Figure 1.
The hypopharynx cavities in the Vocal Tract.
Vocal Tract profile superimposed on an MRI midsagittal slice of a singer while phonating on the vowel as in the word /stːn/ and on a 3/4, details of the hypopharynx cavities which consist of the laryngeal vestibule, the laryngeal ventricles and the two piriform fossae, located posteriorly at the bottom of the pharynx.
Figure 2.
Singers from different voice categories.
Scaled Vocal Tracts of 3 professional singers: from left to right, a Bass-Baritone (Barnaby), a Bari-Tenor (Bartholomew), and a Mezzo-Soprano (Maristela).
Table 1.
Singers' data.
Figure 3.
Overview of the experimental method.
An Exponential Sine Sweep () is given as an input signal to the driver (1). The output recorded via a probe microphone is convolved with the inverse filter (
) (2). It results in a temporal separation of the Linear Impulse Response (LIR) and the harmonic distortions (3). An FFT is performed on the LIR to give the linear transfer function of the system (4). Processes 1 to 4 are repeated twice: once with the Vocal Tract, and once without. Both spectra are then subtracted (logarithmic vertical scale) to give the transfer function of the standalone Vocal Tract.
Figure 4.
Pre- and post-envelope applied to the Exponential Sine Sweep ().
An Exponential Sine Sweep () of the form (1) has a burst of energy across the whole spectrum both at its start and at its end (A1). Once convolved with its inverse filter (A2), it leads to an impulse response and its echoes in the frequency-time space (A3). Providing a smooth start to the (
) (B1), and convolving it with its inverse filter (B2) removes the pre-ringing (B3). Providing the (
) with both a smooth start and a smooth end (C1), and convolving it with its inverse filter (C2) removes both the pre- and the post-ringing (C3).
Figure 5.
Tube resonances (theoretical predictions, numerical results, experimental measurements).
The resonances of a cylinder closed at one end and opened at the other end are given as theoretical predictions (red triangles and dashed lines), numerical simulations (in black) and experimental measurements (in grey).
Figure 6.
Numerical versus Experimental.
Measured (in red) and simulated (in red) transfer functions of MRI-based Vocal Tracts of Barnaby singing on the vowels as in /pːt/, /fuːd/ and /st
ːn/.
Table 2.
Formant frequencies: simulation versus experimental.
Figure 7.
Experimental measurements of the spectral effect of the piriform fossae.
Experimental measurements of MRI-based 3D-printed VT of Barnaby, singing on the vowels as in /fuːd/ (A) and /niːp/ with (greyscale) and without left (red) or right (blue) piriform fossa.
Figure 8.
Numerical results of the spectral effect of the piriform fossae.
Numerical results of MRI-based VTs with (greyscale) and without (green) piriform fossae for Maristela (A), Bartholomew (B) singing on the vowel as in /hαːd/ and Barnaby singing on the vowels as in /hαːd/ (C), /fuːd/ (D), /pːt/ (E), /niːp/ (F) and /st
ːn/ (G). The green arrow indicates the first resonance of the fossae predicted by (16), which relates to the average length of the fossae as measured on the MRI-based VT.
Table 3.
Vocal Tract and piriform fossae dimensions.
Figure 9.
Listening test - perceptual effect of the piriform fossae.
Listening test to assess perceptually the spectral effect of appending the piriform fossae to the main tract. 10 expert listeners were asked to choose between each pair of sound which one they were qualifying as a “resonant voice” [21]. The vertical bars represent the number of positive answers (up to 10) for the sound sample with (blue) and without (red) piriform fossae respectively. The volume of the piriform fossae is plotted in black. B stands for Barnaby, BT for Bartholomew and MS for Maristela.