Calvin, so far as I know, didn't write a single hymn or tune, but his influence on Christian hymnody was so profound that I had to include a post on him as a counterpart to Luther.
Luther's reforms of worship restored the Biblical principle of the "priesthood of believers", and thus moved in the direction of a more scriptural approach to church music by making it once again the province of the congregation, not just the priest or choir. Luther also rejected the idea that a central authority (other than the divine) should regulate the services of the church, and thus opened the door for a conscientious examination of the scriptures on the subject of worship.
Calvin, on the other hand, was far more actively anti-Roman in his views; no gradual reform would do. He was far more likely to reject the Roman Catholic position a priori, and as a strict logician, to drive the "sola scriptura" ("scripture only") principle to its necessary conclusion in every instance. In this sense his reasoning was more that of the "restorationist" than the "reformer", and will sound more familiar to us in the Churches of Christ than does the language of Luther. Take, for example, the statement in his 1544 treatise "The Necessity of Reforming the Church":
I know how difficult it is to persuade the world that God disapproves of all modes of worship not expressly sanctioned by His Word. The opposite persuasion which cleaves to them, being seated, as it were, in their very bones and marrow, is, that whatever they do has in itself a sufficient sanction, provided it exhibits some kind of zeal for the honour of God. But since God not only regards as fruitless, but also plainly abominates, whatever we undertake from zeal to His worship, if at variance with His command, what do we gain by a contrary course? The words of God are clear and distinct: “Obedience is better than sacrifice.” “In vain to they worship me, teaching for doctrines the commandments of men,” (1 Sam. xv. 22; Matth. xv. 9.) Every addition to His word, especially in this matter, is a lie. Mere “will worship” (ethelothreskeia) is vanity. This is the decision, and when once the judge has decided, it is no longer time to debate....(Schwertley, app. A)
Sound familiar? Calvin's "regulative principle", as it is discussed in Schwertley's excellent review of the subject, simply means that if God has spoken on a subject, we are bound to do what He has said, no more, no less. On the use of musical instruments in Christian worship, for example, Calvin said in his commentary on Psalm 81:
With respect to the tabret, harp, and psaltery, we have formerly observed, and will find it necessary afterwards to repeat the same remark, that the Levites, under the law, were justified in using instrumental music in the worship of God; it having been his will to train his people, while they were as yet tender and like children, by such rudiments, until the coming of Christ. But now when the clear light of the gospel has dissipated the shadows of the law, and taught us that God is to be served in a simpler form, it would be to act a foolish and mistaken part to imitate that which the prophet enjoined only upon those of his own time.(Psalms, III, 222)
In his pursuit of New Testament simplicity, Calvin likewise rejected choirs except as a means of teaching the congregation new songs, and encouraged a style of songwriting that was accessible to the entire congregation. Under his influence, the composer Louis Bourgeois (among others) wrote in a simple, chordal style that would come to define the Protestant psalm- and hymn-singing style (e.g. OLD 100TH, "All people that on earth do dwell", PFTL#17).
Calvin went a step further, however, in his pursuit of purely scriptural worship. He posited that only the words of God (primarily the Psalms) are suitable for the worship of God; in other words, he rejected the singing of any hymn not taken directly from Scripture. For hundreds of years the denominations that descended from the Calvinist movement--the Presbyterians and Reformed Churches--sang nothing but a cappella Psalms. (Some in fact still do, such as the Reformed Presbyterian Church.) What of Paul's authorization of "psalms, hymns, and spiritual songs" in Colossians 3:16 and Ephesians 5:19? These are said to be three different designations for Psalms, as occasionally used in the Septuagint, the Greek translation of the Old Testament. (But if one accepts the assumption that these terms must only be interpreted by their usage in the Septuagint to refer to the Psalms, then one is caught in a tautology--of course they refer to "inspired songs", because they are in the Bible!) There is no question that the Greek words "hymn" or "song" could be used to refer to a Psalm (as in Josephus), but there is no reason to suppose that they necessarily must refer to Psalms, especially to the Greek Christians of Ephesus or Colossae, who were familiar with these terms from the music of their own culture. The existence of Christian hymns from as early as the 2nd century(MacMillan) is additional evidence that no such exclusivity was understood by the early Christians.
This being said, it is refreshing to see worship debated on the basis of what the Bible authorizes. Though I strongly disagree with Calvin on the far more important issue of free will, he deserves respect as a man committed to following the Bible and reasoning carefully from scripture to practice, rather than starting from practice and trying to justify it from scripture. And though I obviously disagree with "exclusive psalmody", I regret that we do not sing the Psalms any more than we do. We are the poorer for it.
Under Calvin's guidance, poets such as Clement Marot and composers such as Louis Bourgeois crafted a style of Psalm-singing that was standardized in the Geneva Psalter, published in its first complete edition in 1562. (This included the previously referenced OLD 100TH tune, "All people that on earth do dwell", PFTL#17.) Its influence was far-reaching. When English Protestants fled the reign of Mary Tudor, many came to Geneva and interacted with the Psalm-singing tradition; their own native production, the Sternhold & Hopkins Psalter, was greatly influenced by the Genevan style. This Psalter was used well up into the early 1700s in both England and the American colonies, and was, along with the King James Bible and the Book of Common Prayer, one of the primary English-language texts that accompanied the founding of our country.
Schwertley, Brian. Sola Scriptura and the Regulative Principle of Worship. Lansing, MI: Schwertley, 2000. http://reformedonline.com/view/reformedonline/sola.htm
Calvin, John. Calvin's Bible Commentaries: Psalms, trans. John King, 5 vols. Originally published 1847. Forgotten Books, 2007. http://books.google.com/books?q=calvin%27s+bible+commentaries+psalms
The MacMillan Book of Earliest Christian Hymns, ed. F. Forrester Church & Terrence J. Mulry. New York: MacMillan, 1988.