THE ACOUSTICS OF THE VIOLIN. BY ERIC JOHNSON This Thesis ...

THE ACOUSTICS OF THE VIOLIN.

BY

ERIC JOHNSON

This Thesis is presented in part fulfilment of the degree of Doctor of Philosophy at the University of Salford.

Department of Applied University of Salford Lancashire. Salford, 30 September, 1981.

Acoustics

i


i

TABLE OF CONTENTS

Chapter

1:

page 1

The Violin.

Introduction A Brief History of the Violin Building the Violin The Best Violins and What Makes Them Different References

Chapter

2:

Experimental

Measuring

the

and Theoretical

Frequency

Methods.

Chapter,

3:

15

16 16

Response

Holography The Green's References

1 2 5 11

24 Function

Dynamics

34 40

Technique

of

the

41

Bowed String.

The Bowed String The Wolf- Note

41 53

References

58

Chapter

4:

An Overview

Violin

of

59

Design.

The Violin's. Design The Bridge as a Transmission Element The Function of the Soundpost and Bassbar Modelling the Helmholtz and Front Plate Modes Other Air Modes in, the Violin Cavity References Chapter

5:

Modelling

The Model Evaluating Investigating

the

Response

the

Model Violin

of

Design

References

Chapter

6:

the

Violin.

59 69 73 76 79 84 85 85 93 99 106

Mass-

Manufacturing References

Production Techniques

Applications

107 107 116

I Y.,

a


ii

ACKNOWLEDGEMENTS

Ina

work., such

playedla

part

directiöiis

thät

left

out

ii

role

in

the

no

means

writing

to

has

been

ways

and

'to Amy

interesting.

P.

Yeoman

for

'

discussions

Dr.

for

A.

advised

on

the

these

R.

of

time Ford times

violins

Lord,

and

the

three

have

been

helped any

of

many

subject

Prof.

Jackson me

the

The

with

the

who'supervised

suggestions.

Valiance,

by

by

augmented

amount

ideas.

by

is work

considerable

thanked

and

Finally, 'always

be

to

D.

and

the

this

was

many been

list

the

pdssible

O'Connor,

so

cdnspicuous

most

but

who

doubt

no

the

help

valuable

questions to

'Vernon,

And

his

D.

came from

below

made

those

all

have

financial

this

deserve

also

and

help

listed

itself

Mr.

for

thank

who played

are

thanks

of-interest

" D.

violin-maker; fruitfüil

and

give

lis'tened'

always,

and

special

°'Saunders

'D

have

they

Those

Acoustics.

receiver

wasl'willing

and

aid

University

grant

to

was"appreciated,

_this

The

of-Applied

"shodld

Dr.

Ideas

thesis

of

research

of"a

icult'

evolution. whos'e

söme,

diff

myätküowledgements

Department

he

its

complete.

means

örk';

in

is

it

this

as

in

question

uncounted concerning

photography.

To these

'and the

many others

who helped

me in

this

work

I give

my

thanks*

away place,

To those

who helped

from

United

the

there

is

me in

States,

no way

for

a more

personal

who made England me to

repay

your

way

during

a friendly kindness.

four and

years

hospitable

iii


ABSTRACT

is

The, violin, the_

without.

highly

a

science,

aid. of

Wood, -which-varies individual-attention It-is very

After violin's

include

the

structural

in

the

designed

small

level.

so

it

is

that

the

instruments

are

of

instruments

which

is

is

of. acoustic this

developed

is

and used to answer

back's

that

an

from

does not

greatly

to

additionalis

impedance,

radiation

change

difficult

extremely

suggested

the

the

which

upon

response

As it"is

it

model

shown that,

response

of

the

description

of an automated

plates

cut

concludes

these

a good violin.

used back

the

to is

affect

the

the

low

_

Finally

are

a model

to match

The amount

post..

of

of

design.

violin

sound post

shown tobe

frequency

depend

about

element, the

features

those

most,

questions

improvement

of

plates

mass-produced

requires

another,

thesis.

identifying quality

support

is, the

this

of

several

output

It

the

-

sophistication.

of

to

one sample into

that

surprising

quality.

the. objective

from

be fashioned

to

not_, therefore, poor

evolved

considerably

level

to a high

quite

which,

system,

vibrating

complex

the

and

work..

tested

using

violin

a

construction,

may be predicted

production by

such

process

micro-processor

before in

which, controlled

assembly... the

violin,

machinery

A.

CHAPTER 1

1

PAGE

THE VIOLIN

Introduction.

investigations

Scientific

It

uncommon today. been looked

at,

details

its

of

climbing

over

brings

inevitably In

investigated.

the

which

of

vast

in

good

process,

wolf-note,

but

modelling

the

it

the

this

These by

many

the

violin,

of

the technique

in

Then,

frequency

the

vibrations response

is

the

before

response

the

is

range This

parts.

makes

assembly, possibility is

situation

a mass-poduction

explored.

