[Siyu D]

I think the width of the vocal tract is too short compared with its length and thus the resonant frequencies may be quite high and meaningless for humans’ audition.

[Siyu D]

I am not clear what happened physically, but mathematically speaking, I suppose the property of Fourier Transformation necessarily implies that frequencies of harmonics are whole number multiples of the fundamental frequency. Actually, a complex wave can be analyzed as a series of sines and cosines at different frequencies nω by virtue of Fourier Transformation and ω here is the fundamental frequency and n is a non-negative integer number or 0.

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