LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Beynon, Meurig (2006)
Languages: English
Types: Unknown
Subjects: QA, QA1, ML
The intimate association between mathematics and music can be traced to the Greek culture. It is well-represented in the prevailing Western musical culture of the 18th and 19th centuries, where the traditional cycle of fifths provides a mathematical model for classical harmony that originated with the well-tempered, and later the equal-tempered, keyboard. Equal-temperament gives equivalent status to all twelve tonal centres in the chromatic scale, leading to a high degree of symmetry and an underlying group structure. This connection seems to endorse the Pythagorean concept of music as exemplifying an ideal mathematical harmony. This paper examines the relationship between abstract mathematics and music more critically, challenging the idealized view of music as rooted in pure mathematical relations and instead highlighting the significance of music as an association between form and meaning that is negotiated and pragmatic in nature. In passing, it illustrates how the complex and subtle relationship between mathematics and music can be investigated effectively using principles and techniques for interactive computer-based modelling that in themselves may be seen as relating mathematics to the art of computing - a theme that is developed in a companion paper (viz. paper #082 in this directory).
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] Kofi Agawu, Analyzing music under the new musicological regime, Music Theory Online 2(4), 1996
    • [2] Meurig Beynon, Steve Russ, Willard McCarty, Human Computing: Modelling with Meaning, The Journal of Literary and Linguistic Computing, 2006 (to appear)
    • [3] William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, New York and Oxford: Oxford University Press, 1998
    • [4] Derycke Cooke, The Language of Music, Oxford: Oxford University Press, 1959
    • [5] Richard Cytowic, Synesthesia: Phenomenology & Neuropsychology, Psyche, 2(10), July 1995, http://psyche.cs.monash.edu.au/v2/psyche-2-10-cytowic.html
    • [6] Floyd Grave, Review of William E. Caplin, Classical Form, Music Theory Online 4(6), 1998
    • [7] David Huron, The New Empiricism: Systematic Musicology in a Postmodern Age, http://dactyl.som.ohio-state.edu/Music220/Bloch.lectures/3.Methodology
    • [8] Jim Loy, http://www.jimloy.com/physics/scale.htm
    • [9] Willard McCarty, Humanities Computing, Houndmills, Basingstoke: Palgrave Macmillan, 2005
    • [10] Andy Milne, The Tonal Centre, http://www.andymilne.dial.pipex.com/index.shtml
    • [11] Heinrich Schenker, Free Composition: Vol. 3 of New Musical Theories and Fantasies, Ernst Oster (Ed.) Pendragon Press, 2001
    • [12] Arnold Schoenberg, Structural Functions of Harmony (New York: Norton, 1954); rev. ed., ed. Leonard Stein (New York: Norton, 1969)
    • [13] George Bernard Shaw, G.B.S. on Music, Harmondsworth, Middlesex: Penguin Books Ltd., 1962
    • [14] Donald Tovey, Beethoven, Oxford University Press, London, 1944
    • [15] Sherry Turkle, Seymour Papert, Epistemological Pluralism: Styles and Voices within the Computer Culture. In Harel, I., Papert, S. (Eds.) Constructionism. Norwood, N.J. Ablex Pub. Corp, 161-191, 1991.
    • [16] Derek Waller, Some combinatorial aspects of musical chords. In Mathematical Gazette (March), The Mathematical Association: 12-15, 1978.
    • [17] The EM website at http//www.dcs.warwick.ac.uk/modelling
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article