In adopting

after

predicting

Finally,

plates.

for

frequency

the

for

component

frequency

violin's

prediction

the

in

researchers.

part

to

which

characteristics

obvious

method

to

price.

evident

a

of

incidental

mass-produced

market

most

other

properties

alter

the are

over

to

easy

goal

violin

the

adjust

still

applying

briefly

on

to is

of

complete

based

this

studied.

their

add to

determine

a way in

those

the

of

which

only

to find

is

goal

such as the

consequences

are

problems

are

which

parameters

violins,

new

does not

measured

a

possible

while

of

towards

action

of

developed,

work.

are

curves

The real

like

problem

one

of

elucidated,

the

and the such

subtlest Thus,

details

are

design,

violin's

the

one.

smallest

problems

bowing

step

response

response

the

a way which

violins

not

interesting

majority

As a first

of

the

this

of

the

students,

is

is

govern

the

purpose

improve

of

more distant

non-linear origin

the

another,

Some

principles highly

to view it

is

solution

of

thesis

this

the

series

has

subject

a good violin.

mark of

ridges,

of

means

no

this

it

shows that

the

are

by

are

aspect

every

advance

which

family

violin

nearly

every

action a

of

seems that

and yet

the

F this

approach stressed

perhaps

of a violin

is

also

very

the too

importance much.

important,

of No

yet

the

doubt the

steady-state the'transient

quality

of

most

mass-produced

instruments

proportion

of

the

some

day

Perhaps

will

questions

should

The origins among scholars.

of

rarely

other

medieval

is

instruments)

It

viols

is

has

many

to

modelled

slightly

be copies

on

(1540-1609),

his

from

these

debate

of

subject

from

that

the and

viols

'examples

earlier

the

term

bass

was formerly to

applied

(1514-1570),

a

Bavarian

been

named

of

but

six, of

to

violins

lead

to

the

revival

a recent

until

in

wood,

which-the

enough viol

occasionally

thin

very

is

viol

music.

credit

the

belly

a

violin,

The advantages

the

to

five,

back,

be significant

but

all

of

the

with

arched

to

proved

been given

violins

instruments

viols,

Andrea

the

seems most likely

a violin.

(this

often

due

probably

a flat

universally

Duiffopruggar Frenchman,

had

and renaisance

have

been

families

familiar

resembling

more

most general

assumed to have evolved it

is

everyone

Many luthiers now

the

only

[1,2].

disappearance

complete in

as two distinct

the

over

but

crewth,

and a very

respects

enjoyed

violin

or

today.

more strings,

long

have

has been variously

nearly

seen

time

of

Violin.

It viol,

While

this

at

of

instruments

string

but

out,

importance

the

of

large

be improved.

can only

situation

ä

ignoring

even}

analysis

the

developed

violins

the

detailed

more

the

of

lute,

so

that,

be addressed.

History

rebec,

overall a

low

problems,

be carried

transients

A' Brief

is

2

PAGE

THE VIOLIN

CHAPTER 1

Acnati

as

the

made

by

the

makers

for who

became

originator Vuillaume

of

which

(c1535-c1611),

exist

today

and Maggini

[2].

violin.

nationalized This

violin. were

They

thought

were

in

Gaspar of

but

stringed

the a

the

makers any

of

developing

by Duiffopruggar.

some of' which

lute

to

applied

Brescia

by fact

da Salo have

1

Ch AFTER

THE

been

all

named

still

it

exist,

conclusively.

What

violin

rapidly,

evolved Stradiverius,

and

above

by

luth.

musicianship

all

the

are

field

is

seldom

uutortuiiate

this

that

Amatis,

their and

created

the

Guarnaeris,

tone

both

were

?b

Ey

., i..

d

_ 'h'71

,

r {. *_ý Kh

ýyjz

J"'

".v

us

today,

or

began

many

to

copy ý

these

great

violins

aud

and

experimentation, had

which

master

s

originality

so

quickly

the

violin,

1

9"

IpS..

were

§ '

ý. t.

of

1

violin

led

making,

Merman

the

School

r; 4ýr,

course

of

exceptionsf: ze

There

discarded.

were

,4

C(ýk

and Perhaps

developed u>ývýý

valued

today.

lutIhicrs +gl,

Cremona,

craftsmanship

equaled fur

the

once

in

in

two

question

followers

genius

ujnduubted

which

their

of

Aesthetics

their

is

the

of

school

others.

who with

in

however,

names

the

with

made violins

dominance

their

the

with

decide

to

first

the

to

attributed

violins

said,

3

MAGI:

impossible

be

cau

of

iers,

while

is

along

standing these

but

credit,

hivewi

V1ULIN

by

Jacob

(1621-1683),

Stainer

instruments

produced

of in

beauty

exceptional L'} Y

both these

Figure

1.1:

Stradavarius Note

the

Modern

copies

(right)

and

differently

of

violins

Stainer

shaped

t-holes.

(left).

by

form

and and

Italian

but

the

old

violins

alnust copied

tone-

were

universally for

man y

years.

CHAPTER

1

Before

begining

the

investigation

acoustics one

J

should

spire

a few

moments

look

at

t 114"

Alý to

two

in

which

f]

1.1

few

a

which

made

It

violin.

the

is

the

varnish,

lightness

and which

characterize

a

good

in

violin,

it

easy

fascinated

Figure

1.2:

(left)

is

The much

Stradavarius

arching more

of

abrupt

the

Stainer

than

that

copy the

of

(right).

copy

a

but

photograph

excel

41,-

depth

t_Iie

responsiveness

sets

ýýe"h,

workmanship,

the

make

VL

1ý