References                        

Note:  If the reference can be freely downloaded, then the hyperlink is marked in boldface red.  Other hyperlinks, marked in blue, are to commercial sites.

J.F. Alm and J.S. Walker. (2002). Time-frequency analysis of musical instruments. SIAM Review, Vol. 44, 457--476.

G. Assayag, H. Feichtinger, and J.F. Rodrigues, Eds. (2002). Mathematics and Music: a Diderot Mathematical Forum. Springer, NY.

Audacity software:   http://audacity.sourceforge.net/

Avian music website:  http://www.avianmusic.com/music.html

M. Babbitt,  Set structure as a compositional determinant.  J of Music Theory, 5 (1961), 72-94.  If you have access to JSTOR then
you can download the article from here.

D. Benson. (2006). Music: A Mathematical Offering. Cambridge University Press, Cambridge, UK.

L. Bernstein. (2006).   The Unanswered Question.  Harvard University Press, Cambridge, MA.

L. Bernstein. (2007).  The Infinite Variety of Music.  Amadeus Press, New York, NY.

E. Burger and M. Starbird. (2004).  The Heart of Mathematics.   Key College Press, New York.

S. Carlson.  (1996).  Dissecting the brain with sound.  Scientific American, Dec. 1996.

X. Cheng, J.V. Hart, J.S. Walker.(2007). Time-frequency analysis of musical rhythm. Preprint.

R. Cogan. (1984). New Images of Musical Sound.  Harvard University Press, Cambridge, MA.

I. Daubechies, S. Maes. (1996). A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models. In A. Aldroubi, M. Unser, (Eds.), Wavelets in Medicine and Biology. CRC Press, Boca Raton, FL, 527--546.

M. D\"orfler. (2002).  Gabor Analysis for a Class of Signals called Music.  Dissertation, University of Vienna.

G. Fauconnier and M. Turner. (2003).  The Way We Think: Conceptual Blending and the Mind's Hidden Complexities.  Basic Books, New York.

T. Gardner and M. Magnasco. (2006). Sparse time-frequency representations.  Proc. Nat. Acad. Sci., Vol.~103, 6094-6099.

R. Gregory, Ed. (2004). The Oxford Companion to the Mind, Oxford University Press.

L. Harkleroad. (2006).  The Math Behind the Music. Cambridge University Press, Cambridge, UK.

W. Hodges and R. Wilson. (2002).  Musical patterns.  In G. Assayag, H.G. Feichtinger,
and J.F. Rodrigues (editors), Mathematics and Music. Springer-Verlag, New York.

P. Isihara and M. Knapp. (1993). Basic Z_12 analysis of musical chords. UMAP Journal, 14, 319-348.

M. Kobayashi. (1996). Listening for Defects: Wavelet-Based Acoustical Signal Processing in Japan. SIAM News, Vol. 29, No. 2.

D. Kroodsma. (2005). The Singing Life of Birds. Houghton-Mifflin, NY.

F. Lerdahl. (2004).  Tonal Pitch Space. Oxford University Press, New York.

F. Lerdahl and R. Jackendoff.. (1983). A Generative Theory of Tonal Music. MIT Press, Cambridge, MA.

F. Lerdahl and R. Jackendoff.. (1992). An Overview of Hierarchical Structure in Music. In Machine Models of Music, S. Schwanauer and D. Levitt, Eds.,
MIT Press, Cambridge, MA, 289--312.

D. Levitin. (2006).  This Is Your Brain On Music.  Dutton, New York.

Daniel Levitin's webpage:  http://www.psych.mcgill.ca/levitin/

D. Levitin and V. Menon. (2003).  Musical structure is processed in 'language' areas of the brain: A possible role for Brodmann area 47 in temporal coherence.  NeuroImage, Vol. 20, 2142-2152.

H. Longuet-Higgins (1994). Artificial Intelligence and Musical Cognition.  Phil. Trans. Roy. Soc. London, A349, 115-131.  If you have access to JSTOR, then
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G. Loy. (2007).  Musimathics: The Mathematical Foundations of Music, Vol.~2.  MIT Press, Cambridge, MA.

F.B. Mache. (1993).  Music, Myth and Nature. Contemporary Music Studies, Vol. 6. Taylor \& Francis, London.

S. Mallat. (1999). A Wavelet Tour of Signal Processing. Second Edition. Academic Press, San Diego, CA.

G. Mazzola. (2002). The Topos of Music. Birkhauser, Basel.

A. Nestke and T. Noll. (2000).  Inner Metrical Analysis. In J. Haluska (Ed.), Music and Mathematics, Tatra Mountains Mathematical Publications, Bratislava.

NuHAG webpage:  http://www.univie.ac.at/nuhag-php/home/

W. O'Grady, M. Dobrovolsky, M. Arnoff. (1993).  Contemporary Linguistics, An Introduction.  St. Martins Press, New York.

A.D. Patel. (2003).  Language, music, syntax and the brain.  Nature Neuroscience, Vol. 6, 674 - 681. 

S. Pinker. (1997).  How the Mind Works. Norton, NY.

D. Rothenberg. (2005). Why Birds Sing: A Journey into the Mystery of Bird Song. Basic Books, NY.

S. Schwanauer and D. Levitt, Eds. (1993). Machine Models of Music. MIT Press, Cambridge, MA.

W. Sethares. (2007).  Rhythm and Transforms. Springer, NY.

W. Sethares. (2007).  Rhythm and Transforms. An extended abstract of his plenary address to the Mathematics and Computation in Music conference
in Berlin, May 18, 2007.

L.M. Smith (2000).  A multiresolution time-frequency analysis and interpretation of musical rhythm.  Thesis, University of Western Australia.

L.M. Smith's webpage:  http://staff.science.uva.nl/~lsmith/

N. Spender. (2004). Music, psychology of. Article in The Oxford Companion to the Mind, 625--632, Oxford University Press, Oxford, UK.

J.S. Walker. (1988). Fourier Analysis. Oxford, New York, NY.

J.S. Walker. (1996). Fast Fourier Transforms, Second Edition. \CRC.

J.S. Walker. (1997). Fourier Analysis and Wavelet Analysis. Notices of the Amer. Math. Soc., Vol. 44, 658--670.

J.S. Walker and G.W. Don. (2006).  Music:  A time-frequency approach.   Preprint.

Wavelet Primer website:  http://www.uwec.edu/walkerjs/Primer

The Wavelet Digest website:  http://www.wavelet.org/

Why Birds Sing website: http://www.whybirdssing.com/

L. M. Zbikowski.  (1998).  Metaphor and Music Theory: Reflections from Cognitive Science.  Music Theory Online, Vol. 4.