Bowing forces stiff-string partials into perfect harmonic alignment through phase-locked entrainment

Evidence

As if this were not miracle enough, the bow has another issue to contend with. When a violin string is plucked and the decaying sound recorded, a power spectrum analysis reveals that the partials are not quite evenly spaced. The finite thickness of the string makes it stiff against higher curvature, sharpening the higher partials. Yet when a properly resined bow is moving across the string steadily, a perfectly periodic tone results. The power spectrum must therefore consist of perfectly evenly spaced partials. Apparently, the errant sharp upper partials have been reined in and forced to vibrate at a lower frequency than they want to. This is not an obvious result—one could imagine that all the partials do their vibrating on resonance and therefore impart an aperiodic tone to the bridge. But it is not so. If we assume that some periodic stick-slip will exist; then some modes will be driven slightly off resonance. We know off-resonant driving results in motion at the drive frequency. But the entrainment is more amazing in that the partials are phase-locked. Without phase-locking, the sawtooth shape and organized stick-slip would be lost. — Eric J. Heller, Why You Hear What You Hear- An…, 1760

Categorization

• DEFINE: Explains entrainment and phase-locking as mechanisms by which bowed strings produce perfectly periodic tones despite the string’s stiffness rounding partials upward.
• XREF: Connects to the trumpet mouthpiece resonance discussion in figure 16.13 referenced in the chapter, and to the Helmholtz wave drive mechanism.