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Figure 2. Summary of Auerbach's pitch-, pitch-class-, and duration-preserving operations.

Summary of Auerbach's pitch-, pitch-class-, and duration-preserving operati...

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in Musical Motives: A Theory and Method for Analyzing Shape in Music > Journal of Music Theory
Published: 01 October 2022
Figure 2. Summary of Auerbach's pitch-, pitch-class-, and duration-preserving operations. More
Journal Article

On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces

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Justin Hoffman
Journal of Music Theory (2008) 52 (2): 219–249.
DOI: https://doi.org/10.1215/00222909-2009-016
Published: 01 October 2008
...Justin Hoffman Recent music-theoretical research has proposed two ways of mapping the pitch-class set universe. Fourier spaces, constructed by Quinn, relate sets to one another based upon their composition from members of interval cycles, reflecting what might be called “harmonic quality.” Voice...
View articletitled, On <span class="search-highlight">Pitch</span>-<span class="search-highlight">Class</span> Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces View PDF for article titled, On <span class="search-highlight">Pitch</span>-<span class="search-highlight">Class</span> Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces
Journal Article

Modal Spelled Pitch Class, La-Minor Solfège, and Schubert’s Third Relations

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Nathan L. Lam
Journal of Music Theory (2020) 64 (2): 241–281.
DOI: https://doi.org/10.1215/00222909-8550795
Published: 01 October 2020
...Nathan L. Lam This article develops the notion of modal spelled pitch class by combining Julian Hook’s theory of spelled heptachords and Steven Rings’s heard scale degree. Modal spelled pitch class takes the form of an ordered triple that includes the key signature, the generic pitch classes...
View articletitled, Modal Spelled <span class="search-highlight">Pitch</span> <span class="search-highlight">Class</span>, La-Minor Solfège, and Schubert’s Third Relations View PDF for article titled, Modal Spelled <span class="search-highlight">Pitch</span> <span class="search-highlight">Class</span>, La-Minor Solfège, and Schubert’s Third Relations
Journal Article

Special Cases of the Interval Function between Pitch-Class Sets X and Y

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David Lewin
Journal of Music Theory (2001) 45 (1): 1–29.
DOI: https://doi.org/10.2307/3090647
Published: 01 April 2001
...David Lewin 2001 © Yale University, New Haven, Connecticut 06520 2001 SPECIAL CASES OF THE INTERVAL FUNCTION BETWEEN PITCH-CLASS SETS X AND Y David Lewin 1. Pcset pairs <X,Y> for which IFUNC(X,Y) is constant 1.1.1 Example...
View articletitled, Special Cases of the Interval Function between <span class="search-highlight">Pitch</span>-<span class="search-highlight">Class</span> Sets X and Y View PDF for article titled, Special Cases of the Interval Function between <span class="search-highlight">Pitch</span>-<span class="search-highlight">Class</span> Sets X and Y
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Pitch-class space (pc).

Pitch-class space ( pc ).

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in Violin Fingerboard Space: Intervallic Mappings from Instrumental Space to Pitch Space > Journal of Music Theory
Published: 01 October 2024
Figure 13. Pitch-class space ( pc ). More
Journal Article

Continuous Harmonic Spaces

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Clifton Callender
Journal of Music Theory (2007) 51 (2): 277–332.
DOI: https://doi.org/10.1215/00222909-2009-004
Published: 01 October 2007
...Clifton Callender This article generalizes Ian Quinn's recent harmonic characterization of pitch-class sets in equal tempered spaces to chords drawn from continuous pitch and pitch-class spaces. Using the Fourier transform, chords of any real-valued pitches or pitch classes are represented...
View articletitled, Continuous Harmonic Spaces View PDF for article titled, Continuous Harmonic Spaces
Journal Article

Generalizing Musical Intervals

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Dmitri Tymoczko
Journal of Music Theory (2009) 53 (2): 227–254.
DOI: https://doi.org/10.1215/00222909-2010-003
Published: 01 October 2009
..., since some musical spaces have natural boundaries. It also notes that there are spaces, including the familiar pitch-class circle, in which there are multiple paths between any two points. This leads to the suggestion that we might sometimes want to replace traditional pitch-class intervals with paths...
View articletitled, Generalizing Musical Intervals View PDF for article titled, Generalizing Musical Intervals
Journal Article

