The Effect of String Tension Variation on the Perceived Pitch of a Classical Guitar


  • Wanda Jadwiga Lewis University of Warwick
  • James Raphael Smith Retired Jaguar Chief Research Engineer
  • Wanda J. Lewis University of Warwick
  • James R. Smith University of Warwick



guitar pitch, string vibration, perturbation model, overtones, tension modulation, geometric stiffness


Actual motion of a vibrating guitar string is a superposition of many possible shapes (modes) in which it could vibrate. Each of these modes has a corresponding frequency, and the lowest frequency is associated with a shape idealised as a single wave, referred to as the fundamental mode. The other contributing modes, each with their own progressively higher frequency, are referred to as overtones, or harmonics. By attaching a string to a medium (a soundboard) capable of a response to the vibrating string, sound waves are generated. The sound heard is dominated by the fundamental mode, ‘coloured’ by contributions from the overtones, as explained by the classical theory of vibration. The classical theory, however, assumes that the string tension remains constant during vibration, and this cannot be strictly true; when considering just the fundamental mode, string tension will reach two maximum changes, as it oscillates up and down. These changes, occurring twice during the fundamental period match the frequency of the octave higher, 1st overtone. It is therefore plausible to think that the changing tension effect, through increased force on the bridge and, therefore, greater soundboard deflection, could be amplifying the colouring effect of (at least) the 1st overtone.

In this paper, we examine the possible influence of string tension variation on tonal response of a classical guitar. We use a perturbation model based on the classical result for a string in general vibration in conjunction with a novel method of assessment of plucking force that incorporates the engineering concept of geometric stiffness, to assess the magnitude of the normal force exerted by the string on the bridge. The results of our model show that the effect of tension variation is significantly smaller than that due to the installed initial static tension, and affects predominantly the force contribution arising from the fundamental mode. We, therefore, conclude that string tension variation does not contribute significantly to tonal response.


Photo credit: By Biblola (Own work) [CC-BY-SA-3.0 (], via Wikimedia Commons


Download data is not yet available.

Author Biography

Wanda Jadwiga Lewis, University of Warwick

Professor, Civil Engineering, School of Engineering, University of Warwick


Antman, S. (1980) The Equations for Large Vibrations of Strings. The American Mathematics Monthly 87, (5): 359-370.

Band, B. (2009) ‘Energy-based Synthesis of Tension Modulation in Strings’, in Digital Audio Effects, Proceedings,12th International Conference, Como, Italy: 1-8.

Carrier, F. (1945) On the Non-linear Vibration Problem of the Elastic String. Quarterly of Applied Mathematics 3: 157-165.

Coulson, C.A. (1941) Waves. London: Oliver and Boyd Ltd.

Decker, J.A. (2007) ‘Guitar Acoustics 101’.

Fletcher, N.H., and Rossing (1998) The Physics of Musical Instruments. London: Springer Verlag, 2nd Ed.

Fletcher, N.H. (1999) The Non-linear Physics of Musical Instruments. Reports on Progress in Physics 62, (5): 723.

Legge, K.A., and Fletcher, N.H. (1984) Non-linear Generation of Missing Modes on a Vibrating String. Journal of Acoustical Society of America 76: 5-12.

Lewis, W.J. (2003) Tension Structures. Form and Behaviour, London: Thomas Telford.

Morse, P.M.(1948) Vibration and Sound, New York: McGraw Hill.

Murthy, G.S.S., and Ramakrishna, B.S. (1965) Non-linear Character of Resonance in Stretched Strings. Journal of Acoustical Society of America 38: 461-471.

Ramsey, A.S. (1949) A Treatise on Hydromechanics. Part II Hydrodynamics, London: G. Bell and Sons, Ltd.

Rayleigh, J.W. (1894) Theory of Sound, CUP, 2nd Ed., Vol.2, reprinted by Dover, 1945.

Taylor, J. (1978) Tone Production on the Classical Guitar, London: Musical New Services Ltd. A Guitar Magazine Project.

Tolonen, T., Valimaki, V., and Karjalainen, M. (2000) ‘Modelling of Tension Modulation Non-linearity in Plucked Strings’ in Speech and Audio Processing, IEEE Transactions, 8 (3): 300-310.

Young, R. W. (1947) Inharmonicity of Plain Wire Piano Strings. Journal of Acoustical Society of America 24, (3): 247-273.

Man playing a guitar