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Tuning a musical instrument with vibrato system : a mathematical framework to study mechanics and acoustics and to calculate optimal tuning strategies
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Hebenstreit, Daniel (2018) Tuning a musical instrument with vibrato system : a mathematical framework to study mechanics and acoustics and to calculate optimal tuning strategies. The Journal of the Acoustical Society of America, 143 (6). 3231 . doi:10.1121/1.5039846 ISSN 0001-4966.
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Official URL: https://doi.org/10.1121/1.5039846
Abstract
String instruments such as electric guitars are often equipped with a vibrato system, which allows varying the pitch of all strings as a musical effect. It is usually based on a mobile bridge that is kept in balance by the strings and a coiled spring. Tuning such an instrument is complex, since adjusting the tension on one string will alter all other strings' tensions. In practice, a heuristic method is used where all strings are repeatedly tuned to the desired pitch, which appears to reliably yield correct pitches after a while. It is unclear why this method works; an analysis is lacking. This paper presents a mathematical model to study this subject in detail; the model captures the underlying mechanics and acoustics and can be used to simulate a typical tuning process. The paper then verifies the model with experimental data and shows that the model permits calculation of optimal tuning strategies that use the least number of adjustment steps.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | M Music and Books on Music > ML Literature of music | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Life Sciences (2010- ) | ||||||
| Library of Congress Subject Headings (LCSH): | Electric guitar -- Acoustics, Electro-acoustics, Electric guitar -- Mathematical models., Guitar-- Acoustics, Guitar -- Construction, Guitar amplifiers -- Mathematical models. | ||||||
| Journal or Publication Title: | The Journal of the Acoustical Society of America | ||||||
| Publisher: | Acoustical Society of America | ||||||
| ISSN: | 0001-4966 | ||||||
| Official Date: | June 2018 | ||||||
| Dates: |
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| Volume: | 143 | ||||||
| Number: | 6 | ||||||
| Article Number: | 3231 | ||||||
| DOI: | 10.1121/1.5039846 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 15 May 2018 | ||||||
| Date of first compliant Open Access: | 31 December 2018 | ||||||
| Related URLs: |
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