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Session 02 - Guitars

Guitar models for makers
B E Richardson
Cardiff University, Department of Physics and Astronomy, Cardiff, United Kingdom

Science has given a remarkable insight into the mechanical and acoustical action of stringed instruments such as the guitar. Techniques such as holographic or speckle interferometry or the finite element method give detailed information about the vibrations of the wooden body and their dependence on materials and construction. More recently, there has been interest in measuring and modelling sound radiation fields from guitars. Studies have also been made of the player's interaction with the instrument and of the listener's response to modelled or real sounds. One would expect that by now science could answer that innocent question so often posed by makers: "How do I make better guitars?". This paper aims to give an overview of the acoustics of the guitar as we know it today. It will take a look at both experimental and theoretical attempts to find relationships between guitar construction and the musical performance of the instrument. It will also explore some useful models which might be used for quality control or for the exploration of new musical sounds and go, at least some of the way, towards answering the many practical questions posed by makers.

Physical model of a complete classical guitar body
R Bader
Hamburg, Musikwissenschaftliches Institut, Hamburg, Germany

A physical model for a classical guitar is proposed using the finite-difference method. The aim is to simulate the guitar timbre with all details in the structure of the guitars sounds, like amplitude modulations, the disturbance the strings eigenvalues through the modes of the guitars resonant body during the sound initian and all sorts of coupling between longitudinal and transversal modes. Also the influence of the different guitar parts, like the back, the ribs or the top plate upon the radiated sound, as empirically measured, is tried to be simulated. Therefore algorithms for the solution of second order, fourth order differential equations and higher orders in the case of curved plates is used. The method allows the top plate to have changing thickness over the plates area as detailed as needed to simulate the guitar builders fine tuning of the plate. Also the tention, with which the back plate is put in place is simulated. This transient analysis produces a time series taken from every part of the guitar or any superpositions. Next to the production of sound, this method is used to find the reasons for some fine structure guitar sound behavior, which are not explainable theoretically and could then be associated with a physical cause in the evolution of the vibrating guitar body.

Electric guitar microphone qualities: measurement and modelling
C H Besnainou
Universite Pierre et Marie Curie - Paris6 Marie C , Laboratoire d'Acoustique Musicale, Paris, France

Electric guitar pick-up is a very simple transducers detecting the deplacement of a steel string vibrating in a magnetic field. Musicians are very exacting in their choice devices. Some microphones are highly esteemed than others. We investigated different devices. The main result is that the non linear behaviuor is tied with the sound qualities the musicians prefer.

Measurement of the aging of strings instruments
C H Besnainou¹, P Guy²
¹Universite Pierre et Marie Curie - Paris6 Marie C , Laboratoire d'Acoustique Musicale, Paris, France; ²Institut National des Sciences Appliquées de Lyon, Villeubanne GEMPPM, Villeurbanne, France

It is well known that musicians perceive modifications in the sound qualities when playing their instruments. Especially, it seems that a big step of quality occurs during the beginning of the life of an instrument. In this work we present a method wich can be used to measure the changes of mechanical parameters in situ during the life of the instrument. Using very light piezoelectric actuators and sensors embedded beneath the sound board it is possible to record some kind of "acoustic signature" between each couple of sensor/actuator. We will discribe the signal process treatment to extract pertinent parameters and we will bound their temporal evolution with aging (first weeks, first monthes). First results will be shown.

A comparative study of the vibro-acoustical behaviour of electric guitars produced in different decades
E Esposito
University of Ancona, Department of Mechanics, Ancona, Italy

