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Finding the Inharmonicity Coefficients of Strings for Two Models of Upright Pianos Lagace, Melissa; Cui, Yifei

Abstract

This study seeks to find the inharmonicity coefficients (B values), or the coefficients determining how much an overtone deviates from an integer multiple of the fundamental frequency, for the strings of a Kimball 4274 upright piano and a Yamaha U30BL upright piano. B values were found for notes A and D# from the 0th to 7th octave. B values were found through frequency analysis done by Audacity, fitting the measured harmonic frequencies to the equation for harmonic frequency derived from the harmonic number and fundamental frequency. B value trends for both data sets were analyzed and explanations were proposed. Theoretical B values based on approximate string tension, radius, length, and Young’s Modulus were found for each corresponding string and compared to the actual B values. The B value data sets for the two piano models were also compared and provided in full. Inharmonicity coefficients were studied due to the implications of inharmonicity in piano tuning.

Item Metadata

Title
Finding the Inharmonicity Coefficients of Strings for Two Models of Upright Pianos
Creator
Lagace, Melissa; Cui, Yifei
Date Issued
2021-06-23
Description
This study seeks to find the inharmonicity coefficients (B values), or the coefficients determining how much an overtone deviates from an integer multiple of the fundamental frequency, for the strings of a Kimball 4274 upright piano and a Yamaha U30BL upright piano. B values were found for notes A and D# from the 0th to 7th octave. B values were found through frequency analysis done by Audacity, fitting the measured harmonic frequencies to the equation for harmonic frequency derived from the harmonic number and fundamental frequency. B value trends for both data sets were analyzed and explanations were proposed. Theoretical B values based on approximate string tension, radius, length, and Young’s Modulus were found for each corresponding string and compared to the actual B values. The B value data sets for the two piano models were also compared and provided in full. Inharmonicity coefficients were studied due to the implications of inharmonicity in piano tuning.
Genre
Report
Type
Text
Language
eng
Series
University of British Columbia. Science One Research Projects; University of British Columbia. SCIE 001
Date Available
2021-06-25
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0398548
URI
http://hdl.handle.net/2429/78807
Affiliation
Science, Faculty of
Peer Review Status
Unreviewed
Scholarly Level
Undergraduate
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribution-NonCommercial-NoDerivatives 4.0 International