why does the spectral envelope of human speech not change w.r.t. pitch when taking a Fourier transform? In the context of speech recognition (recognizing individual speech sounds), the pitch of a certain person can change at different times.  

Excerpt from Statistical Signal Processing by Steven Kay: 


  This is a natural variability due to the nature of human speech. The
  spectral envelope will not change with pitch since the Fourier
  transform of a periodic signal is a sampled version of the Fourier
  transform one one period of the signal.


What does the part in bold above mean?
The spectral envelope, which determines where the formant frequencies are, is determined by the shape of the mouth, tongue, lips, and nasal coupling.  That is independent of the pitch, which is dependent on the tension or stiffness of the vocal cords.