Formant
In speech science and phonetics, a formant is the broad spectral maximum that results from an acoustic resonance of the human vocal tract.[1][2] In acoustics, a formant is usually defined as a broad peak, or local maximum, in the spectrum.[3][4] For harmonic sounds, with this definition, the formant frequency is sometimes taken as that of the harmonic that is most augmented by a resonance. The difference between these two definitions resides in whether "formants" characterise the production mechanisms of a sound or the produced sound itself. In practice, the frequency of a spectral peak differs slightly from the associated resonance frequency, except when, by luck, harmonics are aligned with the resonance frequency, or when the sound source is mostly non-harmonic, as in whispering and vocal fry.
A room can be said to have formants characteristic of that particular room, due to its resonances, i.e., to the way sound reflects from its walls and objects. Room formants of this nature reinforce themselves by emphasizing specific frequencies and absorbing others, as exploited, for example, by Alvin Lucier in his piece I Am Sitting in a Room. In acoustic digital signal processing, the way a collection of formants (such as a room) affects a signal can be represented by an impulse response.
In both speech and rooms, formants are characteristic features of the resonances of the space. They are said to be excited by acoustic sources such as the voice, and they shape (filter) the sources' sounds, but they are not sources themselves.
History
From an acoustic point of view, phonetics had a serious problem with the idea that the effective length of vocal tract changed vowels.[5] Indeed, when the length of the vocal tract changes, all the acoustic resonators formed by mouth cavities are scaled, and so are their resonance frequencies. Therefore, it was unclear how vowels could depend on frequencies when talkers with different vocal tract lengths, for instance bass and soprano singers, can produce sounds that are perceived as belonging to the same phonetic category. There had to be some way to normalize the spectral information underpinning the vowel identity. Hermann suggested a solution to this problem in 1894, coining the term “formant”. A vowel, according to him, is a special acoustic phenomenon, depending on the intermittent production of a special partial, or “formant”, or “characteristique” feature. The frequency of the “formant” may vary a little without altering the character of the vowel. For “long e” (ee or iy) for example, the lowest-frequency “formant” may vary from 350 to 440 Hz even in the same person.[6]
Phonetics
Vowel (IPA) |
Formant F1 (Hz) |
Formant F2 (Hz) |
Difference F2 – F1 (Hz) |
---|---|---|---|
i | 240 | 2400 | 2160 |
y | 235 | 2100 | 1865 |
e | 390 | 2300 | 1910 |
ø | 370 | 1900 | 1530 |
ɛ | 610 | 1900 | 1290 |
œ | 585 | 1710 | 1125 |
a | 850 | 1610 | 760 |
ɶ | 820 | 1530 | 710 |
ɑ | 750 | 940 | 190 |
ɒ | 700 | 760 | 60 |
ʌ | 600 | 1170 | 570 |
ɔ | 500 | 700 | 200 |
ɤ | 460 | 1310 | 850 |
o | 360 | 640 | 280 |
ɯ | 300 | 1390 | 1090 |
u | 250 | 595 | 345 |
Formants are distinctive frequency components of the acoustic signal produced by speech, musical instruments[8] or singing. The information that humans require to distinguish between speech sounds can be represented purely quantitatively by specifying peaks in the frequency spectrum. Most of these formants are produced by tube and chamber resonance, but a few whistle tones derive from periodic collapse of Venturi effect low-pressure zones.[9]
The formant with the lowest frequency is called F1, the second F2, the third F3, and so forth. The
Nasal consonants usually have an additional formant around 2500 Hz. The liquid [l] usually has an extra formant at 1500 Hz, whereas the English "r" sound ([ɹ]) is distinguished by a very low third formant (well below 2000 Hz).
In normal voiced speech, the underlying vibration produced by the vocal folds resembles a sawtooth wave, rich in harmonic overtones. If the fundamental frequency or (more often) one of the overtones is higher than a resonance frequency of the system, then the resonance will be only weakly excited and the formant usually imparted by that resonance will be mostly lost. This is most apparent in the case of soprano opera singers, who sing at pitches high enough that their vowels become very hard to distinguish.
Control of resonances is an essential component of the vocal technique known as
Formant estimation
Formants, whether they are seen as acoustic resonances of the vocal tract, or as local maxima in the speech spectrum, like band-pass filters, are defined by their frequency and by their spectral width (bandwidth).