The date of the invention of electric guitar is uncertain, but maybe ascribed to Loyd Loar who worked for Gibson from 1920 to 1924 and there developed the first pick-up. Shortly after, Adolph Rickenbacker produced a Hawaiian guitar that came to be known as the "Frying Pan". It was the first commercially successful instrument to use a modern style electromagnetic pickup. In 1950 Leo Fender started to market the "Telecaster", the first industrially produced two pick-ups modern solid body, followed (1954) by the invention of the quieter humbucking pick-up. At that point the essence of the modern electric guitar was in place.
As we see, the history of the electric guitar spans more than eight decades, and it is practically impossible to study all guitar types and models, so in our work we will investigate the vibro-acoustical behaviour of a single well known guitar, the Fender "Stratocaster". Our aim is to define some measurable parameters that undoubtedly characterize the sound of different guitars and that reflect the human judgement of "good" or "bad" guitar. We have tested Strats from the 50's to the 90's, including one sample of the first ever series produced in 1954. Vibration modes have been investigated by laser Doppler vibrometers, using different types of excitation to study both steady and transient state. Finally, also a commercial Sound Quality software package has been employed to evaluate the psychoacoustics parameters of live played guitars.

Modal radiation from classical guitars: experimental measurements and theoretical predictions
T J W Hill¹, B E Richardson², S J Richardson²
¹Open University, Department of Environmental & Mechanical Engineering, Milton Keynes, United Kingdom; ²Cardiff University, Department of Physics & Astronomy, Cardiff, United Kingdom

In this paper we present input admittance data taken at string positions on the bridge and measurements of the complex sound pressure fields taken on spheres surrounding the guitar. Measurements of input admittance allow the determination of the resonance frequencies, Q-values and effective input masses for each mode. Measurements of the sound field, when an individual mode is predominantly excited, allow the orthogonal monopole and dipole radiation coefficients, to be determined and hence the effective modal area and equivalent source radius to be deduced. The combination of these parameters allows the complex pressure frequency-response to be predicted theoretically and this is shown to agree well with experimental data. It is apparent that monopole and dipole contributions from a few, key, low-frequency modes are responsible for the majority of features in the pressure response at low-frequencies and that these modes also determine the general response at high-frequencies. Evaluation of this small set of acoustical parameters therefore enables the acoustical performance of different instruments to be modelled and compared quantitatively. If coupled with a model of the string-finger interaction, this theory has significant potential for psychoacoustical exploration of the effects that these acoustical parameters have on the tone-quality and musical value of instruments.

New Designs for the kantele with improved sound radiation
J Polkki¹, C Erkut², H Penttinen², M Karjalainen², V Valimaki²
¹Soitinrakentajat AMF, Leppavirta, Finland; ²Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, Espoo, Finland

The kantele is a plucked string instrument belonging to the family of zithers that are used in traditional folk music in Finland, Northwest Russia, and the Baltic states. We propose design rules for a kantele that has a higher loudness than traditional models and present acoustical analysis results to confirm the amplification. The guidelines for making a plucked string instrument louder are to increase the string tension, to add more radiating surface area, and to isolate the top plate from the soundbox with an air gap. We investigate the increased string tension analytically, and show the benefits of the enlarged radiating surface and the isolated top plate experimentally, by acoustical measurements. The input force and the resulting SPL are measured in an anechoic chamber at several points around the instrument, and the measured SPL values are converted to loudness estimates using a computational model. All results are compared against similar figures for a traditional kantele. A playability test, where a professional kantele player is asked to play as softly and as loudly, as she/he feels comfortable, reveals how much we have been able to widen the dynamic range. Finally, the effect of the structural modifications on the timbre is evaluated.

The transient behaviour of guitar strings
J Woodhouse
Cambridge University, Engineering Department, Cambridge, United Kingdom

By analysing the body vibration or the radiated sound from plucked notes on a guitar, two questions of interest to guitar acoustics can be addressed. First, how much can be learned about the behaviour of strings and body by analysing played notes only? Second, how accurately do the results match theoretical models of coupled string/body vibration? Data will be presented from several classical and flamenco guitars which sheds light on both questions. From the set of overtone frequencies, string stiffnesses and intonation errors can be determined. From the pattern of overtone decay rates as a function of frequency, the coupling between strings and body can be explored. By analysis of idealised plucks from the breaking of a fine copper wire, with accurately controlled position and polarisation angle, comparisons can be made with theoretical models which reveal anomalies of detail, some of them quite puzzling.

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