Several requests for references to connections between math and music have yielded these responses. I have not looked at many of these myself. Recent addition: Garland and Kahn, Math and Music Harmonious Connections. Palo Alto: Dale Seymour Publications, c.1995 -djr ============================================================================== From: dennis@mr2.ece.cmu.edu (Dennis J. Ciplickas) Newsgroups: sci.math,sci.math.num-analysis Subject: Re: Relationship(s) between Music and Math: References please? Date: 06 Dec 1994 17:11:21 GMT @book(weigend-gershenfeld-92 ,author="Weigend, Andreas S. and Gershenfeld, Neil A." ,title="Time series prediction: forecasting the future and understanding the past: proceedings of the NATO advanced Research Workshop on Comparative Time Series Analysis" ,publisher="Addison-Wesley" ,address="Reading, MA" ,year="1992" ) There was an interesting article describing the application of time series analysis to (one of?) Bach's Unfinished Fugue(s). I seem to recall references at the end of the chapter. ============================================================================== From: ph@directory.yale.edu (Public Cluster Macintosh) Newsgroups: sci.math,sci.math.num-analysis Subject: Re: Relationship(s) between Music and Math: References please? Date: Tue, 06 Dec 1994 18:55:48 -0500 These books are good and all contain much interesting mathematics: Author: Lindley, Mark, 1937- Title: Mathematical models of musical scales : a new approach / Mark Lindley, Ronald Turner-Smith. Published: Bonn : Verlag fîur Systematische Musikwissenschaft, 1993. Description: 308 p. : ill. ; 25 cm. Author: Panthaleon van Eck, C. L.van. Title: J.S. Bach's critique of pure music / C.L. van Panthaleon van Eck. Published: Netherlands : C.L. van Panthaleon van Eck, c1981. Description: 170 p. : music ; 26 cm. Author: Mann, Chester D. Title: Analytic study of harmonic intervals / by Chester D. Mann. Published: Tustin, Calif. : C.D. Mann, 1990. Description: vii, 196 p. : ill. ; 28 cm. Author: Barbour, James Murray, 1897- Title: Tuning and temperament; a historical survey, by J. Murray Barbour. Published: New York, Da Capo Press, 1972 [c1951] Description: xii, 228 p. 22 cm. Author: Pierce, John Robinson, 1910- Title: The science of musical sound / John R. Pierce. Edition: Rev. ed. Published: New York : Freeman, c1992. Description: xi, 270 p. : ill.; 24 cm. ============================================================================== From: gerry@macadam.mpce.mq.edu.au (Gerry Myerson) Newsgroups: sci.math Subject: Re: Relationship(s) between Music and Math: References please? Date: 4 Dec 1994 18:39:46 -0600 You may or may not be interested in J. Clough & G. Myerson, Musical scales and the generalized circle of fifths, Amer. Math. Monthly 93 (1986) 695--701. ============================================================================== From: maverick@cs.berkeley.edu (Vance Maverick) Newsgroups: sci.math,rec.arts.books Subject: Re: ** Books on Maths & Music ** Date: 20 Jan 1995 17:19:14 GMT Xenakis, _Musiques Formelles_ / _Formalized Music_. Also, flip through back issues of the journal _Perspectives of New Music_, skipping the hippy-dippy impressionist criticism and concrete poetry ;) and stopping when you see equations. ============================================================================== From: mroge02@larry.cc.emory.edu (Michael K. Rogers) Newsgroups: sci.math,rec.arts.books Subject: Re: ** Books on Maths & Music ** Followup-To: sci.math,rec.arts.books _The Fascination of Groups_ by Budden has some chapters on group theory and music. ============================================================================== From: Simon Tong Subject: Music and Maths To: rusin@math.niu.edu Date: Tue, 2 Jan 96 15:42:10 EST This book may be of interest to you :- Emblems of Mind : The Inner Life of Music & Mathematics by Edward Rothstein ISBN 0-8129-2560-2 Regards, Simon Tong ============================================================================== From: adler@pulsar.wku.edu (Allen Adler) Newsgroups: sci.math Subject: Re: Group-theoretical approach of the musical intervals? Date: 28 Mar 1996 03:31:02 GMT In article <4jc10h$5ti@news.cict.fr> Pierre Csillag writes: > A lot of time ago I read, in an computer-made-music review, a paper > about musical intervals considered as a group, where the group > operation was the addition (concatenation) of the intervals. But I > cannot find now this paper. Could you give me a pointer to books, > papers, www or ftp sites about a group-theoretical approach of the > musical intervals? I'm sure you'll get a lot of answers to this. But you might also look at the book of David Lewin, Generalized Musical Intervals and Transformations which takes things a lot further. Allan Adler adler@pulsar.cs.wku.edu ============================================================================== From: John Soward Bayne Newsgroups: sci.math Subject: Re: Music and Mathematics Date: Tue, 10 Dec 1996 13:03:51 -0500 Bazelow, AR and Brickle, F "A combinatorial problem in music theory--Babbitt's partition problem." Proc. 2d. Intl Conf on Combinatorial Math, Annals of NY Acad of Sci. V. 319 (14 May 79), pp. 47-63. (same authors) "A combinatorial problem etc: Babbitt's partition problem (II)" Ars Combinatoria V. 9 (June 1980), pp. 289-306 Perle, George Serial Composition and Atonality (LA: Univ of Calif Press, 1968) Machlis, Joseph Intro to Contemporary Music (NY: WW Norton, 1961) Perle, George Serial Music and Atonality (LA: Univ of Calif Press, 1968) ============================================================================== Juan G. Roederer (The Physics and Psychophysics of Music. Springer-Verlag, Third Ed., 1995) ============================================================================== From: DWCantrell@sigmaxi.org (David W. Cantrell) Newsgroups: sci.math,rec.music.theory Subject: Re: Mathamatics of Musical Harmony Date: 2 Mar 2003 21:52:24 -0800 > The best summary I've seen of the state of research into consonance is > in William Sethares's "Tuning, Timbre, Spectrum, Scale". Many thanks for mentioning that! I finally had a chance to take a look at it, and I was _very_ well impressed. It should be absolutely required reading for anyone interested in "the creation of new musics". > It's valuable mostly because of its treatment of inharmonic timbres. > One shortcoming Or strength, depending on your point of view. > is that it concentrates on those aspects of consonance > related to timbre -- there seems to be an innate ability to recognize > harmonic intervals as well. I recently received the new Springer mathematics catalog. It lists two new books pertinent to this thread: _Mathematics and Music, A Diderot Mathematical Forum_, eds. G. Assayag et al., 2002 _Foundations of Diatonic Theory, A Mathematically Based Approach to Music Fundamentals_, T. A. Johnson, 2003 Best wishes, David Cantrell