vocal tract acoustics The vocal tract is an air-filled cavity of a very complex form. for a male who is a 180 cm tall, the vocal tract ,from the vocal folds to the lips will have a length of of about 17 cm ( figura 7.2) . such a cavity may be considered as a three-dimensional boody of air, which will have a set of resonance frequencies defined by the form and size of the cavity. the relationship between the resonance frequencies and the form and size of the cavity is rather complex. the whole resonatory system is responsible for all the resonance frequencies; that is , no specific part of the vocal tract is responsible for specific resonance features a simple explanation of the relationship between the vocal tract and resonance is gives in the vowel ( chiba y kajiyama 1958) the vocal tract is considered as a uniform pipe, 17 cm long with a constant cross-sectional area, closed at the lower end ( at the glottis) and open at the upper end ( at the lips) . it is shown that such a tube will resonate at 500 hz. 1500 hz , 2500 hz, 3500 hz, 4500 hx and so on that is at all frequencies where the lengt of the tube equals uneven multiples of a 1/ 4 wavelength of the resonance frequency. this corresponds fairly well to the neutral vowel /e/ which has energy maxima at approximately 500 , 1500 , 3500 and 3500 hz. But during speech the vocal tract does not behave like a uniform pipe because its form and size , evem its length change the whole time, therefore the resonance frequencies are changed , too to put it very shematically , when the cross - sectional area of the front part of the tube increases and / or the back part of the tube decreases, the lowest resonance frequency is increased ; when a constriction in the front part of the tube is pushed backwards, the second resonance is lowered; when the entrance of the tube is narrowed , the second and third resonances are loweredthis is what happens during speech . if we consider the various vowels, each one is characterised by a special size and form of the vocal tract which is unique for that volwel . for example , an / t/ has unrounded lips with a narrow distance between the teeth, a narrow passage between the front tongue and the hard palate, closed passage to the nasal cavity ( velum raise) and a very wide and large pharyngeal cavity between the velum and the vocal folds. this configuration results in a lowering of the first resoance ( from 500 to 250 hz) an increased third resonance ( from 2500 to about 3000 hz) and an increased third resonance ( from 2500 to about 3000 hz) in figure 7.1 ( e) the first three resonances of the vocal tract are shown the vowel /t/The unique physiological size of the vocal tract for the three vowels / i/ /u/ and /a/ is shown by means of x-ray profiles in figure 7.9. using such x-ray profiles in combination with frontal x-ray profiles it is possible to calculate the cross- sectional areal of the vocal tract along the centreline. such calculations showing the corresponding areas are shown below each x-ray profile in figure 7.9 . the horiontal axis in these curves represents the distance in centimetres from the lips , and the vertical axis represents the cross-sectional area in square centimetres. the illustracion shows the enormous ability of the articulatory organs to reshape the vocal tract for each vowel. thus the volume of the pharyngeal cavity is at least 25 times greater for an /i/ than for an /a/ when you blow across the mouth of a bottle a sound is generated: the bigger the bottle , the lower the sound. this is because the natural resonance frequency of the bottle amplifies parts of the noise sprectrum generated by the turnulence of air around the bottle opening. the same thing happens when the vocal folds vibrate in the lower end of the vocal tract. the primary voice spectrum is a harmonious spectrum which consists of series of partials. the sound spectrum is emphasided or amplifies at the resonance frequencies , so that partials in the neighbourhood of the resonance frequencies are radiated with a high amplitude, whereas partial between the resonance frequencies are damped

the ability to transport sound from the glottis to the mouth opening is often callen the sound transfer function of the vocal tract and is strongly dependent on the frequency. the transfer function for vowel sound can be calculated when the cross-sectional areas along the centre line of the vocal tract are known ( figure 9) . thus the vocal tract behaves like a filter wich has a frequency dependent gain ; the resonance curve in figure 7.1e represents such a transfer function . the radiated sound spectrum has maxima at the same frecuencies as the resonances of the vocal tract. in the acoustic sprectrum these peaks are called formants and are traditionally numberes so that the lowest maximum is called formant 1 ( 350 hz in figure 7.1 f) , the next is called formant 2 ( 2600 in figure 7.1 f) ; and so on . notice the nomenclature: resonances are properties of the vocal tract, and formants are energy peaks in the acoustic spectrum

