Whether a tilt affects the internal vocal cords, I don’t know. But, it definitely affects the placement, its resulting resonance, and the jaw and its supporting muscles.
Why are these important? A slight tilt may facilitate the sound travelling to more the forward part of the head, without such sound being muffled by the backpart of the nasal-pharynx; thus enabling greater nasal-pharynx resonance and to some degree the sinuses resonance as well.
For louder, far better controlled, and better toned highs, it is far easier to control the resonance first; which means controlling the head tilt, the neck lift and its angle, even the minor degree of the neck length and the degree of protrusion of the head from neck.
As for the comments:
thyroid tilted for a cry….
Emotions are expressed usually as external and internal muscle changes, simultaneously. The externals are more “visible” and hence easier to affect. They are also stronger and larger, thus these are the predominant affects of such vocal tone and expressions. After the external muscles are affected, you might want to try to control the internal–e.g. shaping the internal muscles somehow. However, I believe 80% of the work will be on the external.
So, the answer to your question– tilt itself doesn’t affect the pitch or tone until one determines what the pre-existing tension is already on the vocal cords. Tilt automatically affects the resonacne characteristics, which can affect the volume of various pitches.
The thyroid is very well protected in the larynx, and it’s unclear to me how a gland is affected by a tilt.
The larynx is mostly cartiledge, andthe vocal cords are affixed to some kind of cartiledge with tissues and muscles. If one tilts the larynx, the initial question should be, where was the larynx before the tilt? If the larynx is not optimal positioned, it will exert some minor tension on the vocal cords to begin with. Tilt it to the optimal position, less tension; away, more tension.
So, to reply to the tilt begins with the question, how is the posture in relationship to the larynx?