In Search of the Missing Fundamental: by Richard K. Jones
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Chapter 2: Selected Bibliography and Links

1) Zimmermann, P., Zur Theorie der schwingenden Membran bei Leonhard Euler und Giordano Riccati: Erfindung, Nacherfindung, Fama. Intern. Zs. f. Naturwiss., Technik u. Med. 4 (1996), 145 – 158 und 214 – 230.

2) Chladni, E.F.F., Die Akustik. Breitkopf und Hartel, Leipzig 1802.

3) Rudolf Friedrich Alfred Clebsch. (2011). In Encyclopædia Britannica. Retrieved from

Backus, John. The Acoustical Foundations of Music. Second Edition, New York: W.W.Norton & Company, Inc., 1977.

Benade, Arthur H. Fundamentals of Musical Acoustics. New York: Dover Publicatoins, Inc.,1990.

Berg, Richard E. and David G. Stork. The Physics of Sound. Englewood Cliffs: Prentice Hall Inc., 1982.

Euler, L., De motu vibratorio tympanorum. Novi commentarii academiae scientarium Petropolitanae 10 (1764), 1766, 243-260.

Fletcher, Neville H. and Thomas D. Rossing. The Physics of Musical Instruments. New York: Springer-Verlag, 1991.

Helmholtz, Hermann von. On the sensations of tone as a physiological basis for the theory of music. Second English Edition, London: Longmans, Green, and Co.

Helmholtz, H. L. F. Von. (1863). Die Lehre von den Tonempfindungen als physiologische Grundlage fur die Theorie der Musik. Braunschweig: F. Vieweg & Sohn.

Riccati, G., Delle vibrationi del tamburo. Saggi scientifici e letterari dell’Academia di Padova I (1786), 419-446.

Roederer, Juan G. Introduction to the Physics and Psychophysics of Music . London: The English Universities Press Ltd., 1973.

Rossing, Thomas D., Paul Wheeler, and F. Richard. Moore. The Science of Sound. San Francisco: Addison Wesley, 2002.

Rossing, Thomas D. Science of Percussion Instruments. Singapore: World Scientific, 2000.

Rossing, Thomas D. (Editor) Springer Handbook of Acoustics. ISBN: 978-1-4939-0754-0 (Print) 978-1-4939-0755-7 (Online) ISBN-10: 0387336338, 2014

5) Strutt, John William. The Theory of Sound (1877)/(2d ed. 1894). OUP.

Internet Resources:

Acoustics/Bessel Functions and the Kettledrum

Paul Falstad

Good Vibrations: Vibrating Circular Membrane and Bessel Functions. Heather Cameron and Dana Mullins. April 26, 2000.

4) Georgia State University HyperPhysics

Normal vibration modes of a circular membrane

6), 7) Dr. Dan Russell, The Pennsylvania State University

The vibrating-membrane problem – based on basic principles and simulations. Hermann Härtel 1 and Ernesto Martin. IPN – Institute for Science Education, D-24098 Kiel. Universidad de Murcia, E-30071 Espinardo, Murcia.