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Vowels

D C Miller's analytic experiments showed that the sounding of vowels depended on a certain frequency, rather that a certain order of harmonic, with the results shown below:

Clearly the frequency is the factor that influences the sound, not the harmonic.

So the vowels are characterised by the formant values, and these are used in their synthesis. These are shown for an adult male:

And for an adult female:

One repercussion of the frequency of the formants being important is that if a singer tries to sing a vowel at a pitch above that of the first couple of formants, it becomes very difficult. If a singer tries to sing at a frequency that is above the most prominent first couple of formants, producing the correct vowel sound is very hard.

An example of this was given to me by my music teacher when I was a treble in the choir at school: The descant for O Come All Ye Faithful ends on a 'top A' on the words 'Christ the Lord'. We were told not to sing the i in Christ not as eye but as the i in bid. A look at the table above explains why. Top A is 1760Hz. Eye is a diphthong, the first part of which (and the bit most of the note is sounded on) is similar to the a in bard. This has its second formant at only 1200Hz, whereas bid has its second formant at 2500Hz. So i is possible to get a better sound from since the formant is not below the singing pitch (and it's not that noticeable to people listening!).