Different methods exist to obtain this information. Formant frequencies, in their acoustic definition, can be estimated from the
Formant plots
The first two formants are important in determining the quality of vowels, and are frequently said to correspond to the open/close (or low/high) and front/back dimensions (which have traditionally been associated with the shape and position of the tongue). Thus the first formant F1 has a higher frequency for an open or low vowel such as [a] and a lower frequency for a closed or high vowel such as [i] or [u]; and the second formant F2 has a higher frequency for a front vowel such as [i] and a lower frequency for a back vowel such as [u].[12][13]
Vowels will almost always have four or more distinguishable formants, and sometimes more than six. However, the first two formants are the most important in determining vowel quality and are often plotted against each other in vowel diagrams,[14] though this simplification fails to capture some aspects of vowel quality such as rounding.[15]
Many writers have addressed the problem of finding an optimal alignment of the positions of vowels on formant plots with those on the conventional vowel quadrilateral. The pioneering work of Ladefoged[16] used the Mel scale because this scale was claimed to correspond more closely to the auditory scale of pitch than to the acoustic measure of fundamental frequency expressed in Hertz. Two alternatives to the Mel scale are the Bark scale and the ERB-rate scale.[17] Another widely adopted strategy is plotting the difference between F1 and F2 rather than F2 on the horizontal axis.[citation needed]
Singer's formant
Studies of the frequency spectrum of trained speakers and classical
.See also
- Formant synthesis
- Human voice
- Linear predictive coding
- Praat
- Timbre
- Vocoder
References
- ISBN 978-0-13-717893-3.
- ^ Titze, I.R., Baken, R.J. Bozeman, K.W., Granqvist, S. Henrich, N., Herbst, C.T., Howard, D.M., Hunter, E.J., Kaelin, D., Kent, R.D., Löfqvist, A., McCoy, S., Miller, D.G., Noé, H., Scherer, R.C., Smith, J.R., Story, B.H., Švec, J.G., Ternström, S. and Wolfe, J. (2015) "Toward a consensus on symbolic notation of harmonics, resonances, and formants in vocalization." J. Acoust. Soc. America. 137, 3005–3007.
- ^ Jeans, J.H. (1938) Science & Music, reprinted by Dover, 1968.
- ^ Standards Secretariat, Acoustical Society of America, (1994). ANSI S1.1-1994 (R2004) American National Standard Acoustical Terminology, (12.41) Acoustical Society of America, Melville, NY.
- ^ Hermann, Ludimar (1894). Phonophotographische Untersuchungen [Phonophotographical Studies] (in German) (5th ed.).
- ^ McKendrick, J. G. (1903). Experimental phonetics. In Annual report of the board of regents of the Smithsonian institution for the year ending June 30, 1902 (pp. 241–259). Smithsonian Institution.
- ISBN 978-0198242178
- ^ Reuter, Christoph (2009): The role of formant positions and micro-modulations in blending and partial masking of musical instruments. In: Journal of the Acoustical Society of America (JASA), Vol. 126,4, p. 2237
- ISBN 978-3-662-01564-3.
- ISBN 978-0-230-22455-1.
- .
- ISBN 1-4130-2079-8
- ISBN 0-631-21412-7
- ^ Deterding, David (1997) 'The Formants of Monophthong Vowels in Standard Southern British English Pronunciation', Journal of the International Phonetic Association, 27, pp. 47–55.
- ISBN 0-582-29137-2
- ^ Ladefoged, P. (1967). Three Areas of Experimental Phonetics. Oxford. p. 87.
- ISBN 0-582-29137-2.
- ^ Sundberg, J. (1974). "Articulatory interpretation of the 'singing formant'", Journal of the Acoustical Society of America, 55, 838–844.
- PMID 16325374.
- ISBN 978-0-8283-2181-5.
- ISBN 0-87580-542-6.
External links
- Formants for fun and profit
- Formants and wah-wah pedals
- What is a formant? A discussion of the three different meanings of the word 'formant'
- Formant tuning by soprano singers from the University of New South Wales
- The acoustics of harmonic or overtone singing from the University of New South Wales
- Materials for measuring and plotting vowel formants