If you did your neutral vowel correctly, the pitch it came out on was your home pitch, in other words the natural pitch of your relaxed voice.
At that pitch your voice automatically matches the size of the cavity to the frequency of the waves. Refer back to the section on resonance (waves in cavities) to understand the technical aspects.
To summarise, waves in cavities resonate when the size of the wave 'matches' the dimensions of the resonator. That is so over-simplified it's crazy, but it gives you an idea of what is going on. So as pitch gets higher, the frequency gets higher, and inversely the wavelength ("size") of the wave gets smaller.
Now, the timbre of the voice is directly related to the relationship between wavelength and resonator size. We want the timbre of the voice to remain consisatent over the whole of our range. This was one of the goals on our list in 'Good Voice' earlier.
So if we now increase the pitch (reduce the wavelength) using the same size cavity, the timbre will change. So to prevent the timbre from changing we have to reduce the size of the resonator until it has the same ratio to the wavelength as we satrted with..
Not only that but we have to reduce the size of the resonator without changing the vowel, so it all has to be done in exact proportion. Simply miniaturise the vowel exactly. And of course while in song, this has to be done on the fly, with the vowels and consonants going by at some speed, and continually adjusted for the pitch changes. It sounds hard to do: Isn't it great that the voice's own internal processing mechanism can handle it all for us, if we just learn how to access it and let it run.
We add simple Vowel Narrowing' to our exercises to kick this mechanism into action. Once it fires up, your whole voice will change. It's one of the big moments in learning singing voice.