# Generalized Voice-Leading Spaces

@article{Callender2008GeneralizedVS, title={Generalized Voice-Leading Spaces}, author={Clifton Callender and Ian Quinn and Dmitri Tymoczko}, journal={Science}, year={2008}, volume={320}, 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…

## 143 Citations

### Scale Theory, Serial Theory and Voice Leading

- Art
- 2008

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

- Mathematics
- 2016

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

- Computer Science
- 2013

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’

- Physics
- 2013

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

- Computer Science
- 2011

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

- MathematicsJournal 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

- Computer ScienceMusic Theory Online
- 2019

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

- Physics
- 2009

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

- Computer ScienceJournal of Mathematics and Music
- 2019

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,…

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