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Ageing of Musical Instruments—About the “Old” and “New Violins”

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Handbook of Materials for String Musical Instruments

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Abstract

In a musicians view “good” or “bad”, “old” or “new” descriptions of violins can be related to their perceived tone quality and their acoustic properties. For more than two centuries the Stradivari and other Cremonese violins fascinated the imagination of musicians, scientists and craftsmen. Today, numerous recordings exist allowing subjective and objective appreciation of the remarkable tonal quality of Old Italian violins.  The quality of a “good” or “bad” violin is related to its radiation efficiency. Violin qualities have been described theoretically by mechanical characteristics and it was demonstrated that normal modes of vibration are determined by the corpus (top, ribs and back) the substructural elements (neck-fingerboard, bridge, strings and tailpiece) and the cavity with air. The signature of all violins is characterized by five important resonances: A0 - air mode or Helmholz resonance at about 280 Hz;  A1 is at 470-490 Hz corresponding to the first standing wave in the length of the box with a node at the f- holes;  CBR – the lowest “main resonance” at 380 – 440 Hz ; B1 and B2, two twin modes are at 450-480 Hz and 530-570 Hz. Dünnwald (1991) studied 700 violin spectra and concluded that Old Italian violins can be statistically differentiated from Modern violins. Since 1985 modal analysis greatly contributed to the development of violin dynamics showing that in all violins good or bad, old or new the five modes can be detected. Based on modal analysis “perfect tonal copies” of Old Italian violins can be reproduced in new violins. The parameters which characterize in detail the sound of the violin are the mode shape, the frequency, the total damping and the acoustic radiation efficiency.

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Abbreviations

Y(ω):

Mobility (m/s/N)

<Y corpus >:

RMS corpus mobility (mean squared averaged over the corpus—top, ribs, back)

R(ω):

Radiativity (Pa/N)

<R>:

RMS radiativity created from mean square averaged over 266 microphone measurement around a sphere in an anechoic chamber

f crit :

Critical frequency f crit  = <R>/ <Y corpus >

\(\xi_{tot}\) :

Total damping (in percent)

\(\xi_{\text{int}}\) :

Internal (material) damping (in percent)

\(\xi_{rad}\) :

Radiation damping (in percent)

Reff :

Radiation efficiency

Frad :

Fraction of energy radiated

\(\rho_{0}^{{}}\) :

Density of the air

c :

Velocity of sound in air

A:

Area of spherical surface upon which the microphone is located (m2)

S:

Surface area of violin corpus (m2)

M:

Nominal mass of violin corpus (kg)

<v2>:

Mean squared velocities

<p2>:

Mean squared pressure over a sphere

IP:

In plane motion, extensional

OP:

Out of plane motion, flexural

Y :

Axis perpendicular to the violin plane

X :

Axis across

Z :

Axis along the violin

A0 :

Cavity mode-Helmholtz air resonance f A0  ~ 280 Hz

A1 :

The first longitudinal mode fA1 ~ 1.7 fA0

CBR:

Corpus lowest mode near ~400 Hz weakly radiating, with shear like along axis X relative motion between the top and back plates

B1 − and B1 + near 500 Hz, both strong radiators

Band average taken over 250 Hz intervals

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  1. Melbourne, Australia

    Voichita Bucur

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Bucur, V. (2016). Ageing of Musical Instruments—About the “Old” and “New Violins”. In: Handbook of Materials for String Musical Instruments. Springer, Cham. https://doi.org/10.1007/978-3-319-32080-9_8

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