This page contains the bibliography for the book.  Some of the references are available for downloading by clicking on the appropriate link. There are also some new references, that we were not able to include in the published book:  New References.

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

* W. Anku. Circles and time: A theory of structural organization of rhythm in African music.  Music Theory Online, Vol. 6, Jan. 2000.   Download

* G. Assayag, H. Feichtinger, J.-F. Rodrigues, (Eds.).  Mathematics and music: a Diderot Mathematical Forum. Springer, New York, 2002.

* P. Ball. The Music Instinct: How Music Works and Why We Can't Do Without It.  Oxford Univ. Press, Oxford, 2010.

* D. Barenboim.  Music Quickens Time.  Verso, London, 2008.

* J.W. Beauchamp (Ed.).  Analysis, Synthesis, and Perception of Musical Sounds:  The Sound of Music.  Springer, 2007.

* A. Benade, Fundamentals of Musical Acoustics, second revised edition.  Dover, 1990. 

L. Bernstein.  The Joy of Music.  Amadeus Press, Pompton Plains, NJ, 2004.

* Bis Encore! (2014). CD recording containing Kol Nidrei, Max Bruch, Limen music & arts srl.

* T. Brothers. (2018). Help! The Beatles, Duke Ellington, and the Magic of Collaboration. W.W. Norton, New York.

* J. Cage. (1992). Interview with Charles Amirkhausen, quoted in Writings Through John Cage's Music, Poetry and Art.
   D.W. Bernsteing and C. Hatch (Eds.), Univ. of Chicago Press (2001, p. 1).

* Carey, N. and Clampitt, D. (1989). Aspects of Well-Formed Scales. Music Theory Spectrum, 11(2), 187-206. Download

* X. Cheng, J.V. Hart, J.S. Walker.  Time-frequency analysis of musical rhythm.  Notices of the American Mathematical Society,
Vol. 56 (2009), 344-360.  

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

* R. Cohn, Audacious Euphony: Chromaticism and the Triad's Second Nature. Oxford Univ. Press, 2012

* D. Cooke. (1959). The Language of Music. Oxford University Press.

* G. Cooper and L. Meyer.  The Rhythmic Structure of Music.  Univ. of Chicago Press, Chicago, IL, 1960.

* A. Copland. What to Listen for in Music. McGraw-Hill, New York, NY, 1957.

* T. Cox. (2014). The Sound Book: The Science of the Sonic Wonders of the World. W.W. Norton & Co., New York.

* J. Cross. (2003). Composing with numbers: sets, rows and magic squares. Chap. 8 of Fauvel et. al. (2003).

* A.S. Crans, T.M. Fiore, and R. Satyendra. Musical Actions of Dihedral Groups.  American Mathematical Monthly, Vol. 116 (2009), 479-495.  Download

* S. Dance.  The World of Duke Ellington. Scribner, New York, NY, 1970.

* D. Deutsch. (1986). A musical paradox. Music Perception, Vol. 3, 275-280. Download

* G.W. Don.  Brilliant colors provocatively mixed: Overtone structures in the music of Debussy.  Music Theory Spectrum, Vol. 23 (2001), 61-73.  Download

* G.W. Don, K.K. Muir, G.B. Volk, J.S. Walker.  Music: Broken Symmetry, Geometry, and Complexity.  Notices of the American Mathematical Society, Vol. 51 (2010), 30-49.   Download

* A. Dvorak and Max Bruch (1990). Konzert fur Violincello and Orchester, Deutsche Gramophone.

* W. Everett. The Beatles As Musicians: Revolver through the Anthology.  Oxford Univ. Press, New York, NY, 1999.

* J. Fauvel, R. Flood, and R. Wilson, Eds.  Music and Mathematics: From Pythagoras to Fractals.  Oxford, New York, 2003.

* R. Fleming. The Inner Voice: The Making of a Singer.  Viking, New York, NY, 2004.

* S. Flinn, Shepard's Tones webpage.  Click here. 

* A. Forte. The Structure of Atonal Music.  Yale Univ. Press, New Haven, CT, 1973.

* H. Goodall. 20th Century Greats--The Beatles.  Channel Four Television, 2004.

* H. Goodall. (2006). How Music Works--Rhythm. Channel Four Television.

* H. Helmholtz.  On the Sensations of Tone.  Dover, NY, 1954.

* H.A. Hildebrand. (1997). Pitch detection and intonation correction apparatus and method. U.S. Patent 5973252. Download

* Hilliard. (1989). Perotin. The Hilliard Ensemble. Munchen, ECM, 1989. Recorded Sept. 1988, Boxgrove Priory, Sussex, England.

* A. Hodeir.  Jazz: Its Evolution and Essence.  Da Capo, New York, NY, 1975.

