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I found out the problem in my German recording. I knew I had to open my mouth a bit more when I pronounce an /e/ than in /i/, and I did so. But when I analyzed them in a spectrum, they got all together in the upper-left corner of the vowel chart.

I've also tried to pronounce an [i] when I open my jaw so much as well as in [a] and analyzed it with a normal [i] in spectrum and I found the formants same. And of course, they are perceived the same by ear.

People can pronounce an [a] even if they clench their teeth.

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Height doesn't depend on how open or closed the jaw is, but on how close the tongue is to the roof of the mouth. Try pronouncing [a] versus [i] with your mouth wide open, then again with your teeth clenched. You'll feel in both cases that the [i] has your tongue very high up, while the [a] has it very low down.

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You cannot determine where your tongue is by looking at formants, you have to use a more hi-tech physiological method like ultrasound. Formant frequencies are the result of complex physical factors which include the length of various resonating cavities, which can be determined by the position of the tongue, lips and larynx, as well as jaw position which affects where everything is. The notion that tongue height determines formants (F1) is true enough for normal articulation, but you may have to redefine what you mean by tongue height for "alternative" articulations. This answer discusses what determines formant values. Whether or not radically different articulations of a vowel are "perceived the same" depends on the experiment that you conduct to establish that conclusion (what proves that X and Y are "perceived the same"?).

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