WHEN EVEN BECOMES ODD: A PARTITIONAL APPROACH TO INVERSION

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Brian Alegant
Journal of Music Theory (1999) 43 (2): 193–230.
DOI: https://doi.org/10.2307/3090660
Published: 01 October 1999
...Brian Alegant This paper proposes a refinement of our understanding of pitch-class inversion in atonal and twelve-tone music. Part I of the essay establishes the theoretical foundation. It reviews the index number approach formulated by Milton Babbitt, examines characteristics of even and odd index...
View articletitled, WHEN EVEN BECOMES ODD: A PARTITIONAL APPROACH TO INVERSION View PDF for article titled, WHEN EVEN BECOMES ODD: A PARTITIONAL APPROACH TO INVERSION
Journal Article

Special Collections: Renewing Set Theory

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Jason Yust
Journal of Music Theory (2016) 60 (2): 213–262.
DOI: https://doi.org/10.1215/00222909-3651886
Published: 01 October 2016
...Jason Yust The discrete Fourier transform on pitch-class sets, proposed by David Lewin and advanced by Ian Quinn, may provide a new lease on life for Allen Forte's idea of a general theory of harmony for the twentieth century based on the intervallic content of pitch-class collections. This article...
View articletitled, Special Collections: Renewing Set Theory View PDF for article titled, Special Collections: Renewing Set Theory
Journal Article

Bartók's Polymodality: The Dasian and Other Affinity Spaces

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José Oliveira Martins
Journal of Music Theory (2015) 59 (2): 273–320.
DOI: https://doi.org/10.1215/00222909-3136020
Published: 01 October 2015
..., harmonic functions, or pitch centricity. The Dasian space is a closed, nonoctave repeating scalar cycle, where each element is identified by a unique coordination of pitch class and modal quality. The dual description of each element enables both the specification of location in a given cycle...
View articletitled, Bartók's Polymodality: The Dasian and Other Affinity Spaces View PDF for article titled, Bartók's Polymodality: The Dasian and Other Affinity Spaces
Journal Article

Sum Class

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Joseph N. Straus
Journal of Music Theory (2018) 62 (2): 279–338.
DOI: https://doi.org/10.1215/00222909-7127694
Published: 01 October 2018
...Joseph N. Straus Pitch sets and pitch-class sets whose integers share the same sum are connected by pure contrary voice leading and share a center of balance. This article studies progressions of chords that may belong to different T/I set-classes but that belong to the same sum class. Copyright...
View articletitled, Sum <span class="search-highlight">Class</span> View PDF for article titled, Sum <span class="search-highlight">Class</span>
Journal Article

Generic (Mod-7) Voice-Leading Spaces

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Leah Frederick
Journal of Music Theory (2019) 63 (2): 167–207.
DOI: https://doi.org/10.1215/00222909-7795257
Published: 01 October 2019
... properties of these spaces derive from the properties of diatonic pitch-class sets and generic pitch spaces developed by Clough and Hook. After presenting the construction of these voice-leading spaces and defining the OPTIC relations in mod-7 space, this article presents the mod-7 OPTIC -, OPTI -, OPT...
View articletitled, Generic (Mod-7) Voice-Leading Spaces View PDF for article titled, Generic (Mod-7) Voice-Leading Spaces
Journal Article

Lutosławski's Mid-Century Harmony: Reconceptualizing Chordal Space in the Five Iłłakowicz Songs

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José Oliveira Martins
Journal of Music Theory (2023) 67 (2): 209–249.
DOI: https://doi.org/10.1215/00222909-10699703
Published: 01 October 2023
... qualities to single chordal entities but are also implicated in strategies of harmonic progression, relatedness, complementarity, and contrast. These analytical goals prompt a reconceptualization of chordal elements, which are understood as combinations of pitch class and modal quality rather than simply...
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View articletitled, Lutosławski's Mid-Century Harmony: Reconceptualizing Chordal Space in the Five Iłłakowicz Songs View PDF for article titled, Lutosławski's Mid-Century Harmony: Reconceptualizing Chordal Space in the Five Iłłakowicz Songs
Journal Article

