subharmonic: one construct, many systems

In voice acoustics, subharmonics appear when the vocal folds lock into a period-doubled (or period-tripled) vibration, adding spectral components at f0/2, f0/3 and producing the rough, doubled quality called diplophonia. Herzel, Berry, and Titze (1995), in Chaos, modeled these as bifurcations in the nonlinear dynamics of the folds. The same period-doubling route to subharmonics occurs in driven mechanical oscillators, so the two meanings are one phenomenon.[1]

Unit

One subharmonic component (e.g., f0/2) in a voice signal

Recovery means

Spot spectral lines below the fundamental, or a doubled period in the waveform, during phonation.

Measured by

Narrowband spectrography and nonlinear time-series analysis of the acoustic/EGG signal.

In nonlinear dynamics, subharmonic resonance is the response of a nonlinear oscillator at a frequency that is a submultiple (ω/n) of the driving frequency, a hallmark of the period-doubling cascade. Shen, Li, and Yang (2020), in Nonlinear Dynamics, analyze primary and subharmonic resonance of a Duffing oscillator. This is the same bifurcation structure that generates vocal subharmonics, described in the abstract system rather than the larynx.[2]

Unit

One subharmonic response branch at ω/n

Recovery means

Drive a nonlinear oscillator and detect a stable response at a submultiple of the forcing frequency.

Measured by

Frequency-response and bifurcation analysis (e.g., averaging/perturbation methods, Poincaré maps).