Hawker's Poor Man's Concordance And Dictionary 
We meet with an address, or dedication, at the opening of very many of the psalms: "To the chief Musician." And not a few have been led to suppose, that it means no more than a superscription to the master or chaunter who presided over the temple service; as if the Holy Ghost was more attentive to have the Psalm played or sung well with the instrument or voice, than to have the blessed contents of the Psalm itself impressed upon the heart. We do not know that there was such an office over the choir as chief musician; certain it is, that neither the Chaldee paraphrase, nor any of the other versions, say any thing about this chief musician. Besides, if it be supposed that David had such a character in his band as chief musician, what authority is there to suppose that the prophet Habakkuk knew of any such a character; and yet he also addresseth his hymn to the chief sinner. (See Habakkuk 3:19) I find an author of no small authority observe, that the word which ( 1 Samuel 15:29) is rendered strength, and is a well known title of Christ, is not dissimilar to the word in the Psalms rendered chief musician. See Parkhurst's Lexicon, 410,496. And in confirmation of this, it is well worthy of remark that Habakkuk saith, ( Habakkuk 3:19) "The Lord God is my strength." In this sense, the close of Habakkuk's prophecy will be rendered thus: "The Lord God is my strength, and he will make my feet like harts' feet; and the Giver of victory, or my stringed instruments, will cause me to tread on my high places."
It should be observed, moreover, that the word Lamenetz is rendered by the Seventy to the end. And what end, but the end of Christ's triumphs by virtue of his sacrifice? And as Christ is the end of the law for righteousness to every one that believeth," may not those numberless sweet Psalms which so plainly refer to him, be supposed to be addressed to him as the end? So we find the title of Psalms 6:1-10 and Psalms 12:1-8 to be addressed to the chief musician upon Sheminith. And every one cannot but know that these Psalms are both of them spoken prophetically of the person of Christ, the God-man-Mediator; and therefore, as such, surely it is doing no violence to the word Sheminith, joined with Lamenetz, to suppose that it forms an address to Christ, as the strength of Israel in his Sheminith or abundant riches, suited to his high character as the chief end of salvation to his people. But as I have elsewhere said, in similar observations in my "Poor Man's Commentary on the Psalms," so I beg to add here, I do not decide on the enquiry. I have thought it worth while to give the views I have of it to the reader, and here with humble requests to the Lord to pardon every unintentional error, I leave the subject.
King James Dictionary 
MUSI'CIAN, n. A person skilled in the science of music, or one that sings or performs on instruments of music according to the rules of the art.
Webster's Dictionary 
(n.) One skilled in the art or science of music; esp., a skilled singer, or performer on a musical instrument.
Vine's Expository Dictionary of NT Words