# Harmonograph

Dedicated to John, Antonia and Imogen. Grateful acknowledgements to Harmonic Vibrations and Vibration Figures by Joseph Goold, Charles E. Benham, Richard Kerr and L.R.Wilberforce, edited by Herbert C. Newton, Newton Co. 1909, Science and Music by Sir James Jeans Cambridge, 1937, Sound by John Tyndall, Appleton Co., 1871, Les Recreations Scientifiques by Gaston Tissandier, Masson, 1881. The image on page 47 is taken fromCymatics A Study of Wave Phenomena and Vibration by Hans Jenny, 2001, MACROmedia Publishing, and used here by kind permission. I am particularly grateful to my grandson for help with the intricacies of musical theory. Introduction 1 The Discovery of Harmony 4 The Monochord of Creation 6 Overtones and Intervals 8 Wholetones and Halftones 10 Arranging the Harmonies 12 Lissajous Figures 14 The Pendulum 16 Two Harmonographs 18 Simple Unison 11 20 Near Unison 22 Rotary Unison 24 The Lateral Octave, 21 26 The Rotary Octave, 21 28 The Lateral Fifth, 32 30 The Rotary Fifth, 32 32 The Fourth, 43 34 Further Harmonics 36 Amplitude 38 Tuning Troubles 40 Equal Temperament 42 The Kaleidophone 44 Chladni Patterns 46 Resonance pictures 48 Appendices Tuning and Intervals 52 Appendices Modes and Equations 50 Appendices Tables of Patterns 54 Appendices Building a Harmonograph 56