I think I see what's going on. You're not disputing that we're commanded to serve communion and baptize new Christians. I think those commands are pretty obvious. It seems like your question is why these things differ from everything else we're commanded to do, right?
The usual definition of a sacrament is that it is an outward and visible sign of the inward activity of the Spirit. Luther spoke of baptism as water joined to the Word. Hence Luther rejected marriage as a sacrament, not because it isn't an important Christian action, but because it is itself. It's not the like communion or baptism, which is a sign joined to the Word.
When reading your question, i ask myself how my experience of communion differs from, for example, my experience of hearing the Scripture read. I think the thing that makes the sacrament different is that it involves our senses in doing something, in this case eating bread and drinking wine, and thus reaches us in a way that just hearing the Word may not always do (though I would certainly not wish to belittle hearing the Word preached -- at times one gets the impression that Reformed writers treated preaching almost like a sacrament).
Of course music has some of the same effects, and of course music can be a powerful inspiration. But again, it doesn't have the two levels of the symbolic action and what's really happening spiritually.
Calvin is willing to see a similar combination of symbol with promise in other things, such as the rainbow, but he said he normally used the term for specific actions commanded by Christ for universal use by the Church. Here's what he says in more detail:
"But my present purpose is to discourse especially of those sacraments which the Lord has been pleased to institute as ordinary sacraments in his Church, to bring up his worshippers and servants in one faith, and the confession of one faith. For, to use the words of Augustine, “In no name of religion, true or false, can men be assembled, unless united by some common use of visible signs or sacraments” (August. cont. Faustum, Lib. 9 c. 11). Our most merciful Father, foreseeing this necessity, from the very first appointed certain exercises of piety to his servants; these, Satan, by afterwards transferring to impious and superstitious worship, in many ways corrupted and depraved. Hence those initiations of the Gentiles into their mysteries, and other degenerate rites. Yet, although they were full of error and superstition, they were, at the same time, an indication that men could not be without such external signs of religion. But, as they were neither founded on the word of God, nor bore reference to that truth which ought to be held forth by all signs, they are unworthy of being named when mention is made of the sacred symbols which were instituted by God, and have not been perverted from their end—viz. to be helps to true piety. And they consist not of simple signs, like the rainbow and the tree of life, but of ceremonies, or (if you prefer it) the signs here employed are ceremonies. But since, as has been said above, they are testimonies of grace and salvation from the Lord, so, in regard to us, they are marks of profession by which we openly swear by the name of God, binding ourselves to be faithful to him. Hence Chrysostom somewhere shrewdly gives them the name of pactions, by which God enters into covenant with us, and we become bound to holiness and purity of life, because a mutual stipulation is here interposed between God and us. For as God there promises to cover and efface any guilt and penalty which we may have incurred by transgression, and reconciles us to himself in his only begotten Son, so we, in our turn, oblige ourselves by this profession to the study of piety and righteousness. And hence it may be justly said, that such sacraments are ceremonies, by which God is pleased to train his people, first, to excite, cherish, and strengthen faith within; and, secondly, to testify our religion to men." (Institutes, 4.14.19)
I think it's a useful category of particularly important ceremonies, but I would note that Scripture doesn't specifically put Baptism and Communion into such a category.
