NDLI: Education (SIREAD Vol. 44 Issue. 3)

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Education (SIREAD Vol. 44 Issue. 3)

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Schnabel, Bobby
Copyright Year	2002
Abstract	There is a rich, enduring and fairly well known relationship between mathematics and music---for reasons that probably aren't fully understood, people interested and talented in mathematics often are interested and talented in music as well. Perhaps less well known is the connection between mathematical analysis and musical sound. The paper in this installment of the Education section explores this connection in a beautifully written manner. In "Time-Frequency Analysis of Musical Instruments," Jeremy Alm and James Walker show the connection between musical frequency, or pitch, and several methods of analysis. Fourier analysis is the basic method for expressing the sound from individual notes, but more sophisticated methods are used to capture the sound from a musical passage consisting of several notes. After reviewing the applicability of Fourier transforms, fast Fourier transforms, and discrete Fourier transforms to the expression of musical frequency, the article discusses the uses of two additional techniques, spectrograms and scalograms, for describing the time-frequency behavior of musical passages. Scalograms are based upon the mathematical theory of wavelets. Thus this paper would be an excellent addition to courses or units on Fourier analysis and/or wavelets. It includes many nice examples and figures, and can be supplemented by software available on the Web that contains copies of the sound recordings discussed in the article (from piano, flute, and guitar) and that allows readers to both hear and analyze these recordings. This article should be a valuable applied mathematics module and provide one more link in the time-honored partnership between music and mathematics.
Starting Page	455
Ending Page	455
Page Count	1
File Format	PDF
ISSN	00361445
DOI	10.1137/SIREAD000044000003000455000001
e-ISSN	10957200
Journal	SIAM Review (SIREAD)
Issue Number	3
Volume Number	44
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-04
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computational Mathematics

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