Cosi Fan Tutte and What
Nonlinear Source-Tract Acoustic interaction in the Soprano Voice and Some Implications for the Definition of Vocal Efficiency
Implications for the Soprano Voice
We have shown that a significant reduction in average air flow can result from proper F1 tuning, given a non nasalized production with a complete vocal fold closure for some appreciable portion of the glottal cycle and assuming that the proper vocal fold vibratory pattern can be maintained under these conditions. This conclusion is supported not only by Sundberg's (1975) formant measurements and Schutte and Miller's measurements of supraglottal and transglottal pressure, but also by the strong feeling held by at least two sopranos I have talked to (based on their introspection) that average air flow can be affected significantly by vocal tract posture. For example, one of these singers (Jo Estill) shared with me her intuition of an increased air flow during nasalized vowels. This could be due to an increase in the damping of F1 and a resultant decrease in the nonlinear, interactive effect.
Our model also indicates that, if in addition to these conditions the glottal duty cycle is in the proper range, the reduced air flow due to vocal tract tuning can be accompanied by a strong, harmonic-rich tone. From the qualitative analysis sketched earlier, the optimal duty cycle or open quotient required for the production of strong higher harmonics, as controlled primarily by the degree of vocal fold adduction, is somewhat greater than 50 percent. With the open quotient greater than 50 percent, transglottal pressure increases at the onset and termination of the glottal pulse. This increased pressure will cause a more abrupt onset and offset of glottal air flow and, therefore, somewhat stronger higher harmonics. Open quotients much greater than 50 percent, though theoretically producing a harmonic-rich tone, may not result in a complete glottal closure and thus violate the assumptions of the model. This duty cycle requirement appears to be different than the requirement in modal voice, in which the strength of the higher harmonics tends to increase monotonically with a decrease in open quotient for a given level of average air flow. However, a better specification is required of the effect of glottal duty cycle in the soprano voice and its relation to the optimal vocal tract tuning.
Aside from the optimization of the duty cycle and an essentially complete glottal closure, the details of the waveform of projected glottal area do not appear to be important.
In examining our analysis for possible implications related to vocal abuse, it should be noted that our model indicates the importance of a fairly complete glottal closure during the closed phase of the glottal cycle for an efficient soprano singing voice. Conversely, it is possible that if a singer on a particular day cannot , produce the essentially complete vocal fold closure required for a strong interactive effect, she may experience an excessively high air flow and a resulting increased risk of vocal abuse. Any attempt to compensate by the use of increased vocal fold adduction to reduce air flow might bring its own risk of vocal abuse through fatigue of the adductory musculature, as well as a possibly unacceptable tonal balance due to too small an open quotient.
Since the model described indicates that, for a given Fo, small changes in the frequency or damping of the first formant, or in the degree of vocal fold adduction, can greatly affect the relative strength of all the harmonics of Fo, these factors can conceivably have a significant effect on vowel quality and perceived vowel identity. The possible sensitivity of vowel identity to these factors is not predicted by a linear model nor, apparently, is it present in male singing.
Another tentative conclusion for the soprano voice might be that nasalized vowels or notes at lower pitches may require a technique other than supraglottal vocal tract tuning to reduce the average air flow during the open glottal phase while maintaining a high SPL. The inertive acoustic loading mechanism apparently used by the bass or baritone singer is one candidate for such a mechanism.