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. 

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. 

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