The Piano String

Piano strings are audibly stiff [216,215]. Generic stiff-string modeling was introduced in §4.8. In this section, we discuss further details specific to piano strings.

The main effect of string stiffness is to stretch the partial overtone series, so that piano tones are not precisely harmonic. As a result, piano tuners typically stretch the tuning of the piano slightly. For example, the total amount of tuning stretch from the lowest to highest note has been measured to be approximately 35 cents on a Kurzweil PC88, 45 cents on a Steinway Model M, and 60 cents on a Steinway Model D.^6.1

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Subsections

• Wave Equation
• Stiff-String Dispersion Filter Design

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.