I've been messing around with simple 2-part rounds recently, and also with modulation. The question occurred to me, can a round modulate? Initially I though not, since it would involve having parts in different keys playing against each other. However, maybe this could work musically, or at least the same notes could serve different roles in different keys so that it might somehow work out.
Any thoughts on this? Any examples of simple two part rounds which contain modulation?
It can be done, and in the hands of a good composer, it could be done well.
Using the loosest definition of "modulation", this round moves between C major and G major (or, at least, between two pitch centers), but since the moves are "in sync" (each has two measures of C followed by two measures of G), there's no problem.
Of course, in addition to the questionable claim of modulation, there's also little semblance to staying within the rules of tonality (e.g., parallel fifths).
Here the modulation isn't debatable, but the aesthetics might be. For the sake of discussion, we all love bitonal music, so this round presents no problem for us.
It is assumed without proof that we could create a round in which one part is always resting while the other is singing.
It is also assumed we could create a similarly trivial example via serialism.
A better definition of modulation is there there should be a cadence in the new key, so let's at least require a leading-tone-to-tonic motion. Also, let's stay with the spirit of the question, which seems to presume familiar tonality.
This is by no means a "good" round, but it at least demonstrates the possibility of modulation — again, if only on the fairly trivial side of things. Here, as with the first example, the modulations are "in sync", so there's no concern about being in two different keys simultaneously.
Again, the spirit of the question seems to presume different tonal centers, but there are definitions of "modulation" that admit shifting between major and minor within the same key, as the below example does.
Let us assume without proof that we could create a round that alternates non-trivially between C major and A minor, for example.
The above examples support a sort of proof-of-concept idea of rounds in two keys simultaneously. But, as stated, the spirit of the question seems to be
Can there be an "interesting" round that 1) follows the rules of tonality, 2) doesn't delve too deeply into chromaticism, and 3) has parts simultaneously and unambiguously in two different key signatures.
Yes. Here is an example of how this might work. I've chosen the keys of C major and A major, because they share (enharmonically) a leading-tone diminished chord. This allows for simultaneous modulation in both keys (and even opens the door to a four-key round).
disclaimer: I am no composer.
Yes, it can be done, but mostly in a pretty limited way. I have written a simple canon for you that is in C and modulates to A minor and back to C.
Somewhat surprised that nobody has mentioned Bach's modulating canon (the "Canon a 2 per tonos", inscribed with the allegorical Ascendenteque Modulatione ascendat Gloria Regis [With ascending modulation ascends the King's glory]) from the Musikalisches Opfer (BWV 1079): not exactly a typical "round", but it does have the essential characteristics; in that it includes two voices (the third plays an independent line based on the theme on which the whole volume is based on top), which are playing the exact same thing (albeit a perfect fifth apart): [only beginning pictured]
So that's an example. Of course, its fairly doable to compose an actual strict round (with both voices playing the exact same thing) which does this too. Here's one (starting in G minor and modulating, like Bach's, by whole tones):
