Music and Acoustics E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 256

Veröffentlichungsjahr: 2013

Beschreibung

How can a piano tuner obtain such high precision with no other measuring device than their own ears? How can a sequence of notes seem to rise continuously despite coming back periodically to the same notes? What are the possibilities and the limits of digital sound? These are a few examples of questions that are discussed in this book, which presents an overview on the nature of musical sounds, from their production by acoustic music instruments to synthesized sounds obtained with computers. The topics that are treated include sound propagation, Fourier and time-frequency analysis, psychoacoustics, analog and digital signal processing theory, computer science and MP3 sound compression, and of course... music!

Leseprobe

Table of Contents

Foreword

Chapter 1. Sounds

1.1. Sound propagation

1.2. Music theory interlude

1.3. Different types of sounds

1.4. Representation of sound

1.5. Filtering

1.6. Study problems

1.7. Practical computer applications

Chapter 2. Music Instruments

2.1. Strings

2.2. Bars

2.3. Membranes

2.4. Tubes

2.5. Timbre of instruments

2.6. Study problems

2.7. Practical computer applications

Chapter 3. Scales and Temperaments

3.1. The Pythagorean scale

3.2. The Zarlino scale

3.3. The tempered scales

3.4. A brief history of A4

3.5. Giving names to notes

3.6. Other examples of scales

3.7. Study problems

3.8. Practical computer applications

Chapter 4. Psychoacoustics

4.1. Sound intensity and loudness

4.2. The ear

4.3. Frequency and pitch

4.4. Frequency masking

4.5. Study problems

4.6. Practical computer applications

Chapter 5. Digital Sound

5.1. Sampling

5.2. Audio compression

5.3. Digital filtering and the Z-transform

5.4. Study problems

5.5. Practical computer applications

Chapter 6. Synthesis and Sound Effects

6.1. Synthesis of musical sounds

6.2. Time effects: echo and reverberation

6.3. Effects based on spectrum modification

6.4. Study problems

6.5. Practical computer applications

Bibliography

Index

First published in France in 2005 by Hermès Science/Lavoisier entitled “Musique et acoustique : de l’instrument à l’ordinateur“

First published in Great Britain and the United States in 2006 by ISTE Ltd

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd 6 Fitzroy Square London W1T 5DX UK

www.iste.co.uk

ISTE USA 4308 Patrice Road Newport Beach, CA 92663 USA

© ISTE Ltd, 2006

© LAVOISIER, 2005

The rights of Philippe Guillaume to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Guillaume, Philippe, 1955-

[Musique et acoustique. English]

Music and acoustics: from instrument to computer/Philippe Guillaume.

p. cm.

Includes bibliographical references (p. ) and index.

ISBN-13: 978-1-905209-26-2

ISBN-10: 1-905209-26-6

1. Music--Acoustics and physics. 2. Computer sound processing. I. Title.

ML3805.G8513 2006

781.2'3--dc22

2006028748

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 10: 1-905209-26-6

ISBN 13: 978-1-905209-26-2

Foreword

How does a tuner achieve such a precise tuning of a piano or an organ using nothing but his ears? Why does the clarinet, though equal in length to the C flute, play one octave lower? What difference is there between the Pythagorean scale and the tempered scale? How can a series of notes seem to rise indefinitely even though it always repeats the same notes? What are the possibilities offered by digital sound? What are its limitations? How can a compression technology such as MP3 achieve a tenfold reduction of a sound file’s size without significantly altering it? What is the very simple principle underlying audio synthesis in Yamaha’s famous keyboard, the DX7? These are a few examples of the questions we will try to answer.

The goal of this book is to use these questions to give the reader an overview of the nature of musical sound, from its production by traditional musical instruments to sounds obtained by audio synthesis, without trying to be exhaustive however: this book is not meant as a catalogue, but instead, I hope, as a first step that will enable the reader to move on to more specific areas in this field. Musical sound is addressed from a scientific standpoint, and the succession of causes that lead to a specific type of sound are, as much as possible, described in a simplified but precise manner. The fact, for example, that a particular sound is composed of harmonics (strings, pipes, etc.) or of partials (bells, timpani, etc.) finds its causes in the physical laws that govern the behavior of materials, laws that induce mathematical equations, the nature of which leads to a certain characteristic of the produced sound.

