Harmonograph: A Visual Guide to the Mathematics of Music

by Anthony Ashton

Overview

Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming pocket book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this magical subject. WOODEN BOOKS US EDITIONS. Small books, BIG ideas. Tiny but packed with information. “Stunning" NEW YORK TIMES. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST.

Product Details

ISBN-13:	9781952178047
Publisher:	Wooden Books
Publication date:	03/15/2022
Series:	Wooden Books North America Editions
Pages:	64
Product dimensions:	5.40(w) x 6.50(h) x 0.30(d)

About the Author

Anthony Ashton is a journalist and economist. A lifelong interest in the building blocks of the sciences led him to the Harmonograph, a Victorian machine which draws musical intervals. After building a few in his garage, he wrote this book. He now lives in Girton, Cambridge.

Read an Excerpt

Many of the drawings in this book were produced by a simple scientific instrument known as a harmonograph, an invention attributed to a Professor Blackburn in 1844. Towards the end of the nineteenth century there seems to have been a vogue for these instruments. Victorian gentlemen and ladies would attend 'soirées' or 'conversaziones', gathering round the instruments and exclaiming in wonder as they watched the beautiful and mysterious drawings appear. A shop in London sold portable models that could be folded into a case and taken to a party. There may well be some of these instruments hidden in lofts throughout the country.
From the moment I first saw drawings of this kind I was hooked: not only because of their strange beauty, but because they seemed to have a meaning—a meaning which became clearer and deeper as I found out how to make and operate a harmonograph. The instrument draws pictures of musical harmonies, linking sight and sound.
However, before going any further I feel I should issue a health warning. If you too are tempted to follow this path, beware! It is both fascinating and time-consuming.
I have acknowledged my debt to the book Harmonic Vibrations. It was coming across this book in a library soon after the end of the Second World War that introduced me to the Harmonograph. Seeing that the book had been published by Newton & Co., a firm of scientific instrument makers in Wigmore Street I went one day to see if they were still there. They were, though reduced merely to making and selling projectors. I went into the shop and held up my library copy of the book for the elderly man behind the counter to see.
“Have you any copies of this book left?” I asked him.
He stared at me as though I was some sort of ghost, and shuffled away without a word, returning in a few minutes with a dusty, unbound copy of the book.
“That's marvelous,” I said, “how much do you want for it?”
“Take it”, he said, “it's our last copy, and we're closing down tomorrow”. So I have always felt that someday I must write this book.

Table of Contents

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, 1:1 20

Near Unison 22

Rotary Unison 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

Appendices: Tunings and Intervals 50

Appendices: Modes and Equations 52

Appendices: Tables of Patterns 54

Appendices: Building a Harmonograph 56