An Exploration of Some Non-tonal Pitch-class Spaces with Implications for a Theory of Voice Leading
An Exploration of Some Non-tonal Pitch-class Spaces with Implications for a Theory of Voice Leading

Author: Michael F. Berry

Publisher:

Published: 2007

Total Pages: 175

ISBN-13: 9781109837315

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This dissertation develops a theoretical framework suitable for the analysis of neo-tonal music. Neo-tonal music fuses techniques of traditional tonality with elements of atonality: some representative composers include Debussy, Messiaen, and Stravinsky. Chapter one presents a modular-space approach to transformational voice leading and argues for a reconsideration of conventional approaches to pitch-class space. Chapter 2 provides us with the building blocks for pitch-class spaces, using the notion of maximally even sets as a point of departure. Some of the most common scales and sonorities in music are maximally even, or they deviate from maximal evenness ever so slightly. The chapter looks at the construction of maximally even sets and examines why maximally even structures are privileged. Chapter 3 uses maximally even sets as the building blocks for hierarchical pitch-class spaces similar to those discussed in Lerdahl (2001). These pitch-class spaces permit us to discuss the perceived distances between chords as well as to account for non-harmonic tones and chromaticism. Chapter 4 tackles the problem of pieces that feature different pitch-class spaces either presented successively or concurrently. Chapter 5 contains several analytical essays designed to show the theory in practice.

Tonal Pitch Space
Tonal Pitch Space

Author: Fred Lerdahl

Publisher: Oxford University Press

Published: 2004-12-09

Total Pages: 430

ISBN-13: 0199884404

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Building on the foundation of Lerdahl and Jackendoff's influential A Generative Theory of Tonal Music, this volume presents a multidimensional model of diatonic and chromatic spaces that quantifies listeners' intuitions of the relative distances of pitches, chords, and keys from a given tonic. The model is employed to assign prolongational structure, represent paths through the space, and compute patterns of tension and attraction as musical events unfold, thereby providing a partial basis for understanding musical narration, expectation, and expression. Conceived as both a music-theoretic treatise and a contribution to the cognitive science of music, this book will be of interest to music theorists, musicologists, composers, computer musicians, and cognitive psychologists.

Exploring Musical Spaces
Exploring Musical Spaces

Author: Julian Hook

Publisher: Oxford University Press

Published: 2022-09-08

Total Pages: 681

ISBN-13: 0190246014

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Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric models--the first examples of the musical spaces of the book's title--depicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.

Generalized Transformational Voice-leading Systems
Generalized Transformational Voice-leading Systems

Author: David Ellis Orvek

Publisher:

Published: 2019

Total Pages: 147

ISBN-13:

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David Lewin writes that, “In conceptualizing a particular musical space, it often happens that we conceptualize along with it, as one of its characteristic textural features, a family of directed measurements, distances, or motions of some sort. Contemplating elements s and t of such a musical space, we are characteristically aware of the particular directed measurement, distance, or motion that proceeds `from s to t.’” This thesis is concerned with these measurements, distances, and motions as they relate to the voice leading between two pitch-class sets. We begin with Richard Cohn’s idea that we might understand the total voice-leading interval between two pitch-class sets as the mod-12 sum of the pitch-class intervals traversed by each voice. This “pairwise voice-leading sum” (PVLS) allows us to see that the total voice-leading interval is the same between several pitch-class sets within the same Tn/In set class and also that several pitch-class set transformations will produce the same voice-leading interval when applied to any one set. These sets that are equidistant from a given point are grouped into equivalence classes known as “SUM classes” (because all such sets will return the same value when their constituent pitch classes are summed together mod 12) and the transformations producing the same voice-leading intervals are grouped into equivalence classes known as “SUM-class transformations.” When the set class is not inversionally symmetrical, these transformations will be non-commutative, and we will be able to define a “dual” group of transformations for both the SUM classes and pitch-class sets that provide us with two different ways to navigate through the spaces. Together, the SUM classes/SUM-class transformations and pitch-class sets/pitch-class set transformations form two interrelated Generalized Interval Systems that allow us to conceptualize the “measurements, distances, and motions” of any of the Tn/In set classes and even, in a modified form, for all of the pitch-class sets of the same cardinality. What these constructions reveal, above all, is just how similar the set classes of the same cardinality really are as well as how many different ways there are to express the same background voice leading structures.

Audacious Euphony
Audacious Euphony

Author: Richard Cohn

Publisher: Oxford University Press

Published: 2012-01-01

Total Pages: 256

ISBN-13: 0199773211

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Music theorists have long believed that 19th-century triadic progressions idiomatically extend the diatonic syntax of 18th-century classical tonality, and have accordingly unified the two repertories under a single mode of representation. Post-structuralist musicologists have challenged this belief, advancing the view that many romantic triadic progressions exceed the reach of classical syntax and are mobilized as the result of a transgressive, anti-syntactic impulse. In Audacious Euphony, author Richard Cohn takes both of these views to task, arguing that romantic harmony operates under syntactic principles distinct from those that underlie classical tonality, but no less susceptible to systematic definition. Charting this alternative triadic syntax, Cohn reconceives what consonant triads are, and how they relate to one another. In doing so, he shows that major and minor triads have two distinct natures: one based on their acoustic properties, and the other on their ability to voice-lead smoothly to each other in the chromatic universe. Whereas their acoustic nature underlies the diatonic tonality of the classical tradition, their voice-leading properties are optimized by the pan-triadic progressions characteristic of the 19th century. Audacious Euphony develops a set of inter-related maps that organize intuitions about triadic proximity as seen through the lens of voice-leading proximity, using various geometries related to the 19th-century Tonnetz. This model leads to cogent analyses both of particular compositions and of historical trends across the long nineteenth century. Essential reading for music theorists, Audacious Euphony is also a valuable resource for music historians, performers and composers.

Generalized Musical Intervals and Transformations
Generalized Musical Intervals and Transformations

Author: David Lewin

Publisher: Oxford University Press, USA

Published: 2011

Total Pages: 291

ISBN-13: 0199759944

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Generalized Musical Intervals and Transformations is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the "transformational theory" movement.

The Music Lesson
The Music Lesson

Author: Victor L. Wooten

Publisher: Penguin

Published: 2008-04-01

Total Pages: 289

ISBN-13: 1440637695

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From Grammy-winning musical icon and legendary bassist Victor L. Wooten comes an inspiring parable of music, life, and the difference between playing all the right notes…and feeling them. The Music Lesson is the story of a struggling young musician who wanted music to be his life, and who wanted his life to be great. Then, from nowhere it seemed, a teacher arrived. Part musical genius, part philosopher, part eccentric wise man, the teacher would guide the young musician on a spiritual journey, and teach him that the gifts we get from music mirror those from life, and every movement, phrase, and chord has its own meaning...All you have to do is find the song inside. “The best book on music (and its connection to the mystic laws of life) that I've ever read. I learned so much on every level.”—Multiple Grammy Award–winning saxophonist Michael Brecker

Voice Quality
Voice Quality

Author: John H. Esling

Publisher: Cambridge University Press

Published: 2019-06-20

Total Pages: 327

ISBN-13: 1108498426

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Offers a new model of vocal tract articulation that explains laryngeal and oral voice quality, both auditorily and visually, through language examples and familiar voices.