* D. Huron.  Sweet Anticipation: Music and the Psychology of Expectation.  MIT Press, Cambridge, MA, 2006.

* A.M. Jones.  Studies in African Music.  Oxford Univ. Press, London, 1959.

* S. Kostka and D. Payne.  Tonal Harmony, with an introduction to twentieth century music, Sixth Edition.  McGraw-Hill, New York, NY, 2009.

* S.N. Levine and J.O. Smith III. (2007). A Compact and Malleable Sines + Transients + Noise Model for Sound. Chap. 5 of Beauchamp (2007).

* D. Locke.  Drum Gahu: An Introduction to African Rhythm.  White Cliffs, Tempe, AZ, 1998. 

MetaSynth music software.  Click here. 

* S. McCoy.  Your Voice: An Inside View.  Multimedia Voice Science and Pedagogy.  Inside View Press, Princeton, NJ, 2004.

* R. Miller.  On the Art of Singing.  Oxford Univ. Press, New York, NY, 1996.

* Milne, et. al. (2015). Perfect balance: A novel principle for the construction of musical scales and meters. In T. Collins, D. Meredith, and A. Volk (Eds.),
  Mathematics and Computation in Music, LNAI 9110, 97--108, Springer, Heidelberg. Download

* H.F. Olson.  Music, Physics, and Engineering.  Dover Publications, New York, NY, 1967.

* W. Piston and M.~Devoto.  Harmony, 4th edition. Norton, New York, NY, 1978.

* R. Plomp and W.J.M. Levelt. Tonal consonance and critical bandwidth.  J. Acoust. Soc. Am., Vol. 38 (1965), 548-560.

* J. Powell.  How Music Works.  Little, Brown and Company, New York, NY, 2010.

* M. Puckette. (2007). The Theory and Techniques of Electronic Music. World Scientific.

G. Read.  Music Notation, 2nd Edition.  Taplinger Publishing, New York, NY, 1979.

* S. Reynolds. (2018). How Auto-Tune Revolutionized the Sound of Popular Music. Download

* J. Roederer.  The Physics and Psychophysics of Music, 4th Edition.  Springer, New York, NY, 2008.

* C. Rosen.  Beethoven's Piano Sonatas: A Short Companion.  Yale Univ. Press, New Haven, CT, 2002.

* C. Rosen.  The Classical Style: Haydn, Mozart, Beethoven.  Norton, New York, NY, 1997.

* C. Rosen.  The Romantic Generation.  Harvard Univ. Press, Cambridge, MA, 1995.

* G. Schuller.  The Swing Era: The Development of Jazz. 1930-1945.  Oxford Univ. Press, New York, NY, 1989.

* W. Sethares.  Rhythm and Transforms. Springer, New York, NY, 2007.

* W. Sethares.  Tuning, Timbre, Spectrum, Scale.  Springer, London, 2005.

* W. Sethares.  Webpage on dissonance curves.   Click here

* R.N. Shepard. Circularity in judgements of relative pitch.  J. of the Acoustical Soc. of America, Vol. 36 (1964), 2346-53.

* E. Stern. Comments on Louis Armstrong. From Pandolous,  with search topic: Louis Armstrong.

* I. Stewart. Faggot's fretful fiasco.  Chapter 4, pp. 61-76, of J. Fauvel, R. Flood, and R. Wilson, Eds. (2003).

* G. Touissant. Computational Geometric Aspects of Rhythm, Melody, and Voice Leading.  Computational Geometry,  Vol. 43 (2010), 2-22.   Download

* G. Toussaint.  The Rhythm that Conquered the World: What Makes a ``Good'' Rhythm Good?  Percussive Notes, Nov. 2011, 52-59.   Download

* G. Toussaint. The Euclidean Algorithm Generates Traditional Musical Rhythms.  Proc. of BRIDGES: Mathematical Connections in Art, Music
  and Science.
 Banff, 2005, 47-56.   Download

* D. Tymoczko.  A Geometry of Music.  Oxford Univ. Press, New York, NY, 2011.

* D. Tymoczko.  Lecture Notes for Music 105 course.   Download

* D. Tymoczko.  Lecture Notes for Music 106 course.   Download

* J.S. Walker.  Fourier Analysis.  Oxford Univ. Press, New York, NY, 1988.

* J.S. Walker.  A Primer on Wavelets and their Scientific Applications, Second Edition.  Chapman & Hall/CRC Press, Boca Raton, FL, 2008.

* P. Weiss and R. Taruskin, Eds.  Music in the Western World: A History in Documents, Schirmer Books, 1984.

* C. Wright. (1989). Music and Ceremony at Notre Dame of Paris: 500--1550. Cambridge University Press.

* M. York. (2009). Eldon Burton's Sonatina, Flute Talk, July-August 2009, 16--19 and 37.