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