Making that distinction is Augustine's purpose for writing The City of God. There are many places where the nature of the earthly city is compared to that of the heavenly one. It would be misleading to see the matter as being addressed fully in a single place.
Your example of "music lovers" doesn't capture the tension between the two cities that is demonstrated by the different kinds of association they rely upon. In Book 19, you will find the following:

"This heavenly city, then, while it sojourns on earth, calls citizens out of all nations, and gathers together a society of pilgrims of all languages, not scrupling about diversities in the manners, laws, and institutions whereby earthly peace is secured and maintained, but recognizing that they all tend to one and the same end of earthly peace."

Thank you! That makes perfect sense. Do you happen to know if Augustine used this particular terminology? Did he ever explore the explicit dichotomy of society VS community? If he did so in the City of God, where in the City of God did he do so?

Thanks again for this response. I didn't get a notification of a response and only just now saw it.

You did not get a notification because I wrote my comment before I knew how to use the swoopy arrow that appears when the cursor hovers over the post one wants to respond to. I see that you, too, have not used the reply function to answer me.

I have not read The Dyer's Hand (I plan to, someday) so I don't know the context or exact phrasing of the distinction he is making. I would say that distinguishing "society" from "community" is a modern development where the word "society" went from meaning a club or fellowship in the 16nth century to becoming a form that includes all "people being with people" in a general sense as developed since writings such as Rousseau, Hobbes, and Locke analyzed what are the elements of political structures. In that sense of the word, I don't think a distinction of the kind you ask for is expressed directly in Augustine. I would love to be corrected on this score if I am wrong.

In the passage I quoted, Augustine speaks of a "society of pilgrims." Think of it as a club whose members have dual citizenship; They sojourn within the earthly city but also participate in the heavenly one. Now among the citizens of the earthly city, there are institutions that tend toward peace upon different principles than those embraced by the pilgrims. Drawn as a Venn diagram, there is an overlapping region of shared ends. But the means to those ends are at odds with each other. The pilgrims are working on changing why the good thing comes into being.

City of God by Augustine is a great read. I hope you do read it! I agree with Valentinus. It's a huge work and would be impossible to take a piece here and there. It is done, of course, as Valentinus did it :-) But the work is seamless and Valentinus summed it up quite well with , "It would be misleading to see the matter as being addressed fully in a single place."

Valentius, you were so helpful last time around, I think I'll bother you with another Augustine quote from W. H. Auden's The Dyer's Hand. Auden quotes Augustine as saying (I paraphrase) that if we know the good and do not do it, soon we will cease to know the difference between good and evil.

I don't trust my paraphrase of Auden's paraphrase, so I'd like to identify the original quotation (Auden has no footnotes). Does that ring a bell at all? Any idea where I might find that in Augustine's works?

You are still not using the reply function. I just happened to see this.

Can you quote Auden's paraphrase?

O.k., I begin to suspect that I was conflating two different passages in my fading memory, one by Augustine and the other by C. S. Lewis.

"Let him do anything but act. No amount of piety in his imagination and affections will harm us if we can keep it out of his will. As one of the humans has said, active habits are strengthened by repetition but passive ones are weakened. The more often he feels without acting, the less he will be able ever to act, and, in the long run, the less he will be able to feel."
- C. S. Lewis, The Screwtape Letters, Letter 13

"If, when a thief stole money, he lost an eye, everybody would say that it was a punishment of God. Yet; you have lost the eye of your mind and you think that God has not punished you."
- Saint Augustine, In Ps. 47

Lewis is quoting Joseph Butler's The Analogy of Religion, but the passage does seem to have an echo of what Augustine said.