2Input admittance, eigenmodes ans quality of violins (1).pdf

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Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

Input admittance,

eigenmodes, and quality of

violins

Alonso Moral, J. and Jansson, E. V.

journal: STL-QPSR

volume: 23

number: 2-3

year: 1982

pages: 060-075

http://www.speech.kth.se/qpsr
http://www.speech.kth.se/http://www.speech.kth.se/qpsrhttp://www.speech.kth.se/qpsrhttp://www.speech.kth.se/


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IV. MUSIC ACOUSTICS

A-INPUT ADMITTANCE, EIGENMODES, AND QUALITY OF VIOLINS*

~e sGs lonso Moral and Erik

V

Jansson

Abstract

From a Scandinavian violinmakers' competition, a number of 24 vio-

lins of different qualities were selected. Input admittances

as

function

of frequency were recorded perpendicularly to the top plate at two

positions on top of the bridge. The admittance curves at the side of

the

bass

bar

show

three

resonances at approximately

400

500,

and 700 Hz and

a broad resonance around 3 kHz. Three acoustical quality criteria were

extracted from these curves:

1) the average level of the three resonance

peaks (high is favorable), 2) the discrepancies between

single peak

levels and the average level (small is favorable), and 3) steepness of

upwards slope from a 1.4 to a

3

kHz region (steep is favorable).

Be

tween 1.4 and 3

kHz

the levels or input admittances of the bass

bar

and

soun post sides tend to

be

the same. A fourth acoustical quality crite-

rion was extracted from the two curves:

4)

the level discrepancies bet-

ween the two curves (small is favorable). Calculated acoustical qudli-

ty points correlate well with given tonal quality points (a correlation

me cient of 0.96 with five deficient violins, xcluded.

Introduction

In a previous paper we presented representative acoustical pro-

perties of violins.

In this following paper we report on an investiga-

tion of relations between these acoustical properties and tonal quality

of violins. We seek answers to two questions:

1.

What are the most important properties of the violin?

2. How

well

do

these properties predict the quality of

a violin?

Eigenmodes

and

input admittance

In a previous investigation we recorded representative eigenmodes

for the violin (~lonsooral Jansson, 1982), see Fig

1.

In the eigen-

mode T1 the main vibrations are in the top plate. We have interpreted

this resonance as being the first top plate mode. Similar vibration

pattern is to

be

found for the ~elmholtz' esonance

A0

our labelling),

which seems strongly connected with the T1-resonance. In the eigenmode

C3, the top

and

the back plates vibrate in phase. The vibration patterns

are similar to that of the second mode of each of the two plates free

This paper was presented to the 103rd Meeting of the Acoustical Socie-

ty of America held in Chicago,

Illinois, April 1982, paper U-3.


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(~utchins,980). In the mode labelled C4

the two plates also vibrate

n

phase. The vibration pattern is similar to that of the ring mode of

free plates.

At approximately 3 kHz the violin has its main bridge resonance, a

tilting motion (Reinicke, 1973).

y means of the so-called input admittance, that is, the resulting

velocity at the driving point for given force, resonance frequencies,

vibration levels,

and @factors are easily recorded.

n illustrative exampleof an input admittance curve is given in

Fig 2. The curve shows a small

peak

marked AO,

and

four

prominent pedks

T1,

C3,

C4,and

F.

Thereafter follows a wiggly curve from which we can

extract a hill with a maximum at - say - 3

kHz

These peaks corresponds

to

the resonance frequencies of the eigenmodes A01 T1, C3, C4, and a

mode F yet not mapped.

The 3-kHz hill corresponds mainly to the bridge

resonance (Alonso Moral Jansson, 1982), although oth r contructimal

details may affect it (Hutchins, personal communication).

Violins for the investigation

For the investigation we selected violins from a violin makers'

competition,

FIOG80, arranged by the Nordisk Violinbyggareforening .

The 77 violins of the competition had been tested and given tonal quali-

ty

pants by two professional violin players regarding evenness,

volume,

and brilliance of tones together with playability.

We selected

24

vie

lins covering the full range of ratings, see Table I. The

violins were

grouped in three classes after quality points in order

to

make campari-

sons possible between group averages. In addition,

a concert violin

labelled

ndrea

Guarneri (certificate from amma Sohn gives Fran-

es o Rugeri,

Cremona approx 1690 as maker, place and year of making)

was investgated. Thus

ur

investigation included a total of 25 violins,

24 quality-rated violins, and a concert violin.


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ON ERT VIOLIN

Fig.

2.

Input

admittance at

the

bass bar side

of

the

Andrea Guameri violin.

TABLE

I.

Violins of the investigation: Types of violins, tonal

quality points

TQ

max=80), and number of violins

class limits

selected

by

authors).

Types of violins

TQP

nLOnber

Class

I

72 62 1

Class I

6

50

7

Class

I

48 32

7

Andrea Guarneri

concert violin 1


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Investiuationmetho

For the present investigation it was decided to record the input

admittance in two positions on top of the violin bridge, just outside

the

G-

and E-strings, cf. Fig. 3.

