09 September 2011

Bernard Richardson: Simple Models as a Basis for Guitar Design

(This is a guest article which was first published in the 
Journal Catgut Acoustical Scoiety 4(5) (2002), pp.30-36.
  Bernard Richardson  gave permission reprint his excellent article. If you prefer to print it, you will find the article as pdf. And please have a look at the list of publications of Bernard Richardson. I am quite sure, that you will find a lot of articles which might be of interest for you and me ;-).  If there is an urgent need to get into contact, here is the address: School of Physics and Astronomy, Cardiff University, 5 The Parade, Cardiff CF24 3AA, UK

(The software of this blog is not capable to reproduce mathematical symbols and formulas. So I only reproduced the Introduction and the Conclusion. The pictures give you an impression about the contents and can be enlarged by clicking on it. The full text is provided in the pdf.)



Introduction

The first serious analysis of the vibrational modes of the guitar was undertaken by Erik Jansson in 1971 [1]. In this paper, Jansson shows holographic interferograms of the first five modes of vibration of a guitar soundboard, specially made for the experiment by the Swedish guitar maker George Bolin, and describes experimental techniques for the robust identification of mode frequencies and Q-values using purely acoustical measurements. The soundboard was fixed at its edges and had no backing cavity (the air cavity normally created behind the soundboard by the ribs and back plate) so the vibrations were uncomplicated by their coupling to air modes. In a subsequent paper [2], Jansson investigated the air modes (internal standing waves) of a guitar-shaped cavity. These two papers effectively laid the foundation for later interpretations of the complex vibrations of the whole instrument.





In reference [1], Jansson notes the potential which mode visualisation offers the maker and states that “From these hologram interferograms it can be estimated how a change in a plate will change the modes, i.e. the interferograms can tell an instrument builder what to change for a desired result”. The issues of “quality control” or determining the relationships between construction and sound are extremely difficult and remain an on-going problem. However, through patient interaction between makers, players and scientists, Jansson laid the foundations of sensible working criteria for the acoustical requirements of guitars, some of which are presented in reference [3].


As a young research student in the late seventies, the author derived much inspiration from Erik Jansson’s work on guitars and violins. This led to the setting-up of our own holographic system and in the longer term to the establishment of a research group at Cardiff dedicated primarily to understanding the acoustics of the classical guitar. The purpose of this paper, in line with the sentiments expressed in Jansson’s early work, is to present some simple models which might be used by makers to make “informed choices” during the design and construction of an instrument.








Conclusion
A strong case has been put forward for the importance of mode shapes and effective masses, since it is these which critically effect the ease with which strings interact with the body and because of their influence on the sound radiation. Simple models allow informed choices to be made about wood quality and dimensions of instruments as well as providing an understanding of the basic contributions made by different strutting configurations. It is interesting to note that a modest set of parameters, relating to the first few low-order modes of the guitar, are capable of predicting the detail of the low-frequency response and also the general trends in the mid-frequency range. If this were not the case, it is unlikely that the guitar maker would be able to exercise the degree of control necessary for achieving consistency from one instrument to another which is generally observed.

The effective masses emerge as a more important quantity than mode tuning. In fairness, it must be pointed out that for the maker who builds instruments to a restricted design and from consistent materials, mode frequencies are probably a very good means of quality control, partly because under these circumstances they are a good indicator of the effective masses of modes. However, when reviewing the design of the instrument, or trying out new ideas, effective masses are probably a better quantity to bear in mind.

A case has also been put forward for keeping effective masses low, but this advice must be carefully moderated. Guitar making necessarily must strive for a rather critical balance between “loudness” and the rate of decay of the notes. The two are not reciprocally related as generally supposed, but there is usually an obvious trade off between the two. The effective mass of the (1,1) mode is undoubtedly an important quantity to “get right”, and it is interesting to note that the balance between “treble” and “bass” might be modified by either encouraging or discouraging coupling to modes such as the (1,2) and (3,1) modes.

Acknowledgments
Experimental data presented in this paper was produced by various members of the Cardiff acoustics group, including Dr Mark Lewney, Dr Toby Hill and Dr Stephen Richardson. Recent work at Cardiff on the measurement of acoustical parameters for guitars has been supported by the Leverhulme Trust (ref: F/407/R), for which we are extremely grateful. We would also like to thank John Taylor for the loan of the instrument shown in Figure 5 and to the many makers and players who have participated in our recent and past experimental programs.

References
  1. E V. Jansson, ‘A study of acoustical and hologram interferometric measurements of the top plate vibrations of a guitar’, Acustica, Vol. 25, pp. 95-100 (1971).
  2. E. V: Jansson, ‘Acoustical properties of complex cavities. Prediction and measurements of resonance properties of violin-shaped and guitar-shaped cavities’, Acustica, Vol. 37, pp. 211-221 (1977).
  3. E. V. Jansson (Ed.), Function, Construction and Quality of the Guitar, Publication issued by the Royal Swedish Academy of Music No.38 (1983).
  4. Details of PhD studies undertaken in the Acoustics Group at Cardiff are available at the following web site: www.astro.cf.ac.uk/groups/acoucomp/.
  5. T. J. W. Hill, B. E. Richardson and S. J. Richardson, ‘Measurements of acoustical parameters for the classical guitar’, Proceedings of the International Symposium on Musical Acoustics 2001, Vol. 2, pp. 417-420 (2001).