The sternocleidomastoid muscle and the omohyoid muscle are intersecting on the side of the cervical spine.
When the sternocleidomastoid muscle is swollen or the omohyoid muscle floats, these muscles are touching each other. When this touching happens movements then become obstructed, which causes problems with vocalizing – such as:(1)Hard to let out the voice or to depress vocalizing (2)Make a boxy voice, because the resonance chamber gets narrower (3)Cannot let out a high-pitched voice because moving the cricothyroid articulation is obsrtucted.
Furthermore, some people naturally have conglutination with the fascia of the sternocleidomastoid muscle and the omohyoid muscle which obstructs vocalizing.
The sternocleidomastoid muscle is not directly relevant to vocalization but can cause poor blood flow/circulation in the superior laryngeal artery. This poor blood flow is because the larynx is pressured directly by the conglutination.
Note1:In the case of the conglutination with the fascia of sternocleidomastoid muscle and the omohyoid muscle: if you can make the space increase between the fascia and the muscles, you will improve letting out your voice. Please be careful, gentle and aware if you massage that area by yourself, because the intermediate tendon of the omohyoid muscle is located under the sternocleidomastoid muscle.