Table Of ContentFM Theory & Applications
By Musicians for Musicians
147
Dr.John Chowning
and David Bristow
a
FM Theory
& Applications
By Musicians for Musicians
by
Dr. John Chowning
and David Bristow
First published in 1986 by
Yamaha Music Foundation, 3-24-22 Shimomeguro Meguroku, Tokyo, Japan
Copyright © 1986 by YAMAHA MUSIC FOUNDATION
ISBN 4-636-17482-8 COO73
All rights reserved.
Nopart ofthis publication may be reproduced or transmitted
in any form or by any means,electronic or mechanical,
including photocopy, recording, or any information storage
andretrieval system, without permission in writing from the
publisher.
Printed and bound in Japan by
YAMAHA MUSIC FOUNDATION
Designed by P & B DesignAssociates, Milton Keynes.
CONTENTS
FOREWORD) sccveccsessscrscsense Vv
1.ANINTRODUCTION. 7
2. SOMEBASIC IDEAS 17
3. WHATIS FM? «0.0000 41
4. SIMPLE FM — TheTheory 55
5. SIMPLE FM — The Practice . 83
6. COMPLEX FM...... 113
7.APPLICATIONS.... . 139
APPENDIX 1 — Logarithmic Representation and “Pitch Frequency”... 160
APPENDIX2 — “X” Synth Comparisons by Index vs. Op. OutputLevel 165
APPENDIX3 — Bessel Functions Graphs... 170
APPENDIX4 — Bessel Function Tables. 179)
APPENDIX5 — A Short Bibliography. pet ES!
APPENDIX6 — A Glossary of Terms... ce 190)
APPENDIX 7 — The Sampling Rate of the DX7. . 194
ACKNOW/LEDGEMENTS
This book grew out of an original intention to prepare a short tutorial on the
fundamental theory of FM synthesis. As you cansee,it didn’t stay short, and we
would like to thank those people and institutions who have supported us in
achieving a complete text. At IRCAM in Paris, where Pierre Boulez has generously
encouragedthis work, our thanks to David Wesselfor his continuous support and
Stephen McAdamsforhis useful backgroundinformation on acoustics;to Emmanuel
Favreau and DanTimisfor their help with someofthe figures, and to Robert Gross
and Michelle Dell-Prane for their assistance in mastering the main-frame computer
and notleast in. maintaining our computer link between IRCAM and CCRMA,
Stanford in the latter stages of our work.
Inthe USA,thanks to Gary Leuenbergerforhis programming work and supportand
to the staffand colleagues at CCRMA,Stanford for their help overthe years.Finally, our
thanks to the research and developmentteamatLM Division, NipponGakkiLtd. inJapan,
whotooktime and time and trouble to answer our requests for information regarding
the details ofthe “X” Series synthesizers,to Phil Brimble, who took care of the graphics,
andtoJerry Uwins, Jean-Claude Risset,andDougKeislarforthefinaleditingofthiswork.
FOREV/ORD
John Chowning — the inventor of FM Sound Synthesis Technique — and David
Bristow — the gifted DXSeries FM Voice Maker — have collaborated to producethis
extremely useful “theory meets practice” book.
Their emphasis is on putting FM theory to work, enabling musicians to obtain more
expressively potentcontrol over their FM instruments. Oneofthe really wonderful
things aboutthis bookis that otherwise inaccessible information from acoustics and
Psychoacoustics is clearly explained and applied to musical voicing practice.
David Wessel
IRCAM,Paris
CHAPTER1
AN INTRODUCTION
The remarkable acceptance of the “X” Series musical instruments produced by
Yamahahas led to an equally remarkable need for understanding how the theory
of frequency modulation (FM) synthesis can be effectively used in the creation of
musicalsounds.Inthisbookwehavegleanedfromtheexperienceofmanymusicians
and composers over manyyears whatwebelieve to be the mosteffective meansof
understanding anduse. There is much to learn thatwe can only touch uponin this
text — about acoustics, psychoacoustics (auditory perception), basic mathematics
and indeed musicitself. But touch upon them wemust,for ifwe are to gain a useful
understanding ofFM synthesis we mustbroadenourscope. The required additional
effort will surely be worthit,since the knowledge acquired will be of more general
use than simply understanding basic FM synthesis. W/e will relyonyourdiligence to
read the bookintelligently and seek additional sources, for which direction will be
given.
Computation Transformation
Synthesis Artistic Gesture
In our belief that it is of utmost importance always to rely upon our ears for a
practical and comprehensive understanding,we encourage you to read this book
with an “X”Series synthesizer at hand. As a tool we have found it to be a most
extraordinary aid in elucidating acoustic and psychoacoustic phenomena, as well as
providing the basis of understanding FM. You will see that our strategy is rather
different from other texts on FM in that we are not presenting a recipe book of
“patches,” but rathera meansto understanding,creating, and modifying them.Ifwe
are to be positive in ourapproachto synthesis and FM,a consideration ofthe whole
musical process is important; an awareness of the nature of the transmission and
perception of musical sounds will be of great value when considering thedetails of
FM sound synthesis. The picture belowis to remind usthat the total conceptwecall
Fig. 1.1
Transmission
Acoustics Psychoacoustics
