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The wiki entry for resonance lists 7 factors that contribute to it:

chest
larynx
nasal cavity
oral cavity
pharynx
sinuses
trachea

Given one’s base pitch production, I thought that the oral cavity is the only factor that we can move to affect resonance.

Thus, are vocal resonance differences essentially just a matter of your pitch and how widely you open your mouth when talking/singing?

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Any cavity that is open to the vocal tract can contribute a resonance. Subglottal resonances are not linguistically controllable, but they exist. Resonances produced in the nasal cavities are widely used contrastively – languages have nasal vs. oral vowels, and they are not part of the oral cavity. The lower pharyngeal cavities are technically not part of the oral cavity, but do have resonance properties. Pharyngeal constrictions are used in some languages (Berber, Arabic) and are often contributors to the linguistic phenomenon of "register" esp. as found in souutheast Asian languages.

The one thing that resonances are not about is pitch: that is determined by the rate at which the focal folds vibrate. That sound source is shaped by the various resonating cavities. There is a singing phenomenon whereby you have to change resonance properties of your vocal tract if you have a very high fundamental frequency, because the acoustic effect of normal articulation with very high pitch can aesthetically be undesirable, see this article.

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