We don’t know much about how the early church sang. We have an entire book of psalms, of course, but these pre-date Christianity by hundreds of years. And we have some passages in the NT that scholars believe may have been lyrics for songs, such as Phil 2:5-11. But no one really knows for sure — and even if we could know, we have no way of knowing the tunes for these early songs.
Were they improvised by the song leader? Did he chant a line, to be repeated by the church? Over time, did certain melodies become standard?
Unlike Western music, there was no regular meter or rhyme in the Psalms and other songs we have. Meter is especially important in Western music, because our music is based on measures of repeating rhythm — 3/4 time for a waltz, 4/4 time for an anthem, 5/4 time for “Take Five” by Dave Brubeck, etc. In fact, a Westerner wouldn’t think of anything else as “music.” Ask a Western church to sing a meter-less (rhythmless) biblical psalm as written, and we wouldn’t know where to begin. For us, music is all about the rhythm.
By the mid-Third Century, the early church was insisting on a cappella singing, and they also insisted on unison singing (no harmony) (Everett Ferguson, Church History, Volume One: From Christ to the Pre-Reformation: The Rise and Growth of the Church in Its Cultural, Intellectual, and Political Context), leading Ferguson to argue for unison singing in the assembly — a teaching that, to my knowledge, no Church of Christ congregation has accepted.
In the Middle Ages, the church began experimenting with instruments and with harmonies. Over the centuries, a form of annotation was created to preserve the melodies and instruct on harmonies.
By the Renaissance, very elaborate harmonies were being used in church music, and congregational singing had been replaced with trained choirs. Of course, the singing in the Western church was in Latin, illiteracy rates were high, and hymnals would have been of little use for the common people.
This all changed with the Protestant Reformation — in two ways. In Germany, Luther was an accomplished musician, and he re-introduced congregational singing, personally composing many hymns — including “A Mighty Fortress Is Our God.” Luther also introduced four-part harmony, both for its beauty and to allow for the natural wide range of male and female voices. It’s often been said that Luther converted far more people with his music than his theology.
Luther was personally opposed to instruments in the assembly, although he played instruments at home. But it was not a theological issue for him, and the Lutheran church quickly became instrumental. It wasn’t long before the Lutheran church produced J. S. Bach and many other musical geniuses, blessing the world with some of the most beautiful music ever composed.
One of the challenges facing Protestant churches in the early years of the Reformation was deciding how to purge Catholic practices from the worship of the church. Many considered the Catholic mass idolatrous (because the bread and wine were treated as the literal blood and body of Jesus), and many practices were clearly contrary to sound doctrine. Others were not clearly wrong but very different from early church practices. Practices that aren’t inherently wrong are called adiaphora, and these became major points of contention.
The Lutherans wanted to reform Catholicism and have only one church, and so a major issue was whether some of the Catholic adiaphora could be retained in a reformed church. The Wikipedia gives some examples —
The issue of what constituted adiaphora became a major dispute during the Protestant Reformation. In 1548, two years after the death of Martin Luther, the Holy Roman Emperor Charles V tried to unite Catholics and Protestants in his realm with a law called the Augsburg Interim. This law was rejected by Philipp Melanchthon, on the account that it did not ensure justification by faith as a fundamental doctrine. Later he was persuaded to accept a compromise known as the Leipzig Interim, deciding that doctrinal differences not related to justification by faith were adiaphora or matters of indifference. Melanchthon’s compromise was vehemently opposed by Matthias Flacius and his followers in Magdeburg, who went to the opposite extreme by claiming that adiaphora cease to be adiaphora in a case of scandal and confession. By 1576 both extremes were rejected by the majority of Lutherans led by Martin Chemnitz and the formulators of the Formula of Concord.
In 1577, the Formula of Concord was crafted to settle the question of the nature of genuine adiaphora, which it defined as church rites that are “…neither commanded nor forbidden in the Word of God.” However, the Concord added believers should not yield even in matters of adiaphora when these are being forced upon them by the “enemies of God’s Word”.
The Lutheran Augsburg Confession states that [for] the true unity of the Church it is enough to agree concerning the doctrine of the Gospel and the administration of the Sacraments. Nor is it necessary that human traditions, that is, rites or ceremonies, instituted by men, should be everywhere alike.
Hence, the Lutherans came to adopt what is now called the Normative Principle of Worship (NPW), as did the Anglicans some time later.
Obviously, the NPW doesn’t approve practices that are wrong on other grounds. The worship of Mary is wrong under both the NPW and the Regulative Principle of Worship (those things lacking authority are sin) (RPW) because Mary was a human and not God — a conclusion which depends on neither principle. Neither camp would condone animal sacrifice because that practice was ended by God when he allowed the Temple to be destroyed by the Romans in 70 AD — as even the Jews agree. That is, the NPW is not “anything goes” but rather, if it’s not contrary to scripture and is good for the unity and peace of the church, it’s permitted.
In fact, in practice, there aren’t that many differences between RPW and NPW churches, because neither camp believes in adopting practices that are anti-gospel and both camps are guided by their understanding of God’s purpose in founding the church and in calling us to assemble. For example, 1 Cor 14 requires that our practices be edifying to members and bring glory to God regardless of one’s camp.
(We really should resist the temptation to unfairly attribute to another camp a position the other camp doesn’t really hold. The prohibition on bearing false witness applies to doctrinal debates, too.)
 Many tracts cite Justin Martyr, who wrote in the mid- to late-Second Century, as opposing instrumental music in worship, but for over 100 years, we’ve known that these passages weren’t written by Justin and date to centuries later.
Clement of Alexandria, who wrote in the late Second and early Third Centuries, famously objected to instrumental music — in banquets. According to Everett Ferguson, Clement never criticizes instrumental music in the Christian assembly (although this could be because there was no problem with this question at the time and place where he worked). Clement bases his argument against instruments on pacifism: Since the military uses instrumental music, Christians should not.
 Ferguson is a world-class scholar of New Testament backgrounds, and his books are used as texts in many universities, not just those affiliated with the Churches of Christ. In the Churches of Christ, it’s a rare book or tract that insists on a cappella music that doesn’t cite to Ferguson, who has written often on the subject. I can only respect his historical knowledge, but I believe his hermeneutics are deeply flawed, being built on Zwingli’s Regulative Principle — that is, we must have authority for all “acts of worship” — a doctrine utterly foreign to the same early church fathers on whom Ferguson builds his case. And the fact that Ferguson ultimately insists on unison singing (no harmony) amply demonstrates the weakness of his hermeneutic. This is the same approach to scripture that led J. W. McGarvey to declare the “reading of written prayers” sinful, presumptuous “will worship.”