One of the great ways that music illustrates conversation is through counterpoint- multiple independent moving lines that when put together create something greater. As Daniel Barenboim explains in this Youtube link, musical conversation is different than human conversation. If we tried to continuously talk over one another it would just be noise. In counterpoint multiple lines speaking at the same time create something much more expressive. Here are a couple links to different examples of pieces where the composer used counterpoint to create something truly divine:
Mozart’s Jupiter Symphony, Movement Four Beethoveen’s String Quarter No. 14 in C# Minor
You cannot talk about counterpoint and not mention J.S. Bach! Here is one his most glorious pieces, the Dona Nobis Pacem from the Mass in B Minor. This is an example of a fugue, where each voice starts out presenting the same theme and then creates counterpoint around that original theme.