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
1 - Waves and harmonics
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
What is sound?
The medium for the transmission of music is sound. A proper understanding of music entails at least an elementary understanding of the nature of sound and how we perceive it.
Sound consists of vibrations of the air. To understand sound properly, we must first have a good mental picture of what air looks like. Air is a gas, which means that the atoms and molecules of the air are not in such close proximity to each other as they are in a solid or a liquid. So why don't air molecules just fall down on the ground? After all, Galileo's experiment at the leaning tower of Pisa tells us that objects should fall to the ground with equal acceleration independently of their size and mass.
The answer lies in the extremely rapid motion of these atoms and molecules. The mean velocity of air molecules at room temperature under normal conditions is around 450–500 meters per second (or somewhat over 1000 miles per hour), which is considerably faster than an express train at full speed. We don't feel the collisions with our skin, only because each air molecule is extremely light, but the combined effect on our skin is the air pressure which prevents us from exploding!
The mean free path of an air molecule is 6 × 10−8 meters. This means that on average, an air molecule travels this distance before colliding with another air molecule. The collisions between air molecules are perfectly elastic, so this does not slow them down.
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- Information
- Music: A Mathematical Offering , pp. 5 - 35Publisher: Cambridge University PressPrint publication year: 2006