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What is the relationship between F1 & F2 frequencies and the articulation of vowels?

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What is the relationship between F1 & F2 frequencies and the articulation of vowels?

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We observe by experiment that the major part of perceived vowel quality can be explained with a system comprising only two resonances. Furthermore it turns out that it is only the frequency of these resonances that change much with different articulations (their bandwidth is fairly constant). Thus we should be able to find some regularities between the frequency of F1 and F2 and the articulation of vowels. Bearing in mind always that such regularities are only approximations to the truth, we can see that when a neutral vowel is articulated, the formants are fairly equally spaced apart (F1=500, F2=1500, F3=2500, etc). If we shift the tongue forward, we find that F2 rises in frequency. Since we know that the resonant frequencies of cavities gets higher as they get smaller, it makes sense to ask which cavity is getting smaller when we move front from a neurtal vowel? The answer must be the cavity at the front of the mouth. Similarly if we move from a neutral vowel to an open vowel, we fin

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