Bending stiffness makes bar vibrations dispersive and inharmonic.

Evidence

An example of transversal waves that resemble string behaviour but which are not purely one-dimensional and harmonic in spectral content is wave propagation in a bar. Due to bending stiffness, the transversal waves are dispersive, implying that different frequencies propagate at different velocities (higher frequencies propagate faster than lower ones). This results in modal frequencies that do not have a harmonic relationship. Figure 2.14a illustrates the lowest modes in a free bar and Figure 2.14b the case where the bar is clamped at one end. The resulting sounds are strongly inharmonic. Some degree of inharmonicity can also be found in string instruments, especially in the piano at low frequencies, due to the stiffness of the strings. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 248

Categorization

• XREF: Explains the characteristic inharmonic timbre of marimbas, xylophones, and gamelan metallophones; connects to the physics underlying these sounds. — connects to: A vibrating bar’s higher modes fall outside the musical scale and harmonic spacing. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1309
• CANDY: That piano strings are slightly inharmonic because of stiffness is a neat bar-trivia fact.