The muscles in singing that determine pitch are the arytenoid muscle system and the crico-thyroid muscle system as well as the vocal cords themselves.
The arytenoid muscle system, or “closer” muscle, determines pitch at the lowest part of a person’s voice by keeping the cords thicker and fatter; creating the low pitch.
The crico-thyroid muscle system, or “stretcher” muscle, determines pitch by stretching and thinning the vocal cords as one ascends the scale, and lets one back down as well. There is less length, width, and depth of cords vibrating which gives us higher pitches.
The inter-arytenoids also play a role in this process by pressing the cords together and stopping cordal vibration little by little so that the glottal slit is closed like a zipper being zipped.
The vocal cords determine pitch by having their vibrating size altered as one ascends and descends the scale. They are muscles that are adjusted by other muscles.
Hoorah for so many muscles intricately coordinating. When all these muscles play nice, then we are all tuned up!