The laryngeal muscle most responsible for stretching (elongating) the vocal ligament is the:

Cricothyroid draws the thyroid cailage forward, tensing the vocal ligaments. This is the one muscle innervated by the external branch of the superior laryngeal nerve. Posterior cricoarytenoid is a very impoant muscle; it's the only muscle that adducts the the vocal folds. This muscle is innervated by the inferior laryngeal nerve, which is a continuation of the recurrent laryngeal nerve. If this muscle is denervated, the vocal folds may be paralyzed in an adducted position, which would prevent air from entering the trachea. Lateral cricoarytenoid, thyroarytenoid, and arytenoid are all muscles that adduct the vocal folds. They are all innervated by the inferior laryngeal nerve.