Generalized Voice-Leading Spaces

  title={Generalized Voice-Leading Spaces},
  author={Clifton Callender and Ian Quinn and Dmitri Tymoczko},
  pages={346 - 348}
Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord sequences are represented. This model reveals connections between music… 

Scale Theory, Serial Theory and Voice Leading

The notion of voice leading is formalised, how to classify voice leadings according to transpositional and inversional equivalence is shown and algorithms for identifying maximally efficient voice leading between arbitrarily chosen chords are supplied.

Voice Leading : Extending the General Chord Type and Directional Interval Class Representations

  • Computer Science
  • 2018
This paper explores a novel data-driven extension of the GCT and DIC representations that embodies voice leading properties of chord transitions and develops a novel model for harmonic generation tasks.

Constrained voice-leading spaces

Dmitri Tymoczko describes the voice-leading space of N-note chords as the orbifold , the N-torus modulo the Nth symmetric group action, “an N-dimensional prism whose simplicial faces are glued

Scalar context in musical models

This paper determines how to expand the signature group using FiPS, and map familiar transformational graphs to maximally even coordinate spaces, thereby separating transformational groups from the scalar contexts in which they are most often explained.

Tonal prisms: iterated quantization in chromatic tonality and Ravel's ‘Ondine’

The mathematics of second-order maximal evenness has far-reaching potential for application in music analysis. One of its assets is its foundation in an inherently continuous conception of pitch, a

Generating Music Using Concepts from Schenkerian Analysis and Chord Spaces

A generative grammar for classical Western chord progressions using ideas from Schenkerian analysis is described, which gives the general structure of a chord progression over time, but is still an abstract representation that requires additional information to become a complete score.

Generalized Tonnetze and Zeitnetze, and the topology of music concepts

  • Jason Yust
  • Mathematics
    Journal of Mathematics and Music
  • 2020
This article examines how interval and chord duplications can relate to important musical concepts such as key or pitch height, and details a method of removing such redundancies and the resulting changes to the homology of the space.

Chord Proximity, Parsimony, and Analysis with Filtered Point-Symmetry

In this work, many FiPS configuration spaces are presented; some are isomorphic to commonly referenced voice-leading spaces like the neo-Riemannian Tonnetz, and others show tonal networks that have not previously been explored.

Three Conceptions of Musical Distance

This paper considers three conceptions of musical distance (or inverse “similarity”) that produce three different musico-geometrical spaces: the first, based on voice leading, yields a collection of

Pseudo-distances between chords of different cardinality on generalized voice-leading spaces

In this paper, we study the possibility of defining pseudo-distances between musical chords of different cardinality, from the distance defined on the generalized voice-leading space by Callender,



The Geometry of Musical Chords

A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of

New Directions in the Theory and Analysis of Musical Contour

Musical contour is one of the most general aspects of pitch perception, prior to the concept of pitch or pitch class, for it is grounded only in a listener's ability to hear pitches as relatively

Perspectives of New Music

4 General Equal-Tempered Harmony: Par ts 2 and 3 IAN QUINN 64 On Tempo Relations ANDREW MEAD 110 Symmetrical Permutation, the Twelve Tones, and Messiaen’s Catalogue d’oiseaux WAI-LING CHEONG 138

Generalized Musical Intervals and Transformations

This paper focuses on the development of knowledge structures in the context of discrete-time dynamical systems and their role in the history oftonal theory.

Music perception.

  • D. Deutsch
  • Art
    Frontiers in bioscience : a journal and virtual library
  • 2007
It is shown that, for certain types of configuration, the music as it is perceived can differ substantially from the music that is notated in the score, or as might be imagined from reading the score.

Compositional theory in the eighteenth century

Introduction 1. Zarlino and His Legacy 2. Species Counterpoint and Fux's Gradus 3. Thoroughbass Methods 4. Rameau's Early Works 5. Rameau's Later Works and Controversies 6. Mattheson and the Study of

Finite subset spaces of S^1

Given a topological space X denote by exp_k(X) the space of non-empty subsets of X of size at most k, topologised as a quotient of X^k. This space may be regarded as a union over 0 exp_k(S^1) is (deg

Psychological Review

The site contains one file. You will need to have Adobe Acrobat® Reader software (Version 4.0 or higher) to read it. If you have any problems with downloading your article from the Rapid Proof site,

The American statistician

This chapter discusses Statistical Training and Curricular Revision, which aims to provide a history of the discipline and some of the techniques used to train teachers.

Music Theory Spectrum .