Formalization of voice-leadings and the nabla algorithm

Pozo Ortego, Isaac and Gomez Martin, Francisco (2019). Formalization of voice-leadings and the nabla algorithm. In: "The Seventh International Conference on Mathematics and Computation in Music", 18/06/2019 - 21/06/2019, Madrid, España. ISBN 978-3-030-21391-6. pp. 352-358. https://doi.org/10.1007/978-3-030-21392-3_30.

Description

Title: Formalization of voice-leadings and the nabla algorithm
Author/s:
  • Pozo Ortego, Isaac
  • Gomez Martin, Francisco
Item Type: Presentation at Congress or Conference (Article)
Event Title: The Seventh International Conference on Mathematics and Computation in Music
Event Dates: 18/06/2019 - 21/06/2019
Event Location: Madrid, España
Title of Book: Mathematics and Computation in Music
Título de Revista/Publicación: 7th International Conference on Mathematics and Computation in Music
Date: 31 May 2019
ISBN: 978-3-030-21391-6
ISSN: 978-3-030-21391-6
Volume: 11502
Subjects:
Freetext Keywords: Voice-leadings; Chord progressions; Matrix algebra; distance functions; Nabla distance; Optimal voice-leadings
Faculty: E.T.S.I. de Sistemas Informáticos (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This work presents some concepts related to voice-leadings and proposes a formalization of them. The aim is to teach voice-leadings in a systematic way by using elements of mathematical music theory. Within this formalization, we defined the nabla distance of a chord progression. This distance is a measure of how close the voices are among them. One of its applications is to produce voice-leadings with nice properties, especially for jazz music. The nabla distance has been implemented in the form of an application, the ∇ application. This application computes the optimal voice-leading for a given chord progression.

More information

Item ID: 67781
DC Identifier: https://oa.upm.es/67781/
OAI Identifier: oai:oa.upm.es:67781
DOI: 10.1007/978-3-030-21392-3_30
Official URL: https://mcm19.etsisi.upm.es/home
Deposited by: Memoria Investigacion
Deposited on: 31 Jan 2022 17:02
Last Modified: 31 Jan 2022 17:02
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