Modeling source-filter interaction in belting and high-pitched operatic male singing

Abstract

Nonlinear source-filter theory is applied to explain some acoustic differences between two contrasting male singing productions at high pitches: operatic style versus jazz belt or theater belt. Several stylized vocal tract shapes (caricatures) are discussed that form the bases of these styles. It is hypothesized that operatic singing uses vowels that are modified toward an inverted megaphone mouth shape for transitioning into the high-pitch range. This allows all the harmonics except the fundamental to be "lifted" over the first formant. Belting, on the other hand, uses vowels that are consistently modified toward the megaphone (trumpet-like) mouth shape. Both the fundamental and the second harmonic are then kept below the first formant. The vocal tract shapes provide collective reinforcement to multiple harmonics in the form of inertive supraglottal reactance and compliant subglottal reactance. Examples of lip openings from four well-known artists are used to infer vocal tract area functions and the corresponding reactances.

Figure 1

Diagram of vocal folds and lower vocal tract to illustrate source-filter interaction.

Figure 2

Glottal impedances for different phonatory control (clear bars), and characteristic vocal tract input impedance Z_c (cross hatched bars) for different cross sectional areas A_e of the epilarynx tube.

Figure 3

(a) Vocal tract caricatures and (b) corresponding input impedances as a function of frequency; thick lines are reactances and thin lines are resistances.

Figure 4

Computer simulation of glottal airflow with a self-sustained oscillation vocal fold model that interacts with three uniform tubes as shown in the top graph.

Figure 5

Computer simulations of glottal airflow (bottom three panels) with a self-sustained oscillation vocal fold model that interacts with a neutral tube and three epilarynx areas A_e.

Figure 6

Six tube shapes (left) and their corresponding inertograms (right).

Figure 7

Normalized maximum flow declination rate (MFDR_n) for the six simulations of Figs. 45.

Figure 8

(Left) Vocal tract shapes derived from MRI data of a lyric baritone singer with various shape modifications, and (b) corresponding inertograms.

Figure 9

(a) Mouth area and head area for Luciano Pavarotti singing A₄ on an ∕ɔ∕ vowel. (b) Corresponding frequency spectrum. (c) Mouth area and head area for Cab Calloway singing A₄ on an ∕a∕ vowel, and (d) corresponding frequency spectrum.

Figure 10

(a) Mouth area and head area for Roberto Alagna singing A₄ on an ∕ɔ∕ vowel. (b) Corresponding frequency spectrum. (c) Mouth area and head area for Tony Vincent singing A-flat₄ on an ∕a∕ vowel, and (d) corresponding frequency spectrum.