Complex periodic waves can be expressed as the summation of simple sine and cosine waves.  This is called the Fourier series.  The sine/cosine combination that establishes the perception of pitch is defined as the fundamental frequency.  Within the fundamental is a superstructure of frequencies, integral multiples of the fundamental frequency.  These are often called the harmonic series.  The "tone" of the sound depends on the relative amplitudes of the each of the sine and cosine waves of the harmonic series.

Spectral analysis of spoken vowel sounds reveals bands of relatively high amplitude frequencies within the harmonic series.  These bands are called formants.  Formants play a large role in shaping the tonal characteristics of spoken sounds.

I have sampled me, speaking a string of vowels (a,e,i,o,u).  The sample rate is 44100 Hz with a bit depth of 24.

First, we will listen to vowel sounds with the formants unaltered.

Vowels with unaltered formants:  Listen

I will then shift the formants down.  This means that the bands of high amplitude have been shifted from their natural position to low in the frequency spectrum.

Because I am using a "black box" formant shifter, I do not know the algorithm used.  I assume that logarithmic scaling is used to maintain the relative perceptual distance between the formants, but I cannot be specific.

Vowels with formants shifted down:  Listen

I will now shift the formants up.  This means that the bands of high amplitude have now been shifted from their natural position to higher in the frequency range.

Vowels with formants shifted up:  Listen

Here is a formant sweep from low to high, then high to low.

Formant Sweep Low to High:  Listen

Formant Sweep High to Low:  Listen

When pitch shifting, if we allow the formants to shift upward with all the other frequencies, we get a "chipmunk" effect.  The voice is thin and cartoonish.  This would seem to be because defining bands of high amplitude are now high in the frequency spectrum.

"a" pitch shift/no formant adjustment:  Listen

"e" pitch shift/no formant adjustment:  Listen

"i" pitch shift/no formant adjustment:  Listen

"o" pitch shift/no formant adjustment:  Listen

"u" pitch shift/no formant adjustment:  Listen

You will notice that the vowels "e" and "u" do not pitch shift well.  The pitch shifted vowels are very distorted.  This is because the pitch shifter has trouble identifying the fundamental frequency.  We will address this issue shortly.

But first, before dealing with the "e" and "u" distortion issue, let us try moving the formants down as we move the pitch up.  That way, even though the overall frequency is much higher, those bands of frequency that are emphasized do not change.

"a" pitch shift/formant adjusted:  Listen

"e" pitch shift/formant adjusted:  Listen

"i" pitch shift/formant adjusted:  Listen

"o" pitch shift/formant adjusted:  Listen

"u" pitch shift/formant adjusted:  Listen

This sounds much more natural.

Vocal formants result from the resonant characteristics of the vocal mechanism.  For example, although the vocal chords may stretch and relax resulting in a raising and lowing of the voice, the size of the head and nasal cavities, and their resonant frequencies, remains the same.  Therefore, keeping the formants in the same place in the frequency spectrum help maintain the original tonal quality of the voice.

Lastly, what do we do about "e" and "u"?  The pitch shifter I use continually misidentifies one of the upper harmonic series as the fundamental frequency.  Therefore, application of the pitch shifting algorithm results in a weird restructuring of the harmonics.

Here is how I fixed it.  I figured out the frequency that was confusing the pitch shifting software, and used a parametric equalizer to remove that frequency before pitch shifting.  I hypothesized that the pitch/formant shifting module, when not misdirected by the offending frequency, would identify the correct fundamental.  As you will hear, I was right.  I did this for both the "e" and "u" vowels.

After doing this, the distortion was no longer a problem.

"e" pitch shift/pre equalized/no formant adjustment:  Listen

"e" pitch shift/pre equalized/formant adjusted:  Listen

"u" pitch shift/pre equalized/no formant adjustment:  Listen