The Source-Filter Theory of Vowels
Although voice production does not specifically deal with speech articulation, all human vocalizations require some configuration of the vocal tract. Unless a vocalist is deliberately humming or hissing, the configuration is usually an open tract, as in a vowel. Vowel formation is therefore an integral part of the phonation process and needs to be discussed in detail.
Overview
The acoustic properties of vowels have traditionally been described on the basis of a source-filter theory (Fant, 1960). In this theory, the sound source is the time-varying glottal airflow and the filter is the vocal tract. Whereas the glottis produces a sound of many frequencies, the vocal tract selects (filters) a subset of these frequencies for radiation from the mouth.
This chapter introduces the source-filter theory with tools of analysis developed in previous chapters. We revisit the principle of resonance, introduced in Chapter 4 with regard to vocal fold vibration and aerodynamic driving forces. This time resonance is applied to the interference of acoustic waves traveling in opposite directions.
What You’ll Learn
Acoustic Fundamentals
- Sound propagation in tubes: How acoustic waves behave in confined spaces
- Acoustic impedance: The relationship between pressure and flow in tubes
- Wave reflection: How area changes create reflections and standing waves
- Resonance frequencies: The natural frequencies of the vocal tract
Vowel Acoustics
- Formants: The resonance frequencies that characterize vowels
- F₁-F₂ vowel space: How the first two formants define vowel categories
- Articulatory-acoustic relationships: How tongue position affects formant frequencies
- Tube models: Simplified approximations of vocal tract shapes
Analysis Tools
- Fourier transformation: Converting time-domain signals to frequency spectra
- Filters and filtering: How the vocal tract selectively amplifies frequencies
- Spectrographic analysis: Visual representation of vowel spectra
- Formant bandwidth: The effect of energy loss on resonance peaks
Practical Applications
- Vowel modification: Rules for changing formant frequencies through articulation
- Vocal tract adjustments: Effects of larynx height, lip rounding, and jaw position
- Vowel focus: The relationship between acoustic pressure patterns and sensations
- Clinical and pedagogical implications: Applications for voice training and therapy
Theoretical Foundation
The source-filter theory provides a powerful framework for understanding how the same sound source (the vibrating vocal folds) can produce many different vowel qualities simply by changing the shape of the vocal tract. This theory explains:
- Why vowels have characteristic formant patterns
- How singers and speakers modify vowels for different acoustic effects
- Why certain vowel modifications increase vocal power or change tone quality
- How spectral analysis can reveal information about vocal tract configuration
Connections to Previous Material
This chapter builds directly on concepts from earlier chapters. The acoustic wave propagation discussed in Chapter 5 is now applied to confined spaces (tubes). The principle of resonance from Chapter 4, previously used to understand vocal fold vibration, is now applied to the air column of the vocal tract. The glottal airflow waveform and its spectrum, introduced in Chapter 5, becomes the “source” in the source-filter framework.
This chapter provides essential knowledge for understanding how vocal tract shape determines vowel quality, a fundamental concept in voice pedagogy, speech therapy, and vocal performance.
Check Your Understanding
Five short questions on how the vocal tract shapes vowels. Each one explains itself as soon as you answer, so treat them as a way to test your reasoning rather than a test to pass.
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This reverses the roles of source and filter. Harmonic frequencies are fixed by the source (multiples of F₀); they cannot move unless the pitch does. It is the envelope—the filter—that changes with the vowel.
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Output spectrum = source spectrum × filter function (a sum in dB). The glottal source supplies a line spectrum at multiples of F₀ that does not depend on the vowel; the vocal tract supplies a formant envelope that does. For [ə] the 5th, 15th and 25th harmonics sit near the formants; for [i] the 3rd, 23rd and 30th do. Same lines, different envelope—that is the source–filter theory in one example.
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Only the filter changed. Vowels are produced by reshaping the vocal tract while the source keeps vibrating at the same rate, so the harmonic lines are unchanged and only the formant envelope that selects among them moves.
