Computer simulation of vocal tract resonance tuning strategies with respect to fundamental frequency and voice source spectral slope in singing

High and Wide: An In Silico Investigation of Frequency, Intensity, and Vibrato Effects on Widely Applied Acoustic Voice Perturbation and Noise Measures

OBJECTIVES

This in silico study explored the effects of a wide range of fundamental frequency (fo), source-spectrum tilt (SST), and vibrato extent (VE) on commonly used frequency and amplitude perturbation and noise measures.

METHOD

Using 53 synthesized tones produced in Madde, the effects of stepwise increases in fo, intensity (modeled by decreasing SST), and VE on the PRAAT parameters jitter % (local), relative average perturbation (RAP) %, shimmer % (local), amplitude perturbation quotient 3 (APQ3) %, and harmonics-to-noise ratio (HNR) dB were investigated. A secondary experiment was conducted to determine whether any fo effects on jitter, RAP, shimmer, APQ3, and HNR were stable. A total of 10 sinewaves were synthesized in Sopran from 100 to 1000 Hz using formant frequencies for /a/, /i/, and /u/-like vowels, respectively. All effects were statistically assessed with Kendall's tau-b and partial correlation.

RESULTS

Increasing fo resulted in an overall increase in jitter, RAP, shimmer, and APQ3 values, respectively (P < 0.01). Oscillations of the data across the explored fo range were observed in all measurement outputs. In the Sopran tests, the oscillatory pattern seen in the Madde fo condition remained and showed differences between vowel conditions. Increasing intensity (decreasing SST) led to reduced pitch and amplitude perturbation and HNR (P < 0.05). Increasing VE led to lower HNR and an almost linear increase of all other measures (P < 0.05).

CONCLUSION

These novel data offer a controlled demonstration for the behavior of jitter (local) %, RAP %, shimmer (local) %, APQ3 %, and HNR (dB) when varying fo, SST, and VE in synthesized tones. Since humans will vary in all of these aspects in spoken language and vowel phonation, researchers should take potential resonance-harmonics type effects into account when comparing intersubject or preintervention and postintervention data using these measures.

Acoustical Theory of Vowel Modification Strategies in Belting

Various authors have argued that belting is to be produced by "speech-like" sounds, with the first and second supraglottic vocal tract resonances (f_R1 and f_R2) at frequencies of the vowels determined by the lyrics to be sung. Acoustically, the hallmark of belting has been identified as a dominant second harmonic, possibly enhanced by first resonance tuning (f_R1≈2f_o). It is not clear how both these concepts - (a) phonating with "speech-like," unmodified vowels; and (b) producing a belting sound with a dominant second harmonic, typically enhanced by f_R1 - can be upheld when singing across a singer's entire musical pitch range. For instance, anecdotal reports from pedagogues suggest that vowels with a low f_R1, such as [i] or [u], might have to be modified considerably (by raising f_R1) in order to phonate at higher pitches. These issues were systematically addressed in silico with respect to treble singing, using a linear source-filter voice production model. The dominant harmonic of the radiated spectrum was assessed in 12987 simulations, covering a parameter space of 37 fundamental frequencies (f_o) across the musical pitch range from C3 to C6; 27 voice source spectral slope settings from -4 to -30 dB/octave; computed for 13 different IPA vowels. The results suggest that, for most unmodified vowels, the stereotypical belting sound characteristics with a dominant second harmonic can only be produced over a pitch range of about a musical fifth, centered at f_o≈0.5f_R1. In the [ɔ] and [ɑ] vowels, that range is extended to an octave, supported by a low second resonance. Data aggregation - considering the relative prevalence of vowels in American English - suggests that, historically, belting with f_R1≈2f_o was derived from speech, and that songs with an extended musical pitch range likely demand considerable vowel modification. We thus argue that - on acoustical grounds - the pedagogical commandment for belting with unmodified, "speech-like" vowels can not always be fulfilled.

Dynamic System Coupling in Voice Production

Voice is a major means of communication for humans, non-human mammals and many other vertebrates like birds and anurans. The physical and physiological principles of voice production are described by two theories: the MyoElastic-AeroDynamic (MEAD) theory and the Source-Filter Theory (SFT). While MEAD employs a multiphysics approach to understand the motor control and dynamics of self-sustained vibration of vocal folds or analogous tissues, SFT predominantly uses acoustics to understand spectral changes of the source via linear propagation through the vocal tract. Because the two theories focus on different aspects of voice production, they are often applied distinctly in specific areas of science and engineering. Here, we argue that the MEAD and the SFT are linked integral aspects of a holistic theory of voice production, describing a dynamically coupled system. The aim of this manuscript is to provide a comprehensive review of both the MEAD and the source-filter theory with its nonlinear extension, the latter of which suggests a number of conceptual similarities to sound production in brass instruments. We discuss the application of both theories to voice production of humans as well as of animals. An appraisal of voice production in the light of non-linear dynamics supports the notion that voice production can best be described with a systems view, considering coupled systems rather than isolated contributions of individual sub-systems.