Abstract
In this paper, a simple mathematical model was proposed to answer such a question: what’s the relationship between the finger pressing position and the corresponding pitch for stringed instruments? Furthermore, we compared the theoretical results with measurement results which were obtained from a guitar to prove that the model we propose is reliable. Result shows that relative errors of theoretical results and measurement results are from 0.18% to 1.8%. The mathematics model is more concise, direct and clear than physical model.
Highlights
IntroductionWe have guitar and mandolin, in China, Pipa, Liuqin and Ruan, in India, Sitar
Stringed instrument with frets is a big member in the stringed instrument family
Continuity Distribution of Pitch The whole string is full of pitches just as the real number axis is full of real number
Summary
We have guitar and mandolin, in China, Pipa, Liuqin and Ruan, in India, Sitar. It seems that, in the whole world, all the appearances of these stringed instruments are similar: the frets are not uniform distributed, whereas interval of adjacent frets decreases close to the plucking region. Pure mathematical model is rare to be found, people tend to study the stringed instruments physically and acoustically as [1]-[4]. This is so complex that only people who have relevant knowledge can understand well.
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