Modelling the similarity of pitch collections with expectation tensors

Milne, Andrew J.; Sethares, William A.; Laney, Robin and Sharp, David B. (2011). Modelling the similarity of pitch collections with expectation tensors. Journal of Mathematics and Music: Mathematical and Comptational Approaches to Music Theory, Analysis, Composition and Performance, 5(1) pp. 1–20.

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DOI (Digital Object Identifier) Link:	http://dx.doi.org/10.1080/17459737.2011.573678

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Abstract

Models of the perceived distance between pairs of pitch collections are a core component of broader models of music cognition. Numerous distance measures have been proposed, including voice-leading [1], psychoacoustic [2–4], and pitch and interval class distances [5]; but, so far, there has been no attempt to bind these different measures into a single mathematical or conceptual framework, nor to incorporate the uncertain or probabilistic nature of pitch perception.

This paper embeds pitch collections in expectation tensors and shows how metrics between such tensors can model their perceived dissimilarity. Expectation tensors indicate the expected number of tones, ordered pairs of tones, ordered triples of tones, etc., that are heard as having any given pitch, dyad of pitches, triad of pitches, etc.. The pitches can be either absolute or relative (in which case the tensors are invariant with respect to transposition). Examples are given to show how the metrics accord with musical intuition.

Item Type:	Journal Article
Copyright Holders:	2011 Taylor & Francis
ISSN:	1745-9745
Extra Information:	Author Posting. (c) Taylor & Francis, 2011. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Journal of Mathematics and Music, Volume 5 Issue 1, March 2011. doi:10.1080/17459737.2011.573678
Keywords:	music cognition; tone; tonality; microtonality; pitch; salience; expectation; expectation tensor; metric
Academic Unit/Department:	Mathematics, Computing and Technology > Computing & Communications Mathematics, Computing and Technology > Engineering & Innovation
Interdisciplinary Research Centre:	Centre for Research in Computing (CRC)
Related URLs:	http://www.informaworld.com/smpp/content...(Other)
Item ID:	28353
Depositing User:	Andrew Milne
Date Deposited:	27 May 2011 11:12
Last Modified:	10 Dec 2012 22:35
URI:	http://oro.open.ac.uk/id/eprint/28353
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