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Mathematics and Music

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Example: Clarinet Wave (using Fourier series) ... vaguely like the waveform produced by a clarinet, where odd harmonics dominate. ... – PowerPoint PPT presentation

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Title: Mathematics and Music


1
Mathematics and Music
  • A Presentation by
  • John Carden
  • Van Mildert College

2
  • What is sound and how is it mathematical?
  • Some instrument-specific examples
  • The musical scale
  • Music written mathematically
  • Mathematics understood musically!

3
Sound
  • Sound is a wave
  • Harmonic Motion
  • Sin Waves

4
Fastest Intro to Fourier Series Ever...
  • Any expression constructed from summing sin
    curves is called a fourier series

with
5
Examples of Sound Waves
  • String fixed at both ends
  • Harmonics

6
Example Clarinet Wave (using Fourier series)
  • The square wave sounds vaguely like the waveform
    produced by a clarinet, where odd harmonics
    dominate. It is the function f (?) defined by
  • f(?) 1 for 0 ? lt Pi and f(?) -1 for Pi ?
    lt 2Pi (and then extend to all values of p by
    making it periodic, f(?) f(? 2Pi) ).

7
(No Transcript)
8
The Scale
  • Building the scale
  • Pythagoras and the Scale

9
The Scale (cont)
  • Equal temperament

10
Music written Mathematically
  • Music of Pi (in A Minor)
  • Bach, Messiaen Quartet for the End of Time,
    Beethoven...

11
Mathematics understood Musically!
  • Music of the primes

12
THE END!
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