Piano strings are audibly inharmonic due to stiffness [212,211]. General stiff-string modeling was introduced in §6.9. 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.10.17