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The effect of string tension variation on the perceived pitch of a classical guitar
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Lewis, W. J. (Wanda J.) and Smith, James R. (2014) The effect of string tension variation on the perceived pitch of a classical guitar. Exchanges: the Warwick Research Journal, Volume 2 (Number 1). pp. 53-81. ISSN 2053-9665.
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Official URL: http://exchanges.warwick.ac.uk/exchanges/index.php...
Abstract
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | M Music and Books on Music > M Music | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||
| Library of Congress Subject Headings (LCSH): | Guitar strings, Tone color (Music) | ||||
| Journal or Publication Title: | Exchanges: the Warwick Research Journal | ||||
| Publisher: | Institute of Advanced Study | ||||
| ISSN: | 2053-9665 | ||||
| Official Date: | October 2014 | ||||
| Dates: |
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| Volume: | Volume 2 | ||||
| Number: | Number 1 | ||||
| Number of Pages: | 30 | ||||
| Page Range: | pp. 53-81 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Date of first compliant deposit: | 28 July 2016 | ||||
| Date of first compliant Open Access: | 28 July 2016 |
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