Fourier Phase and Pitch-Class Sum

Dmitri Tymoczko; Jason Yust

doi:10.1007/978-3-030-21392-3_4

Fourier Phase and Pitch-Class Sum

Dmitri Tymoczko, Jason Yust

Music

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

7 Scopus citations

Abstract

Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.

Original language	English (US)
Title of host publication	Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings
Editors	Mariana Montiel, Francisco Gomez-Martin, Octavio A. Agustín-Aquino
Publisher	Springer Verlag
Pages	46-58
Number of pages	13
ISBN (Print)	9783030213916
DOIs	https://doi.org/10.1007/978-3-030-21392-3_4
State	Published - 2019
Event	7th International Conference on Mathematics and Computation in Music, MCM 2019 - Madrid, Spain Duration: Jun 18 2019 → Jun 21 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11502 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Conference on Mathematics and Computation in Music, MCM 2019
Country/Territory	Spain
City	Madrid
Period	6/18/19 → 6/21/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Keywords

Chord geometry
Fourier transform
Musical scales
Tonal harmony
Voice leading

Access to Document

10.1007/978-3-030-21392-3_4

Cite this

Tymoczko, D., & Yust, J. (2019). Fourier Phase and Pitch-Class Sum. In M. Montiel, F. Gomez-Martin, & O. A. Agustín-Aquino (Eds.), Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings (pp. 46-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11502 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-030-21392-3_4

Tymoczko, Dmitri ; Yust, Jason. / Fourier Phase and Pitch-Class Sum. Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings. editor / Mariana Montiel ; Francisco Gomez-Martin ; Octavio A. Agustín-Aquino. Springer Verlag, 2019. pp. 46-58 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.",

keywords = "Chord geometry, Fourier transform, Musical scales, Tonal harmony, Voice leading",

author = "Dmitri Tymoczko and Jason Yust",

year = "2019",

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language = "English (US)",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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pages = "46--58",

editor = "Mariana Montiel and Francisco Gomez-Martin and Agust{\'i}n-Aquino, {Octavio A.}",

booktitle = "Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings",

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Tymoczko, D & Yust, J 2019, Fourier Phase and Pitch-Class Sum. in M Montiel, F Gomez-Martin & OA Agustín-Aquino (eds), Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11502 LNAI, Springer Verlag, pp. 46-58, 7th International Conference on Mathematics and Computation in Music, MCM 2019, Madrid, Spain, 6/18/19. https://doi.org/10.1007/978-3-030-21392-3_4

Fourier Phase and Pitch-Class Sum. / Tymoczko, Dmitri; Yust, Jason.
Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings. ed. / Mariana Montiel; Francisco Gomez-Martin; Octavio A. Agustín-Aquino. Springer Verlag, 2019. p. 46-58 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11502 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Fourier Phase and Pitch-Class Sum

AU - Tymoczko, Dmitri

AU - Yust, Jason

PY - 2019

Y1 - 2019

N2 - Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.

AB - Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.

KW - Chord geometry

KW - Fourier transform

KW - Musical scales

KW - Tonal harmony

KW - Voice leading

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings

A2 - Montiel, Mariana

A2 - Gomez-Martin, Francisco

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PB - Springer Verlag

T2 - 7th International Conference on Mathematics and Computation in Music, MCM 2019

Y2 - 18 June 2019 through 21 June 2019

ER -

Tymoczko D, Yust J. Fourier Phase and Pitch-Class Sum. In Montiel M, Gomez-Martin F, Agustín-Aquino OA, editors, Mathematics and Computation in Music - 7th International Conference, MCM 2019, Proceedings. Springer Verlag. 2019. p. 46-58. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-21392-3_4

Fourier Phase and Pitch-Class Sum

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All Science Journal Classification (ASJC) codes

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