A couple of weeks ago I played with some new musicians, and one piece we tried together was Joy, which I had notated in 3/4 time. Of course the pianist sight-read it as a waltz, and it was very much the wrong feel! I played for her how jaunty the melody should sound, and she got it — heard that it was almost more in 2 beats per measure rather than 3. She suggested I notate it in 4. I could hardly wrap my mind around that leap, from 3/4 to 4. However, I was also suffering from bad brain fog from the second vaccine (I realized afterwards!).

When I was able to focus this morning, I realized that yes I go back and forth every other measure — first measure is in 6/8, next measure is in 3/4, for almost the whole piece! So the lightbulb went off in my head, why not notate it in 12/8? And then do the beaming of the eighth notes in the pattern of 3,3,2,2,2. And once I looked up how to do that in Sibelius I was able to make that transformation, and even find a measure that was very difficult to play the melody against the harmony line because I had not followed that pattern exactly, so I changed the melody. Aha!

 Here's the first few measures originally:

And here's the re-written version in 12/8

Can you see the difference? Each measure of the 12/8 version contains 2 measures of the 3/4 version. But after playing the 12/8 version a bit to try to get used to it, I realize I'm missing the very clear emphasis on the first beat in each 3/4 measure. 

So I've come to the conclusion that really this piece uses serial polyrhythms -- instead of two contrasting rhythms being played against each other, the 2 contrasting rhythms are played one after the other, by both parts together.  I suppose the "correct" way to notate this is to actually alternate the measures, but I don't think that is a very good solution; it is not practical for sightreading or even for ultimately understanding the piece.

For me, the 3/4 time signature says something wonderful about one of the pulses that is important (the downbeat of the measure), and the alternating internal subdivisions of the measure add another critical feature. Why can't I have both?

Please let me know in the comments!