Resonnance has to do with the higher frequencies created as the direct sound from you vocal cords exits your mouth.
Reducing the size of the resonnant chamber, smiling, opening mouth, keeping tongue flat and up and forward, will produce a higher resonnant pitch. Even without changing anything else, your voice will sound brighter, higher pitched, even if your pitch doesn't change. Say HEED and play with those things and see how it modifies the sound. Best thing is to record it with a decent sound recorder. The answering machine is a very lousy recorder, it doesn't record higher harmonics well.
You also lift the voice box (shortening the vocal tract and creating higher harmonics), but that is a less flexible and rapid way (the box is heavier and the muscles harder to control than the tongue and mouth) of modifying resonnance. It modifies the sound of all vowels uniformly, which I don't like; though it can be used selectively.
Just shifting to a head voice by reducing chest vibration tends to create the typical "gay" flat nasal voice, especially if you go to close to falsetto. Better have a lower pitch with more higher harmonics from the mouth, sounds MUCH better. If you increase you pitch without increasing your resonnance, the energy of your voice will be more contrained and weak and strained (bad combination). Little bass AND little top end and a week middle. I hear this ALL THE TIME in TS. I call in the TS voice disease...