Action and Agency Revisited

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Seth Monahan
Journal of Music Theory (2013) 57 (2): 321–371.
DOI: https://doi.org/10.1215/00222909-2323497
Published: 01 October 2013
...Seth Monahan For centuries, metaphors of agency have pervaded music-analytical writing. Today, as in generations past, critics routinely vivify their analytical narrations by ascribing sentience, emotion, and volition to musical works, their internal elements (pitch classes, contrapuntal voices...
View articletitled, Action and Agency Revisited View PDF for article titled, Action and Agency Revisited
Journal Article

Schubert’s Harmonic Language and Fourier Phase Space

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Jason Yust
Journal of Music Theory (2015) 59 (1): 121–181.
DOI: https://doi.org/10.1215/00222909-2863409
Published: 01 April 2015
...Jason Yust This article introduces a type of harmonic geometry, Fourier phase space, and uses it to advance the understanding of Schubert’s tonal language and comment upon current topics in Schubert analysis. The space derives from the discrete Fourier transform on pitch-class sets developed...
View articletitled, Schubert’s Harmonic Language and Fourier Phase Space View PDF for article titled, Schubert’s Harmonic Language and Fourier Phase Space
Journal Article

Cycles in Webern’s Late Music

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Brian Moseley
Journal of Music Theory (2018) 62 (2): 165–204.
DOI: https://doi.org/10.1215/00222909-7127658
Published: 01 October 2018
... principle produces an ordering of pitch classes that lies behind small formal units, cycles order the presentation of twelve-tone rows and give structure to large formal spans. The present study explores four cyclic organizational principles in works from the String Quartet, op. 28 (1938), to the Second...
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Journal Article

From Ramos to Rameau: Toward the Origins of the Modern Concept of Harmony

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David E. Cohen
Journal of Music Theory (2022) 66 (1): 1–42.
DOI: https://doi.org/10.1215/00222909-9534115
Published: 01 April 2022
...David E. Cohen Abstract This article explores the advent of two foundational characteristics of the modern concept of harmony inaugurated by Rameau's Traité de l'harmonie (1722): first, that its principal objects are sonorities of three or more distinct pitch classes, that is, consonant...
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View articletitled, From Ramos to Rameau: Toward the Origins of the Modern Concept of Harmony View PDF for article titled, From Ramos to Rameau: Toward the Origins of the Modern Concept of Harmony
Journal Article

Violin Fingerboard Space: Intervallic Mappings from Instrumental Space to Pitch Space

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Leah Frederick
Journal of Music Theory (2024) 68 (2): 201–252.
DOI: https://doi.org/10.1215/00222909-11398444
Published: 01 October 2024
...Figure 13. Pitch-class space ( pc ). ...
FIGURES | View All (37)
View articletitled, Violin Fingerboard Space: Intervallic Mappings from Instrumental Space to <span class="search-highlight">Pitch</span> Space View PDF for article titled, Violin Fingerboard Space: Intervallic Mappings from Instrumental Space to <span class="search-highlight">Pitch</span> Space
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Example 1. Lutosławski's “Morze,” Iłłakowicz Songs: mm. 20–23. The two lists of pitch classes represent the registral ordering of pitches, from lowest to highest.

Lutosławski's “Morze,” Iłłakowicz Songs : mm. 20–23. The two lists of pitc...

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in Lutosławski's Mid-Century Harmony: Reconceptualizing Chordal Space in the Five Iłłakowicz Songs > Journal of Music Theory
Published: 01 October 2023
Example 1. Lutosławski's “Morze,” Iłłakowicz Songs : mm. 20–23. The two lists of pitch classes represent the registral ordering of pitches, from lowest to highest. More
Image
(a) A variety of generalized interval systems: fingerboard space (fgbd), pitch space (pitch), pitch-class space (pc), and fingerboard-class space (fbc), along with the GIS homomorphisms between these spaces; (b) the interval G♯4–F♯5 from m. 4 of Thomas's Incantation (score in Figure 28) represented in each of these GISes.

(a) A variety of generalized interval systems: fingerboard space ( fgbd ), ...

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in Violin Fingerboard Space: Intervallic Mappings from Instrumental Space to Pitch Space > Journal of Music Theory
Published: 01 October 2024
Figure 37. (a) A variety of generalized interval systems: fingerboard space ( fgbd ), pitch space ( pitch ), pitch-class space ( pc ), and fingerboard-class space ( fbc), along with the GIS homomorphisms between these spaces; (b) the interval G♯ 4 –F♯ 5 from m. 4 of Thomas's Incantation More