New Evidence That Nonlinear Source-Filter Coupling Affects Harmonic Intensity and fo Stability During Instances of Harmonics Crossing Formants

Abstract

The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths.

Keywords: formant; nonlinearity; pitch instability; source-filter theory; voice registration.

FIGURE 1

Source-filter conceptualization: (upper) non-interaction source filter concept; (lower) two levels of source filter interaction.

FIGURE 2

Spectrogram of a subject producing a glide through a tube 5 cm in length. Formants one, two, and three are identified on the left. Pitch instabilities are shown with vertical arrows where 4f_o≈F₂ and where f_o≈F₁.

FIGURE 3

Rendering of mouthpiece, tube, and microphone apparatus.

FIGURE 4

(a) Derivative of the rate of f_o change during a f_o glide with a best fit polynomial, (b) derivative of f_o change with thresholding applied, (c) derivative with thresholding and regions where harmonics ≈ formants identified.

Figure 5

Harmonic intensity contours before (above) and after (below) drift correction for f_o, plotted against frequency (a).

FIGURE 6

Harmonic intensity contours for computer simulated f_o glide plotted against frequency. Grey bars indicate 50 Hz windows, in which f_o and 2f_o are in the vicinity of F₁ (508 Hz) and F₂ (1,448 Hz).

FIGURE 7

Harmonic intensity contours for human-produced f₀ glide plotted against frequency (a) and time (b) with inherent vocal tract interactions.