In

both cases the input admittances

were recorded in perpendicular to the top plates of the violins. Fur-

thermore, it was decided to accurately measure the peak frequencies of

four resonances, AO, T1,

C3

and C4. The corresponding peak levels were

generally measured and noted too. The long term stability of the meas-

urements were controlled

by

repeated calibration every hcur.

The measured peak frequencies and levels (average and standard

deviations) for the AO, T1, C3, and C4 peaks are given in Table

11.

When

the Tl-peak consisted of a double or a triple peak,

the peak of the

highest level was selected to represent the T1 resonance.

Analyzed acoustical parameters

Three

types of acoustical properties and their possible relations

with tonal qualities were tested. First we tested relations between

tonal quality and resonance frequencies of the AO, T1, C3, and C4

Secondly we tested relations between quality and levels: below 1 k b the

levels of the AO, T1, C3, and C4 peaks and above 1 kHz the levels

averaged in critical bands of hearing, Bark. Finally we tested relations

beween quality points and level differences bass bar sound post

sides. The importance of different acoustical properties were tested,

mainly by calculating the correlation between their acoustical meas-

ures and given tonal quality points for each violin. In some cases a

first study was done

by

comparing averages of classes.

Calculated correlations, for instance, average frequencies of the

different classes,

showed a somewhat astonishing result. The

A arsd

T1

peaks of the violins of class I

and

class

111

have higher resonance

frequencies than class 11 . This means that one should not expect a

simple correlation between tonal quality and

resonance frequencies. For

A there is a relative

g o

correlation (correlation coefficient ~0.45)

between low frequencies and high tonal quality for class

I

but small

(~0.12) or all three classes taken together. The same trend was found

for several parameters.


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L FT

RI HT

Fig. 3. Positions and directions

of input admittance meas-

wements

Table

11

Measured frequencies and levels of resonance peaks,

average and standard deviations 0

dB

corresponds to 3 s/kg).

Peak

A0 T1 C3 C

Average frequency Hz) 272 403 500

686

Standard deviation Hz) 11 22 27 54

Average level dB)

-35 -24 -27 29

Standard deviation

a)

4

4

3


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obtained for the T1 and the C4 levels, the steps T1 to C3 and C3 to C4.

Moderate correlations approx. 0.2) are obtained for the A0 level, the

level step A0 to T1, and the equality of steps.

High T1 level, large

downward step T1 to C3

large upward step C3 to C4,

nd

a large average

step are favorable. A high A level,

a large step A0

to

T1, nd equality

of levels are favorable, but not as clear as previously mentimed

param-

eters.

The calculated correlations between levels, averaged

in

Bark bands,

and tonal quality are given in Fig

4.

The calculations

indicate that

low levels are favorable between 10 to 15 Bark and above 18 Bark a

correlation of approx 0.4).

3. Level differences between bass bar nd sound post sides

For frequencies below the C4 peak the input admittance is higher

for the bass bar side than for the sound post side, cf. Fig.

5.

Out of

the 25 violins 20 have, say 5 10 dB, higher levels at the bass bar

side, three less clear difference, one approximately the same level,

nd

only one with lower level at the bass bar side. For higher frequencies

the inadmittance levels tend to be the same for both sides. Possible

relations between tonal quality nd balance bass

bar

sound post sides

were investigated.

The following correlations were found between quality and level

differences bass

bar

sound post sides: H.32 for T1, 0.21 for

C3 and

0.36 for the average of T1 and C3 A0 is not measurable at sound post

side). Furthermore, a small level difference between the two sides is

favorable for C4 ~0.42).

For frequencies above 1.4 kHz small level differences seem favor-

able in absolute values, ~0.14or 1.4 to 10 kHzI r=0.17 for 1.4 to 3

kHzI and ~ 0.08or 3 to 10 kHz).


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INPUT ADMITTANCE

LEVEL 10

d ~ / d i v


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and given tonal quality points

is 0.39 for all violins,

0.46 for the

nine best violins.

Acoustical parameter four, AP4:

he discrepancies between input admittance levels calculatedas

the standard deviation) from 1.4 to 3 kHz A small summed discrepancy is

favorable. The correlation-coefficient between this acoustical parameter

and

given tonal quality points is 0.17

nd

0.19, respectively.

In extensive experiments with violins for many years, including

amysis,

making

nd

designing, Saunders, Hutchins and Schelleng found

that two resonances, the Helmholtz and the Main ood resonances, fall

close to the open middle strings in good violins, Hutchins 1980). The

peak level, used in this investigation, is a measure that combines

efficency of driving and resonance amplification,

and

gives thus cnly

an

indication of the properties outside the resonance frequency range as,

for instance, in

Bark

bands. Still, the previous findings by Gabriels-

son and Jansson l979), cf. Fig. 4, indicate that a high AO, T1, and C4

are favorable.