This book is intended for any reader interested in sound and music, and with a basic scientific background: students, teachers, researchers, people who work in a scientific or technical field. It describes and relies on concepts of acoustics, mathematics, psychoacoustics, computer science and signal processing, but only to the extent that this is useful in describing the subject. In order to broaden its reach, it was written in such a way that the reader may understand sound phenomena with simple analytical tools and the smallest possible amount of required knowledge. Those who teach this material will find diverse and motivating study problems, and students will find ideas for different kinds of ‘projects’ they may encounter in their undergraduate and graduate studies. In the end, my greatest wish would be to succeed in sharing with the reader the pleasure I find in understanding the basic mechanisms underlying the manifestation and the perception of the sound and music phenomenon.

After an introduction to acoustics, a bit of music theory, and a study of sounds and their representation in Chapter 1, we will discuss vibrational modes and the timbre of a few typical instruments in Chapter 2, and in Chapter 3, we will relate this with the question of scales and tuning systems. After wandering off into psychoacoustics in Chapter 4, and using the opportunity to discover a beautiful acoustic illusion, we will discuss several aspects of digital sound in Chapters 5 and 6: sampling, compression technology based on the properties of hearing (such as the widely known MP3 format), sound effects (vibrato, reverberation, the Leslie effect) and synthesized sounds, such as for example those produced using the Chowning technique, made popular by DX7 synthesizers.

For further development, each chapter ends with the following:

–study problems, to explore certain themes, or to study them further in depth. For the reader’s information, the difficulty and the amount of work required are indicated with stars: (*) means easy, (**) is average and (***) is difficult;

–practical applications meant to be carried out on a computer, where the reader will create different kinds of sounds and play them on a crude synthesizer, experimenting on the phenomena described in the book, as well as put his or her hearing to the test, and practice his or her scales! Practical instructions relevant to these applications are given at the end of the first chapter.

Website. A website is available to illustrate the book. It contains many examples of sounds, as well as the programs used to generate them. It also contains the programs and sound files necessary to perform the practical applications, along with the answers. The address of the website is:

www-gmm.insa-toulouse.fr/~guillaum/AM/

Throughout the book, it will be referred to simply as the AM website.

Reading advice. The chapters were written in a particular, logical order, and the concept and methods developed in a given chapter are assumed to be understood in the chapters that follow. For example, the approach used to go from the wave equation to the Helmholtz equation, which is detailed in Chapter 1, will not be explained again when studying the vibrations of sonorous bodies in Chapter 2. However, you can also browse through it in any other order, referring if necessary to the previous chapters, and using the cross-references and the index to easily find where a given concept was discussed. Finally, because some phenomena are easier heard than explained, listening to the website’s audio examples should shed light on any areas that may still be unclear!

Philippe GUILLAUME

Chapter 1

Sounds

Sound and air are closely related: it is common knowledge that the Moonians (the inhabitants of the Moon) have no ears! This means we will begin our study of sound with the physics of its traveling medium: air. Sounds that propagate through our atmosphere consist of a variation of the airs pressure p(x, y, z, t) according to position in space x, y and z and to the time t. It is these variations in pressure that our ears can perceive. In this chapter, we will first study how these sounds propagate as waves. We will then describe a few different types of sounds and various ways of representing them. Finally, we will explain the concept of filtering, which allows certain frequencies to be singled-out.

1.1. Sound propagation

The propagation of a sound wave can occur in any direction, and depends on the obstacles in its path. We will essentially be focusing on plane waves, that is to say waves that only depend on one direction of space. We will assume that this direction is the x-axis, and therefore that the pressure p(x, y, z, t) is independent of y and z. Hence it can simply be denoted by p(x, t). This type of function represents a plane wave propagating through space, but also a sound wave inside a tube (see Figure 1.1), such as for example the one propagating through an organ pipe.

1.1.1. A look at the physical models

The propagation of sound through air is governed by the wave equation (see page 21), an equation we will come across several times since it also determines the movement of sound waves in the vibrating parts (strings, membranes, tubes...) of many instruments. In the following paragraphs, we will see that, in the case of air, this equation is inferred from three fundamental equations of continuum mechanics.