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.