Both

the present investigation and that by Gabrielsson

and Jansson suggest that C3 in isolation is not important for the quali-

ty*

The correlation between tonal quality

and

levels

in Bark bands do

not agree in the present investigation and that by Gabrielsson and

Jansson. Possibly the differences derives from a combination of effec-

tive radiation and low driving level. The AP3 criterion may, however,

fit well also in the previous investigation, i.e., the favorable large

level increase is not contradicted.

Thus the suggested parameters are reasonable, but not fully in

agreement with previous findings. Furthermore, they do not cover all

possible differences between violins. The suggested parameters can,

however, be tested on the investigated 24

violins, and thereby a measure

of goodness for the suggested parameters is obtained.

The four acoustical parameters were weighted and summed according

to the formula to an Acoustical Quality Point, AQP

AQP 6x 0.6xAP1 0.4 AP2 AP3

-4

27)


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TON L QU LITY POINTS

Fig. 6

Iielation between Acoustical Quality Points,

AQP:s and Tonal Quality Points, W:s: Ap

proxhte

r e la t io n ( f u l l l i n e ) ,

separate

vio-

lins marked

with

circles

th Guameri v io l in

w i t AG and

divergent vio li ns with squares.

Class

limits m r k e d I

11 and 111.


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investigation. Such gross parameters, as balance-unbalance between the

bass bar and the sound post sides, and levels from 900 to 1300 Hz are

not included.

Four of the five divergent violins score poorly in these parame-

ters. Two have the very lowest levels from 900 to 1300

Hz

and two other

have exceptionally small level differences between the bass bar and the

soun

post sides for, he T1 and the C3 peaks.

Possibly, these proprties give the serious divergencies not ac-

counted for. The fifth violin has a split, a double, T1 peak. Several

violins have this and it does not seem likely that this defect ex-

plains the

P

divergency from the prediction.

Conclusions

Simple calculations have shown that the levels

of

resonances la-

belled AO T1, and C4 correlates with tonal quality. Furthermore, pro-

perties around the frequency of the main bridge resonance correlates

with the quality. For low frequencies, below C4, the bridge foot

on

the

bass bar side is most efficient in driving the violin, while for higher

frequencies both bridge feet are abcut equally efficient. The difference

at low frequencies and the equality at high frequencies also correlate

with tonal quality.

function, weighting together levels of the T1, C3, C4 peaks

and

average levels from 1 to 3 kHz, predicts the tonal quality well for 19

of the 24 violins, and especially well for the six highest rated vio-

lins. The C3 level does not correlate separately with the tonal quality,

but increases the correlation noticeably together with the T1 and C4

peaks. This makes us believe that we have traced major parameters of

quality, not only for the nineteen tested violins, but for the violin n

general.

Thus, this investigation has given the following answers to the

introductory questions:

1. The resonance peaks T1, C3, and C4, and a hill around 3 kHz are the

most important properties of the input admittance. The resonance

peaks

r


18/18

STL-QPSR 2-3/1982

should be equally high when excited at the bass

bar

side. The favorable

high peak levels indicate: 1) that stiff and light wood with low inter-

nal friction is favorable, and

2)

that the properties in top and back

should match (C3 and C4). The 3 kHz hill should have

a

large level

increase from 1.4 to

3

kHz, and it should be equallly well driven from

the bass bar and the sound post sides. This indicates that a well

developed bridge resonance and a good balance

between the bass bar and

sound post sides are important.

2.

These properties predict tonal quality reasonably well (~0.76) or

all violins, very well (r=0.96) with five divergent violins excluded.

The rather high correlation between tonal quality and low frequency

properties indicates that good low frquency properties may predict

good

high frequency properties to a large extent. Some additional factor

must, however be important as the five violins represent large divergen-

cies from predictions.

This investigation was possible through the cooperation of ''KbNordisk

Violinbyggareforening

and

Mr. Gunnar Mattsson. The measurements were

made at the Stockholm Music Museum. Lars Frydgn

lent us his Guarneri

violin for the investigation. This support

and

cooperation is gratefully

acknowledged.

Alonso Mral, J.

and Jansson,

E.V.

(1982):

Eigammdes, nput admittance, and

fhctidn of

the

violin , Acustica 50, pp. 329-337.

-

Gabrielsson,

A

and Jansson, E.V. (1979): Long-tim-average-spectra and rated

qualities of twnty-two violins , Acustica 42,

pp

47-55.

-

Hutchins, C.M. (1980):

The new violin family ,pp 182-203 in Sound Genera-

tion in Winds, Strings, Computers, faoyal Shedish Acaderry of Music, Stockholm.

Hutchins, C. M. 1980)

Tuning of violin plates , ~nSound rkneration in

winds,

Strings, Camputers Royal Swedish Acadq of Music, Stockholm, Fig.

Hutchins, C.M., personal comication.

Reinicke W. 9

:

ijbertraWgseigenschaften des Streichins~tenstegs

Dr.?hesis, Technische Universitat, Berlin 1972; shortened version in Catgut

Ac

Soc Newsletter

No.

19, pp 26-34.

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