Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

Input admittance,eigenmodes, and quality of

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

journal: STL-QPSRvolume: 23number: 2-3year: 1982pages: 060-075

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

IV. MUSIC ACOUSTICS

A-INPUT ADMITTANCE, EIGENMODES, AND QUALITY OF VIOLINS* ~esGs Alonso 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 sound 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££ icient of 0.96 with five deficient violins, excluded.

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 (~lonso Moral & 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' resonance (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.

(~utchins, 1980). In the mode labelled C4 the two plates also vibrate

in 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).

By 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.

An 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 I resonance (Alonso Moral & Jansson, 1982), although other contructimal

details may affect it (Hutchins, personal communication).

1 Violins for the investigation I

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 Andrea Guarneri (certificate from Hamma & Sohn, gives "Fran-

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

was investgated. Thus our investigation included a total of 25 violins,

24 quality-rated violins, and a concert violin.

CONCERT 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 TQP (max=80), and number of violins (class limits selected by authors).

Types of violins TQP nLOnber

Class I 72 - 62 10

Class I1 60 - 50 7

Class I11 48 - 32 7

Andrea Guarneri concert violin 1

Investiuation method

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 kEb 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 A0 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

A0 there is a relative g o d correlation (correlation coefficient ~0.45)

between low frequencies and high tonal quality for "class I" but small

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

for several parameters.

LEFT RIGHT

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 C4

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 4

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, and a large average step are favorable. A high A0 level, a large step A0 to T1, and 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 and 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, and

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 and 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, ~0.14 for 1.4 to 10 kHzI r=0.17 for 1.4 to 3

kHzI and ~0.08 for 3 to 10 kHz).

INPUT ADMITTANCE

LEVEL (10 d ~ / d i v )

and given tonal quality points is 0.39 for all violins, 0.46 for the

nine best violins.

Acoustical parameter four, AP4: -- The discrepancies between input admittance levels (calculated as

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 and 0.19, respectively.

In extensive experiments with violins for many years, including

amysis, making and designing, Saunders, Hutchins and Schelleng found

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

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

I peak level, used in this investigation, is a measure that combines I I efficency of driving and resonance amplification, and gives thus cnly an

I I indication of the properties outside the resonance frequency range as,

1 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:

I AQP = 6x(0.6xAP1 + 0.4(AP2 + AP3 + -4) + 27)

TONAL QUALITY POINTS

Fig. 6. Iielation between Acoustical Quality Points, AQP:s, and Tonal Quality Points, W:s: Ap- proxhted relat ion ( fu l l l i n e ) , separate vio- lins marked with circles, the Guameri v io l in w i t h AG, and "divergent" viol ins with squares. Class limits mrked I, 11, and 111.

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

sound post sides for, the 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 M 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.

A 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 in

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 e

ir -

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) for

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, input 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", ~n -Sound rkneration in winds, Strings, Camputers , Royal Swedish Acadq of Music, Stockholm, Fig. 1 . Hutchins, C.M., personal comication.

Reinicke , W. ( 1 9 7 3 1 : "ijbertraWgseigenschaften des Streichins~tenstegs " , Dr.?hesis, Technische Universitat, Berlin 1972; shortened version in Catgut Ac. Soc. Newsletter No. 19, pp. 26-34.