What an intriguing question! Here's an intriguing quote from Doug Floyd:
"You don’t get harmony when everybody sings the same notes."
What would John Calvin have made of that? The point is that harmony can sometimes wrongly be mistaken for uniformity. In music, there may be total uniformity with different singers and/or players sticking to the exact same notes, bleating out the same tune. But for musical harmony, you must have a variety of complementary notes being sung (or played) at the same time!
The situation in the Middle Ages was that in Catholic worship the liturgy was almost entirely restricted to the celebrant and the choir. The congregation only joined in a few responses in the vernacular. Luther so developed this element that he may be considered the father of congregational song. Portions of the liturgy were converted into hymns, the Creed and the Sanctus. Yet Calvin could hardly be said to have been reluctant to accept congregational singing given that:
In 1524, Theodore de Beze introduced congregational psalmody to the
German-speaking Calvinist churches in Strasbourg where he was pastor.
In 1533, Calvin presented the Genevan Psalter that was followed by the
editions of 1542, 1551. When Calvin became the pastor of the
French-speaking congregation in Strasbourg in 1538, he introduced the
French Psalter that was later published in its complete form in 1562.
Clement Marot and Beza, the latter Calvin’s eventual successor at
Geneva, translated the texts from the psalms, with Loys Bourgeois
composing the melodies using a simple chord style. Calvinist
congregations sung the metrical psalms unaccompanied and in unison.
The quote you provide about a reason for Calvin objecting to harmony singing being "violating the unity of the body" hardly makes sense given the Pauline passages about all the different parts of the body being needed to make the body (i.e. the Church) function! Paul shows how ludicrous it would be for the foot to say to the hand it did not belong to the body. "But in fact God has arranged the parts of the body, every one of them, just as he wanted them to be. If they were all one part, where would the body be? As it is, there are many parts, but one body." - 1 Corinthians 12:14-20 Violating the unity of the body only happens when the diversity of the body is denied! Calvin would have known that, and the parallels that can be drawn with the church worshipping God together musically are striking.
Calvin was not a person gifted in art or music, as was Luther, and that appears to account to a major extent for their different approaches to music in the congregation.
Unfortunately, Calvin was not motivated to promote a legitimate use of
music. And unlike Luther he did not require would-be-pastors to pass a
musical test before they could be accepted for ministerial training.
That Luther did, and because his young men went on to start and to
pastor churches all over Germany, and then throughout much of Europe,
partly explains the early and rapid proliferation of the Lutheran
style of music when no such comparable development took place among
the Calvinist churches.
However, in the article from which the above two quotations are taken, it only says Calvin took a firm stance against the use of musical instruments for Psalm-singing. It does not say he took a stand against vocal harmonies amongst the singers in the congregation. There is only that one tiny sentence where singing in unison is mentioned, which is not the same as saying harmonies were disallowed, or even discouraged.
On that point the observation might be worth making that, anywhere in the world where a few people get together and sing, harmony singing will be lacking amongst those who are fairly musically illiterate. It takes a certain minimum standard of musical knowledge, training and appreciation to get several people to sing harmoniously, in parts. If a congregation has never learned how to do that, it will take a brave individual indeed to start singing harmonising notes the congregation has never heard before! Usually, the more unmusical a congregation is, the more likely they are to feel comfortable sticking to unison singing. That may have more to do with the lack of harmony singing in some congregations than anything Calvin might have said centuries ago about the matter!
The second and third quotes are to be found in http://thirdmill.org/newfiles/joh_barber/PT.joh_barber.Luther.Calvin.Music.Worship.pdf from the Reformed Perspectives Magazine article by John Barber, PhD, 'Luther and Calvin on Music and Worship' (Volume 8, Number, 26, June 25 to July 1, 2006). This article is full of references to other related sources, so I recommend you search it for more information.