The frequency of the first vocal tract resonance, as a function of the pitch frequency, for the four vowels indicated.	Soprano Kristen Butchatsky with the sound source and microphone at her mouth.

In singing or speech, periodic vibrations of the vocal folds produce a sound rich in harmonics, whose frequency determines the pitch. The vocal tract acts like a variable megaphone, one of whose roles is to match the acoustic impedance between the lower vocal tract (high impedance) and the radiation field (low). It does this most effectively at the resonances of the tract, so the harmonics falling near those resonances are boosted. The frequencies of the resonances depend on the mouth shape and tongue position and we can distinguish vowel sounds and other details of the voice from hearing which harmonics get boosted.

Normally, these processes are independent: we can sing “la la la la la” on different notes (constant resonances with varying pitch), and the monotone Daleks on Dr Who can be understood (“Ex-ter-min-ate”: varying resonances at constant pitch). However, there is a problem in the high range of women’s voices, because the pitch frequency of the notes enters the range of the lowest vocal tract resonance. If the singers did nothing about this problem, then notes would be louder or softer depending on how well the pitch coincided with a resonance in the tract and the voice quality would be uneven. It has been suspected that sopranos actually tune the resonance of their vocal tract to the note that they are singing: the evidence for this is that they tend to open the mouth wider as they sing successively higher notes. However, this could not previously be confirmed because there was no way to measure the acoustics of the tract while it was being used for singing. The technique developed recently by our Acoustics Laboratory does this by injecting a carefully synthesised broad band acoustic current into the mouth and measuring simultaneously the voice and the response of the tract to this signal.

In the low range of the voice, sopranos do just what we all do in speech and singing: the pitch and the vocal tract resonances are largely independent. In the high range, however, they tune the lowest resonance of the vocal tract to match the pitch they are singing.

This resonance tuning gives them uniform loudness and vocal quality, but it also means that vowel sounds become very similar. However, the amount of intelligibility sacrificed is not great. In the high range, it is very difficult to understand vowel sounds anyway, because of the wide spacing of harmonics. Berlioz’ famous treatise on orchestration warns opera composers about the high pitch problem. And it is possibly one of the reasons why the opera house uses surtitles even when the words are in the language of the audience.

Sound files illustrating the effect are at http://www.phys.unsw.edu.au/~jw/soprane.html

Elodie Joliveau, John Smith and Joe Wolfe