Acoustical Theory of Vowel Modification Strategies in Belting

Christian T. Herbst; Brad H. Story; David Meyer

doi:10.1016/j.jvoice.2023.01.004

Acoustical Theory of Vowel Modification Strategies in Belting

Christian T. Herbst, Brad H. Story, David Meyer

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English (US)
Journal	Journal of Voice
DOIs	https://doi.org/10.1016/j.jvoice.2023.01.004
State	Accepted/In press - 2023

Keywords

Belt
Broadway
CCM
Formant tuning
Formants vs. resonances
Resonance tuning
Singing
Source filter theory

ASJC Scopus subject areas

Otorhinolaryngology
Speech and Hearing
LPN and LVN

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10.1016/j.jvoice.2023.01.004

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@article{76d5675980e24903897eb9adb09c611d,

title = "Acoustical Theory of Vowel Modification Strategies in Belting",

abstract = "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.",

keywords = "Belt, Broadway, CCM, Formant tuning, Formants vs. resonances, Resonance tuning, Singing, Source filter theory",

author = "Herbst, {Christian T.} and Story, {Brad H.} and David Meyer",

note = "Funding Information: The authors acknowledge a research grant received from Land Salzburg (to CTH). Partial funding for this study was provided by a Galileo Circle Fellows grant from the College of Science at the University of Arizona (to BHS). Author contributions: CTH conceptualized and designed the study, performed all analyses, created the graphs, and wrote the initial version of the manuscript. BHS created the vocal tract transfer functions in silico and contributed to the interpretation of the data material. DM contributed to the formulation of the overarching research goal and to the interpretation of the data material. All authors contributed to writing the final version of the manuscript. The authors would like to thank Emily Castleton for her thought-provoking conversations about “belt” and for her rich pedagogical insights. As with any style of singing, belting requires the production of sustained vowels at the fundamental frequency (fo), of the musical pitch to be sung. The fundamental production phenomenon is described by the source-filter theory. 50 In short, the aerodynamic energy of a steady air stream, coming from the lungs, is converted into cyclically varying flow pulses by fluid- structure interaction with the vibrating laryngeal tissue (typically the vocal folds). This sets up a series of pressure pulses at the level of the larynx, constituting the voice source sound. In periodic phonation, which makes up most of singing, a harmonic series emerges. Typically, the fundamental (i.e. the first harmonic) is the strongest, and the higher order harmonics – occurring at frequencies that are integer multiples of fo – have monotonically decreasing amplitudes, i.e. the higher the harmonic number (and thus the respective harmonic's frequency), the smaller its amplitude will typically be. Owing to this characteristic, the spectral composition of the voice source can thus be described by its (spectral) slope, indicated in negative deciBels per octave [dB/oct]. The voice source spectral slope typically varies in the range of -6 dB/oct (for strong, “brassy” voice source) to -18 dB/oct (for weak, “fluty”) voice sources 28,29,42–44 – see Figure 3, panels I.a, II.a, and III.a, for examples. The harmonics of the voice source are filtered by the supraglottic vocal tract, whose resonance structure introduces a frequency-dependent amplitude scaling, and potentially sets up a feedback loop to the source, 51,52 resulting in so-called level 1 or level 2 interactions 53 that may affect the characteristics of the glottal flow pulse (level 1 interaction) and/or the periodicity and fo of the voice source (level 2 interaction). Finally, radiation from the mouth introduces a high-pass filter, giving a boost of 6 dB/oct to high-frequency harmonics. 54, p.128 The spectrum of the radiated voice sound typically shows local maxima (spectral peaks) around the frequencies where the vocal tract resonances are found. Those spectral peaks in the radiated acoustic signal are termed “formants.”, For the discussion presented here, it is important to conceptually distinguish resonances (physical properties of the vocal tract) and formants (features of the radiated sound). For low-pitched phonation the frequencies of individual formants and resonances are approximately equal, due to close spacing of harmonics from the voice source. However, there is an increasing discrepancy between formants and vocal tract resonances as fo (and therefore the frequency spacing between the individual harmonics) is raised. 55,56 For this reason, this study focuses on the acoustic interaction of the voice source harmonics and the resonances of the vocal tract, rather than looking at formants (which cannot be accurately estimated above fundamental frequencies of approximately 400 Hz 55,56). Funding Information: The authors acknowledge a research grant received from Land Salzburg (to CTH). Partial funding for this study was provided by a Galileo Circle Fellows grant from the College of Science at the University of Arizona (to BHS). Publisher Copyright: {\textcopyright} 2023 The Voice Foundation",

year = "2023",

doi = "10.1016/j.jvoice.2023.01.004",

language = "English (US)",

journal = "Journal of Voice",

issn = "0892-1997",

publisher = "Mosby Inc.",

}

TY - JOUR

T1 - Acoustical Theory of Vowel Modification Strategies in Belting

AU - Herbst, Christian T.

