Hebenstreit D
School of Life Sciences, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, United Kingdom.
J Acoust Soc Am. 2018 Jun;143(6):3231. doi: 10.1121/1.5039846.
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.
电吉他等弦乐器通常配备有颤音系统，该系统可将所有琴弦的音高作为一种音乐效果进行改变。它通常基于一个由琴弦和螺旋弹簧保持平衡的可移动琴桥。调准这样一种乐器很复杂，因为调整一根琴弦的张力会改变所有其他琴弦的张力。在实践中，使用一种启发式方法，即反复将所有琴弦调至所需音高，一段时间后似乎能可靠地产生正确音高。目前尚不清楚这种方法为何有效；缺乏相关分析。本文提出了一个数学模型来详细研究这个问题；该模型捕捉了潜在的力学和声学原理，可用于模拟典型的调音过程。然后本文用实验数据验证了该模型，并表明该模型允许计算使用最少调整步骤的最优调音策略。
