Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Introduction
- 1 Waves and harmonics
- 2 Fourier theory
- 3 A mathematician's guide to the orchestra
- 4 Consonance and dissonance
- 5 Scales and temperaments: the fivefold way
- 6 More scales and temperaments
- 7 Digital music
- 8 Synthesis
- 9 Symmetry in music
- Appendix A Bessel functions
- Appendix B Equal tempered scales
- Appendix C Frequency and MIDI chart
- Appendix D Intervals
- Appendix E Just, equal and meantone scales compared
- Appendix F Music theory
- Appendix G Recordings
- References
- Bibliography
- Index
2 - Fourier theory
Published online by Cambridge University Press: 05 March 2013
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Introduction
- 1 Waves and harmonics
- 2 Fourier theory
- 3 A mathematician's guide to the orchestra
- 4 Consonance and dissonance
- 5 Scales and temperaments: the fivefold way
- 6 More scales and temperaments
- 7 Digital music
- 8 Synthesis
- 9 Symmetry in music
- Appendix A Bessel functions
- Appendix B Equal tempered scales
- Appendix C Frequency and MIDI chart
- Appendix D Intervals
- Appendix E Just, equal and meantone scales compared
- Appendix F Music theory
- Appendix G Recordings
- References
- Bibliography
- Index
Summary
To be sung to the tune of Gilbert and Sullivan's Modern Major General:
I am the very model of a genius mathematical,
For I can do mechanics, both dynamical and statical,
Or integrate a function round a contour in the complex plane,
Yes, even if it goes off to infinity and back again;
Oh, I know when a detailed proof's required and when a guess'll do
I know about the functions of Laguerre and those of Bessel too,
I've finished every tripos question back to 1948;
There ain't a function you can name that I can't differentiate!
There ain't a function you can name that he can't differentiate [Tris]
I've read the text books and I can extremely quickly tell you where
To look to find Green's Theorem or the Principle of d'Alembert
Or I can work out Bayes' rule when the loss is not Quadratical
In short I am the model of a genius mathematical!
For he can work out Bayes' rule when the loss is not Quadratical
In short he is the model of a genius mathematical!
Oh, I can tell in seconds if a graph is Hamiltonian,
And I can tell you if a proof of 4CC's a phoney 'un
I read up all the journals and I'm ready with the latest news,
And very good advice about the Part II lectures you should choose.
Oh, I can do numerical analysis without a pause,
Or comment on the far-reaching significance of Newton's laws
I know when polynomials are soluble by radicals,
And I can reel off simple groups, especially sporadicals. […]
- Type
- Chapter
- Information
- Music: A Mathematical Offering , pp. 36 - 90Publisher: Cambridge University PressPrint publication year: 2006