AU - Story, Brad H.

AU - Meyer, David

N1 - Funding Information: The authors acknowledge a research grant received from Land Salzburg (to CTH). Partial funding for this study was provided by a Galileo Circle Fellows grant from the College of Science at the University of Arizona (to BHS). Author contributions: CTH conceptualized and designed the study, performed all analyses, created the graphs, and wrote the initial version of the manuscript. BHS created the vocal tract transfer functions in silico and contributed to the interpretation of the data material. DM contributed to the formulation of the overarching research goal and to the interpretation of the data material. All authors contributed to writing the final version of the manuscript. The authors would like to thank Emily Castleton for her thought-provoking conversations about “belt” and for her rich pedagogical insights. As with any style of singing, belting requires the production of sustained vowels at the fundamental frequency (fo), of the musical pitch to be sung. The fundamental production phenomenon is described by the source-filter theory. 50 In short, the aerodynamic energy of a steady air stream, coming from the lungs, is converted into cyclically varying flow pulses by fluid- structure interaction with the vibrating laryngeal tissue (typically the vocal folds). This sets up a series of pressure pulses at the level of the larynx, constituting the voice source sound. In periodic phonation, which makes up most of singing, a harmonic series emerges. Typically, the fundamental (i.e. the first harmonic) is the strongest, and the higher order harmonics – occurring at frequencies that are integer multiples of fo – have monotonically decreasing amplitudes, i.e. the higher the harmonic number (and thus the respective harmonic's frequency), the smaller its amplitude will typically be. Owing to this characteristic, the spectral composition of the voice source can thus be described by its (spectral) slope, indicated in negative deciBels per octave [dB/oct]. The voice source spectral slope typically varies in the range of -6 dB/oct (for strong, “brassy” voice source) to -18 dB/oct (for weak, “fluty”) voice sources 28,29,42–44 – see Figure 3, panels I.a, II.a, and III.a, for examples. The harmonics of the voice source are filtered by the supraglottic vocal tract, whose resonance structure introduces a frequency-dependent amplitude scaling, and potentially sets up a feedback loop to the source, 51,52 resulting in so-called level 1 or level 2 interactions 53 that may affect the characteristics of the glottal flow pulse (level 1 interaction) and/or the periodicity and fo of the voice source (level 2 interaction). Finally, radiation from the mouth introduces a high-pass filter, giving a boost of 6 dB/oct to high-frequency harmonics. 54, p.128 The spectrum of the radiated voice sound typically shows local maxima (spectral peaks) around the frequencies where the vocal tract resonances are found. Those spectral peaks in the radiated acoustic signal are termed “formants.”, For the discussion presented here, it is important to conceptually distinguish resonances (physical properties of the vocal tract) and formants (features of the radiated sound). For low-pitched phonation the frequencies of individual formants and resonances are approximately equal, due to close spacing of harmonics from the voice source. However, there is an increasing discrepancy between formants and vocal tract resonances as fo (and therefore the frequency spacing between the individual harmonics) is raised. 55,56 For this reason, this study focuses on the acoustic interaction of the voice source harmonics and the resonances of the vocal tract, rather than looking at formants (which cannot be accurately estimated above fundamental frequencies of approximately 400 Hz 55,56). Funding Information: The authors acknowledge a research grant received from Land Salzburg (to CTH). Partial funding for this study was provided by a Galileo Circle Fellows grant from the College of Science at the University of Arizona (to BHS). Publisher Copyright: © 2023 The Voice Foundation

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Belt

KW - Broadway

KW - CCM

KW - Formant tuning

KW - Formants vs. resonances

KW - Resonance tuning

KW - Singing

KW - Source filter theory

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U2 - 10.1016/j.jvoice.2023.01.004

DO - 10.1016/j.jvoice.2023.01.004

M3 - Article

SN - 0892-1997

JO - Journal of Voice

JF - Journal of Voice

ER -

Acoustical Theory of Vowel Modification Strategies in Belting

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