Vocal tract resonances from broad band excitation

Vocal tract resonance measurements:

The principal use of the device is in measuring vocal tract resonances. (For the differences between resonances and formants see here.) The 'ecological' way uses a microphone and small sound source located at the lower lip. It is also possible, with suitable calibration, to use this software for measuring acoustic impedance spectra, but we concentrate here on the 'ecological' application.

An acoustic current is synthesised to give high resolution frequency information over the frequency range of interest. We first calibrate the system by making a measurement of sound pressure just outside the lips, with the mouth closed (p_closed). We then inject the same acoustic current into the vocal tract in parallel with the external field and again measure the pressure at the lips (p_open). The ratio γ = p_open/p_closed then shows the frequencies of the tract resonances.

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The vocal tract behaves is an acoustic duct about 170 mm long, nearly closed by the vocal folds and open at the mouth. A cylinder, length L, closed at one end has resonances at f₀ = v/4L , at 3f₀, 5f₀ etc, where v is the speed of sound. (See pipes and harmonics.) For such a cylinder the resonances would fall at frequencies of about 0.5, 1.5, 2.5, 3.5 and 4.5 kHz. The vocal tract shape varies as the lips and tongue are moved in speech. So here, while R1 and R4 fall close to the values for the cylinder, R2 is lower and R3 higher than for a cylinder.

Schematic diagram. (a) shows the spectrum of the speech signal alone. This male voice has harmonic partials spaced at the pitch frequency 126 Hz. (b) The injected signal has frequencies spaced at 5 Hz, whose amplitudes are calibrated (in this case) using the radiation field outside the speaker's mouth. (c) The sum of the speech signal and the broad band signal (including the effects of the resonances) goes from the microphone to the analogue-digital converter. The speech signal is used to measure pitch and amplitude; then the harmonic components below 1 kHz are removed. (d) The resonances are detected from the remaining interpolated signal. Similarly, the broadband signals may be removed to leave just the speech harmonics. In the version of the device used for speech training, the resonance frequencies were used to position the cursor on the vowel plane (see below). Notice that the signal:noise ratio in these figures is worse than in the preceding figure. This is a consequence of making the measurements rapidly.

Examples of how measurements at the lips can identify different vocal tract configurations. The measured ratios γ(f) are at right. The particpant produces seven different gestures. The schematics on the left are cartoon 1D models of the tract (not to scale and highly simplified). Notice that, for inhalation, the vocal tract and trachea are connected, which roughly doubles the length of the former. This means roughly twice as many resonances in a given frequency range. Some of the same effect is seen, for low frequencies, in breathy phonation. (Figure from Jeanneteau et al (2020) below.)