in the opening between the lips the air molecules are shifted backwards and forwards because of the oscillating sound pressure level in the vocal tract. the air molecule displacement is greatest for the low frequencies, because the primary voice spectrum has most energy round the fundamental frequency. ( as mentioned previusly, the slope of the primary voice sourse is 13 dB per octave) beacause the displacement is greatest for low frequencies , these frequencies will also meer the greatest resistance at the mouth opening during radiation of the sound pressure wave . therefore the radiation resistance supports the higher frequencies of the acoustic spectrum. calculations prove that the radiation resistance emphasises the partials above approximately 3000 hz with 60 dB per octave. therefore the radiates acosutic spectrum for the vowels has a slope of - 6 dB above 3000 hz , because of the radiation resistance which increases the amplitude above 3000 hz ( fant 1960 ; flanagan 1965) the sum up: the radiated acoustic sound pressure spectrum is a product of ( a) the volume velocity spectrum generated by the primary voice source at the glottis (b) the transfer function of the vocal tract, and (c) the radiation resistance at the lips.

the vowel soundthe vowels and semi-vowels have a free passage through the vocal tract, that is, without any constriction, giving rise to air turbulence Acosutic structure of vowelseach vowel is characterised by a unique set of formants which contains the perceptual cues for that vowel. only the three lowest formants, below approximately 3000 hz , are important for the definition of a vowel , because the physiological / articulatory changes in form and size of the vocal tract are too gross to affect the higher resonances at the sites of minymun or maximun particle velocity. formant frequencies , bandwidths and formant levels can be measured by several methods , the best known being sound spectrography , wich is an acoustic analysis of speech based on a mathematical analysis called FFT ( fast fourier transformation). the analysis is based upon an analogue an analogue to digital conversion os the speech signal followed by computerised calculation of the acoustic spectrumover the last 50 years the satnadard layout of the spectral analysis of speech has been based upon sound spectrograms ( sonograms) . figure 7.1 shows a sound spectrogram of the three vowels / i, u , a/ spoken by a male subject F0: 110 Hz. the upper curves (B) is a broadband spectrogram , the middle curve ( C) is a narrowband spectrogram and the lower curves ( A) is the microphone signal. the horizontal axis represents time, and the formant frequencies are represented along the vertical axis. the formants are shown as dark belts in the spectrogram

the degree of darkness is proportional to the intensity .the centre frequencies of the formants is proportional to the intensity. the centre frequencies of the formants of the three volwes are drawn separately in order to make their positions clearer. it is easy to see that the /i/ and / u/ have a lower F1 than /a/ because / i/ and /u/ are close ( also called high or narrow) vowels and / a/ is a low (open) vowel, /i/ has a higher F2 than /u/ because /i/ is a front vowel and /u/ is a back vowel . the upper sound spectrogram (B) is analsed with a good time resolution, but with a bad frequency resolution because it is analysed with a 286 HZ wide band filter, wich makes it possible to see the individual vocal fold vibrations as vertical lines. But the filter bandwidth is too broad for viewing the single partials ( harmonics) of the spectrum

The middle illustration (c) shows the same three vowels recorded with a 61 HZ narrow band filter which gives a better frequency resolution but a bad time resolution. the narrow filter makes it a possible to see the formants clearly ; even some partials are seen as horizontal lines, but the individual vocal fold vibrations are less pronounced because the narrow filter reacts slowly. In both illustrations the frequency scale used is linear and shown at the right hand side of the spectrograms Such acoustic analyses may be used to find the formant frequencies. normally , the lowest first three or four formants , which are the most important , are measured. A set of vowel frequency measurements for males, females and children are shown in table 7.1. Because of the smaller female resonance cavities, the female formants are on average 17 per vent higher than the male formant frequencies

The children in this investigation ( from a boys choir) have 29 per cent higher formant frequencies than the men.using the distinctive features mentioned, it is possible to set up a complete vowel chart covering the ditinctions front/back tongue position , spread/ rounded lips, closed/half closed/ half open/ open jaw ( table 7.2) ( of course, such a chart will also cover non-english vowel articulations) it is important to have some knowledge about the mechanism used in vowel production , as then it is easier to choose the correct vowel for the voice exercises. which vowel should be used for training specific articulatory disturbances is explained in chapter 10 after the basic tempo 1, 2, and 3 exercises have been introduced