ASA/CAA '05 Meeting, Vancouver, BC

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Complete Geometric Computer Simulation of a Classical Guitar

Rolf Bader
Institute of Musicology, University of Hamburg,
Neue Rabenstr. 13, 20259 Hamburg, Germany

Popular version of paper 2aMU3
Presented Tuesday morning, May 17, 2005
149th ASA Meeting, Vancouver, BC

Fig. 1: Computer model of the classical guitar.

Why is the classical guitar constructed in such a complicated fashion, with, for example, a curved back plate under continual tension? To answer this question, we used computer software to "build" a complete classical guitar which could vibrate in slow motion and produce audible sounds with virtually plucked strings.

Fig. 2: Vibrating state of the guitar's top plate.

The answer to the question lies mostly within the initial burst of sound ("transient") from the guitar tone. Here, special interactions between the different guitar parts take place. So, for example, the vibrations of the top plate make their way to the back plate much faster over the sides ("ribs") of the guitar than by the air enclosed in it. These vibrations travel parallel to the ribs rather than perpendicular to them, and so are not radiated in the ribs. So these waves travel 'underground' to the guitar's back plate and are radiated there, making the back plate sound very bright (rich in high frequencies) at the beginning and only coming down to its standard frequency range after the tone's beginning phase. Also, the back plate sounds much brighter because of its tension. But also the ribs have a time-varying sound within the initial transient because the air inside the guitar at first does not really accelerate them.

Fig. 3: Time series of the different guitar parts during the initial transient phase.
From top to bottom: top plate, back plate, ribs, neck, enclosed air

All these and many other features of the initial transient phase of guitar sounds contribute much to the instrument's overall character and playabiliy. All these fine structures are nearly independent of the guitar player which was found experimentally. Although the player has the possibility to determine to brightness of the tone, the basic character of the classical guitar in the initial transient phase is not dependent on the brightness and also not on the loudness with which the guitar is plucked.

The knowledge of these features can help instrument builders to create new geometries with interesting and characteristic "nonlinear coupling behavior," in other words where there are rich and complex interactions between the various parts of the guitar. Also, these very individual differences of guitar body reaction to the different pitches could result in a very lively reproduction of physical modelled classical guitar sounds.

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