For reports of applications, see these papers

• Jeanneteau, M., Hanna, N., Almeida, A., Smith, J. and Wolfe, J. (2020) "Using visual feedback to tune the second vocal tract resonance for singing in the high soprano range", Logopedics Phoniatrics Vocology, DOI: 10.1080/14015439.2020.1834612
• Hanna, N., Smith J. and Wolfe, J. (2018) "How the acoustic resonances of the subglottal tract affect the impedance spectrum measured through the lips" J. Acoust. Soc. America, 143, 2639-2650. Copyright (2018) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article may be found at J. Acoust. Soc. America.
• Hanna, N., Smith J. and Wolfe, J. (2016) "Frequencies, bandwidths and magnitudes of vocal tract and surrounding tissue resonances, measured through the lips during phonation" J. Acoust. Soc. America, 139, 2924–2936. Copyright (2015) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article may be found at J. Acoust. Soc. America).
• Henrich Bernadoni, N., Smith, J. and Wolfe, J. (2014) "Vocal tract resonances in singing: variation with laryngeal mechanism for male operatic singers" J. Acoust. Soc. America. 135, 491-501. Copyright (2014) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article appeared in (JASA 135, 491-501) and may be found at (J. Acoust. Soc. America).
• Bourne, T. and Garnier, M. (2012) "Physiological and acoustic characteristics of the female music theater voice" J. Acoust. Soc. America. 131, 1586-1594. Copyright (2012) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article appeared in (JASA 131, 1586-1594) and may be found at (J. Acoust. Soc. America).
• Garnier, M., Henrich, N., Crevier-Buchman, L., Vincent, C., Smith, J. and Wolfe, J. (2012) "Glottal behavior in the high soprano range and the transition to the whistle register" J. Acoust. Soc. America. 131, 951-962. Copyright (2012) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article appeared in (JASA 131, 951-962) and may be found at (J. Acoust. Soc. America).
• Henrich, N., Smith, J. and Wolfe, J. (2011) "Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones" J. Acoust. Soc. America. 129, 1024-1035. Copyright (2011) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article appeared in (JASA 29, 1024-1035) and may be found at ( J. Acoust. Soc. America).
• Garnier, M., Henrich, N., Smith, J. and Wolfe, J. (2010) "Vocal tract adjustments in the high soprano range" J. Acoust. Soc. America. 127, 3771-3780. Copyright (2010) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article appeared in (JASA 127, 3771-3780) and may be found at ( J. Acoust. Soc. America).
• Swerdlin, Y., Smith, J. and Wolfe, J. (2010) "The effect of whisper and creak vocal mechanisms on vocal tract resonances" J. Acoust. Soc. America. 127, 2590-2598. Copyright (2010) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article appeared in (JASA 127, 2590-2598) and may be found at ( J. Acoust. Soc. America).
• Henrich, N., Kiek, M., Smith, J. and Wolfe, J. (2007) "Resonance strategies in Bulgarian women's singing", Logopedics Phoniatrics Vocology, 32, 171-177.
• Joliveau, E., Smith, J. and Wolfe, J. (2004) "Vocal tract resonances in singing: the soprano voice", J. Acoust. Soc. America, 116, 2434-2439.
• Joliveau, E., Smith, J. and Wolfe, J. (2004) "Tuning of vocal tract resonances by sopranos", Nature, 427, 11
• Donaldson, T., Wang, D., Smith, J. and Wolfe, J. (2003) "Vocal tract resonances: a preliminary study of sex differences for young Australians", Acoustics Australia, 31, 95-98.
• Dr Malte Kob, in Aachen, developed a system working on similar principles: Kob, M. and Neuschaefer-Rube, C. (2002) "A method for measurement of the vocal tract impedance at the mouth" Med. Eng. & Physics. 24, 467-471.
• Dowd, A., Smith, J.R. and Wolfe, J. (1998) "Learning to pronounce vowel sounds in a foreign language using acoustic measurements of the vocal tract as feedback in real time" Language and Speech, 41, 1-20.
• Epps, J., Smith, J.R. and Wolfe, J. (1997) "A novel instrument to measure acoustic resonances of the vocal tract during speech" Measurement Science and Technology 8, 1112-1121.
• J., Dowd, A., Smith, J.R. and Wolfe, J. (1997) Real time measurements of the vocal tract resonances during speech Eurospeech'97 (G. Kokkinakis, N. Fakotakis & E. Dermatas, eds.) Rhodes, 721-724.

Using the resonance measurements as visual feedback

This photo shows Noel Hanna using the system, holding the flexible tube at his bottom lip.

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A screen grab of the feedback system. The sharp vertical lines on the graphs show voice harmonics, which are displayed on the musical staves as black dots. (The 'double treble clef' is the supertreble clef, two octaves above the treble clef.) The peaks in the continuous line on the upper graph indicate the tract resonances. A description of the study using visual feedback is in this paper

Hardware, software and training

The electronic hardware includes a sound card, a microphone (very high linearity and low sensitivity), a small audio power amplifier and a horn driver. You can download the .stl file for the adaptor that matches a horn driver to the hose used as a source. (The design software we used is Blender and the 3d printer was a Cubicon plus, but this should be of little importance.) The larger end is clearance diameter for a 1" thread so that plumbing tape can be used for a good seal. The hose we use is 9.5 mm OD, 5 mm ID and about 1 m long. None of these values are expected to be critical.

The software is available for download for Mac and download for Windows. The software is in a compiled version of file written in Matlab. In principle, Matlab is not required to run it. The fig file is here but is also not needed to run the compiled version. The software may be slow to download.The software was written for a research project: it is not commercial software written by professional softward developers and it is not supported. Setting up the system, both hardware and software, requires considerable technical experience. It is not recommended as a home project.

The training used to learn R2 tuning is described in a journal paper here. Again, this is somewhat technical.

This soundfile is the note E6 sung with R2:fo tuning by a volunteer participant who has no formal singing training but who used the feedback mentioned above to learn R2:fo tuning. Using R2:fo tuning, she increased her comfortable limit from A5 to E6 (A below high C to E above).

More pages on related topics

• Introduction to the voice acoustics is written at two levels: the brief overview, followed by a more detailed account.
• An explanation and some sound files of helium speech.
• In an article in Nature, we showed how soprano singers tune the vocal tract to the note they are singing. We also show how Wagner makes it easier.
• We give an explanation of the acoustics of harmonic singing.
• What is a decibel?
• What is a sound spectrum?
• Formants: what are they? A discussion of the different meanings of this term.
• What is acoustic impedance and why is it important?