Applied Mathematics > Vol.5 No.10, June 2014

Nan Yang, Dawei Zhang, Yanling Tian

School of Mechanical Engineering, Tianjin University, Tianjin, China.
School of Mechanical Engineering, Tianjin University, Tianjin, China;Tianjin Key Laboratory for Control Theory & Applications in Complicated Systems, Tianjin, China;School of Mechanical Engineering, Tianjin University of Technology, Tianjin, China.

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.

Stringed Instrument, Fret, Pitch, Mathematical Model

Yang, N. , Zhang, D. and Tian, Y. (2014) A Pure Mathematical Relationship between Pitch and Position for Stringed Instruments. Applied Mathematics, 5, 1503-1507. doi: 10.4236/am.2014.510143.