1

Since that the F0 i.e. the pitch is the first harmonic and all formants are the i-th harmonics, is it possible that the formants of a vowel in a high tone are higher than those in a lower tone?

For example, imagin a language which has a L tone and a H tone, and there is a vowel in the L tone satisfies:

F0=100Hz, F1=800Hz, F2=1500Hz

Then, if that vowel in the H tone(assume that F0=200Hz) satisfies:

F0=200Hz, F1=1600Hz, F2=3000Hz

If so, should I use the value F1/F0, F2/F0 etc. instead of F1, F2 etc. to eliminate such influence?

  • I think those are two different vowels, and the only real answer is 'it's much more complicated than that'. If you have Praat (free download) you can experiment with this, but I can say from experience that you can't define a vowel by the ratio of its formant frequencies - the absolute values count for at least something. – user23078 Mar 24 '19 at 16:30
3

F0 does not affect formant frequency, for a slightly obscure reason. When you look at a spectral cross section, you see the amplitudes of individual harmonics (determined via a Fourier transform). The peaks occur pretty much at multiples of the fundamental. The harmonic with the highest amplitude in the area where you expect a formant is not necessarily at the formant's frequency: the actual formant's peak is usually between two harmonics.

A formant frequency is computed using LPC analysis, usually, which gives you a general picture of the resonances in the vocal tract, independent of fundamental frequency. The underlying theory is known as the source-filter theory, where a given glottal source (pitch and voice quality characteristics) is "shaped" by the LPC coefficients to give an actual waveform.

In other words, the mathematics of formant analysis guarantees that pitch and formant frequency are independent. However: the situation you describe in the formulas does not correspond to a real situation, an you will not find a vowel whose formant's are doubled when pitch is doubled. 3000 Hz is not a realistic F2, nor is 1600 a realistic F1

  • Are the 'formants' calculated by Praat really the resonances, though, or are they the peaks in the spectrum - i.e. those harmonics that are near enough to a resonance to be amplified by it? – user23078 Mar 25 '19 at 16:26
  • Least really computed formant's from LPC analysis, not peak picking from Spectra. You can get a spectral slice, ctrl-l if I recall correctly – user6726 Mar 25 '19 at 20:23
  • I am a little confused, because the Praat manual speaks only of "resonances (formants)" They link papers for the many LPC methods they implement, of which "autocorrelate" follows Markel and Gray's "Linear Prediction of Speech", which is in gbooks at least, and seems like a good entry. – vectory Mar 25 '19 at 20:23
  • 1
    I got it. What we called as formants are the properties of the vocal trace i.e. the resonator, which can be predicted by the LPC anlysis. However harmonics are the properties of the output sounds, which can be derivated directly through Fouier Transformation. They are in fact two different things, right? – C.K. Mar 26 '19 at 8:34
  • @c.k. yes, exactly. – user6726 Mar 26 '19 at 22:40

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