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 (fR1 and fR2) 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 (fR1≈2fo). 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 fR1 - 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 fR1, such as [i] or [u], might have to be modified considerably (by raising fR1) 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 (fo) 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 fo≈0.5fR1. 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 fR1≈2fo 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.