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 ($f_{R1}\approx 2f_o$). 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 $f_o\approx 0.5f_{R1}$. 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 $f_{R1}\approx 2f_o$ 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.