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Articulation is how the spectrum is changed. Moving the tongue forward and up creates an oral constriction that lowers F₁ and raises F₂, and the output spectrum's envelope shifts accordingly— which is why the two vowels sound different.
Rule 1: all formant frequencies decrease uniformly as vocal tract length increases—roughly a 10% drop for a 10% lengthening. Longer resonators sound lower, whether organ pipes or pharynxes.
Choose an answer for this row, then check again.
In the two-tube model a narrow pharynx below a wide mouth shortens the acoustic length for F₁ (raising it to 700–900 Hz) and lengthens it for F₂ (lowering it to 1000–1300 Hz). The formants move toward each other—spectral compacting.
Choose an answer for this row, then check again.
A wide pharynx behind a narrow mouth does the opposite: F₁ falls to about 250–350 Hz and F₂ rises to 2200–2500 Hz. The formants spread apart—spectral diffusion.
Choose an answer for this row, then check again.
Rule 3: jaw lowering raises F₁ substantially by enlarging the mouth opening and shortening the effective acoustic length for the first formant. This is the adjustment sopranos use to bring F₁ up to a high F₀.
Choose an answer for this row, then check again.
Rule 2: lip spreading raises all formants (rounding lowers them). A flared opening reduces pressure at the lips and shortens the effective acoustic length.
Choose an answer for this row, then check again.
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A low, back configuration gives a high F₁ (700–900 Hz) and a low F₂ (1000–1300 Hz): compact formants. Here F₁ is very low and F₂ very high—the opposite pattern.
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[u] shares the low F₁ of a high vowel, but its back constriction and rounded lips pull F₂ down to about 700–900 Hz. An F₂ of 2300 Hz rules out lip rounding and a back tongue.
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F₁ falls with tongue height, so 300 Hz indicates a high vowel; F₂ rises with tongue advancement, so 2300 Hz indicates a front constriction with a long pharynx behind it and a short oral cavity in front. Spread lips keep the formants from being lowered. This is the upper-left corner of the F₁–F₂ chart.
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The neutral tract behaves as a uniform tube with formants near 500 and 1500 Hz. Both measured values are far from those, so the tract was clearly constricted—at the front.
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When F₀ climbs above a vowel's normal F₁, the fundamental falls in a spectral valley and loses power. Sopranos respond by opening the jaw, which raises F₁ (Rule 3) until it approaches the fundamental. Output power rises at the cost of vowel identity, and every closed vowel migrates toward more open ones at the top of the range. The balance between power and intelligibility is a judgment about repertoire and venue.
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Raising the larynx shifts all formants up by only about 10% and is associated with a pressed, tight quality. It cannot move F₁ from 300 to 880 Hz, and it is not the strategy the chapter describes.
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The pitch is fixed by the score. The singer adjusts the filter to suit the source, not the other way round.
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Lip rounding lowers all formants, pushing F₁ further from a high F₀ and worsening the mismatch. The needed adjustment raises F₁, and jaw lowering is the most effective way to do that.
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This conflates two different pressures. Bernoulli's law concerns the steady flow of air through a narrowing; it is not about propagating sound waves. For the acoustic wave, the chapter's result is the opposite: pressure rises at a constriction.
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In a tube the impedance is ρc/A, so a smaller area means higher impedance. A wave entering a constriction reflects with positive polarity, and the transmitted pressure pᵢ(1 + r) exceeds the incident pressure. The chapter stresses that acoustic pressures are always higher in constricted regions, even though aerodynamic (Bernoulli) pressure is lower there. This is also why vowel "focus" is often sensed at the constriction.
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Density and sound speed are the same on both sides, but area is not—and in the vocal tract area change is by far the most important cause of reflection. The reflection coefficient reduces to (A₁ − A₂)/(A₁ + A₂) precisely because the medium is unchanged.
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Inversion with a pressure null is what happens at an expansion— ultimately at the open lips, where r ≈ −1. Entering a narrower section gives a positive reflection coefficient and no inversion.
Want more? The practice section has recall flashcards for this chapter's key terms, plus these questions one at a time.