Figure 3. The elastic property involved in the vibration of bars is usually stated in terms of Young's Modulus. Bar Vibrational Modes
It is not intuitive to work with such configurations. Since density and elasticity of the material are relevant data, necessary for frequency calculations of vibrational modes, it can be hard for the common instrument builder, sound sculptor, or amateur explorer to predict the pitch of a clamped shape.30 This can be said for modelling any complex physical phenomena, but the non-harmonic behaviour of clamped shapes makes it even less intuitive. This is a significant reason that the Baschets relied on empirical trial and error methods, observing the results of various configurations of a specific material rather than attempting to calculate in advance.
Physics (formulas and calculations) can predict the first few partials for a clamped rod with regular prismatic geometry, but it is harder to predict the ratios of the partials above the third and fourth overtones. The difficulty of predicting higher partial ratios is even greater when the shape is not a uniform cylindrical rod. In most cases we are able to hear more than just the first few overtones, and so these calculations would be useful for predicting the resultant sound.
Our perception of all those overtones provides us with timbral information and provides a wide range of tonal perceptions (from clearly tonal to noise with no perceptible pitch), depending on the envelope of each overtone and the relationship of their frequencies.31
It is remarkable that many of the sound devices we have presented here feature lengths that create infrasonic frequencies (lower than 20Hz or close to the 50Hz but too weak to be heard), so the sounds we hear are actually only the higher overtones that appear in our hearing range. When we hear the upper partials without the fundamental, their ratios can be quite different than we would expect, resulting in unique timbres and distinctive cluster tones.32 That implies that a single rod can produce several kinds of sounds, not just high or low, but monodic, polyphonic, atonal, or “clustery,” depending on its length. Bart Hopkin demonstrates these phenomena with bright and accurate terms with his sliding rod, What a Shame, in this part of his lecture demonstration "Exploring the Science of Sound with Invented Musical Instruments."