Harmonograph: A Visual Guide to the Mathematics of Music

Overview

During the nineteenth century, a remarkable scientific instrument known as a harmonograph revealed the beautiful patterns found in music. Harmonograph is an introduction to the evolution of simple harmonic theory, from the discoveries of Pythagoras to diatonic tuning and equal temperament. Beautiful drawings show the octave as triangle, the fifth as pentagram; diagrams show the principles of harmonics, overtones, and the monochord. Anthony Ashton examines the phenomenon of resonance in Chladni patterns, describes...

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Overview

During the nineteenth century, a remarkable scientific instrument known as a harmonograph revealed the beautiful patterns found in music. Harmonograph is an introduction to the evolution of simple harmonic theory, from the discoveries of Pythagoras to diatonic tuning and equal temperament. Beautiful drawings show the octave as triangle, the fifth as pentagram; diagrams show the principles of harmonics, overtones, and the monochord. Anthony Ashton examines the phenomenon of resonance in Chladni patterns, describes how to build a harmonograph of your own, and provides tables of world tuning systems. This inspiring book will appeal to musicians, mathematicians, designers, and artists alike.

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Product Details

  • ISBN-13: 9780802714091
  • Publisher: Walker & Company
  • Publication date: 4/1/2003
  • Series: Wooden Books Series
  • Pages: 1
  • Sales rank: 746,856
  • Product dimensions: 6.14 (w) x 6.89 (h) x 0.47 (d)

Meet the Author

Anthony Ashton is an economist and journalist.

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Table of Contents

Introduction 1
The Discovery of Harmony 4
The Monochord of Creation 6
Overtones and Intervals 8
Whole Tones and Halftones 10
Arranging the Harmonies 12
Lissajous Figures 14
The Pendulum 16
Two Harmonographs 18
Simple Unison--1:1 20
Near Unison 22
Rotary Unison--1:1 24
The Lateral Octave--2:1 26
The Rotary Octave--2:1 28
The Lateral Fifth--3:2 30
The Rotary Fifth--3:2 32
The Fourth--4:3 34
Further Harmonics 36
Amplitude 38
Tuning Troubles 40
Equal Temperament 42
The Kaleidophone 44
Chladni Patterns 46
Resonance Pictures 48
Appendix A Tunings, and Intervals 50
Appendix B Modes and Equations 52
Appendix C Tables of Patterns 54
Appendix D Building a Harmonograph 56
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