The TA (thyroarytenoid) muscle lies within and runs the length of the membranous vocal cord. The muscle provides most of the filling or mass of the vocal cord. It tightens to increase the pitch, mostly by isometrically tensioning the vocal cord. For singers when they are not engaging the CT muscles, the TA muscle essentially is used to change pitch throughout their lower or chest register.
We can see the bulk of this muscle during endoscopy on a healthy vocal cord. The easiest way to appreciate the bulk is in the patient where one vocal cord is completely paralyzed, especially when viewed along the length of the vocal cord. In a complete paralysis, the paralyzed vocal cord would consist of only the mass of the vocal ligament. The difference in size between these vocal cords then represents the mass of the thyroarytenoid muscle.