The discussion in the comments on the previous post brought about the present post. Here is a different approach to notating the first page of my Scherzo for piano.
As with the previous version, I have not fine-tuned the slurs, aligned everything properly, etc. This is just a draft, so don’t jump all over me, you connoisseurs of fine notation. The point is that I tried it with tuplets instead of dotted 32nds when there are four notes in the time of three sixteenths. Of course, this is quite reasonable, and it would work out OK. I’m not sure it is actually an improvement, but it would work fine. The spot that makes me nervous, and the kind of thing that led me to use dotted notes, can be seen in bars 5 and 6 where there are plain 16ths and tuplet 16ths against beat units of different lengths. (There is more of this type of thing later in the piece.) The dotted 32nds make a more immediate distinction between the durations in these two measures. It does help that I broke the sixteenths of m. 5 into four groups of two instead of two groups of four, but the notes still look too similar to me. The tuplets do get rid of the slightly bizarre looking dotted 32nds, I suppose that is a good thing. But it doesn’t strike me as a compelling reason to change.
I didn’t change the dotted 16ths in m. 12 - I suppose if I went with quadruplet 16ths I should write duplet eighths to be consistent, no?
One thing I did change in this version is definitely an improvement - the right hand in m. 8 now reflects the 3+3+2 beat units suggested by the left hand - before I had two eighths and a sixteenth for the high f-sharps. This is better.
I’d be interested to hear from readers with their thoughts on this, especially if any of my pianists are reading this.
Of course, if the dotted 32nds in the scherzo bug you, I imagine you won’t care for this page from a piece I wrote for the Prism Quartet:
Doing this page with dots lets me vary the length of the beat unit. Besides, it was exciting to write a measure of 27/32 time.
James Primosch, composer 
As the person who suggested 4-tuplets, I agree that mm. 5-6 clearly demonstrate the drawbacks; to me it’s not so much that the groupings look similar as much as the fact that we’ve temporarily lost the 3/16 pulse that generally makes the 4-tuplets more semantically natural to me. That said, I just tried tapping it out and didn’t have a problem.
But I may be an outlier in that I almost always prefer tuplets (up to 4) to seeing everything written out in the lowest common denominator. I feel like it helps me understand what the piece is doing better than laboriously counting out one-a-and-a’s.
I agree that if you went this way, the left hand in m. 12 should be duplet eighths.
With the quartet example I don’t mind it as notated (and it’s not really possible to notate the second measure as tuplets anyway because of the ninth note) but I would certainly think of it as “four in the time of three” while playing it.
Thanks, Dan. I agree, no matter what the notation, “four in the time of three” is definitely on my mind whether the passage is actually notated as a tuplet or not. I certainly wouldn’t expect somebody to be counting 64th notes in my passages written in dotted 32nds.
Your comment brings up an interesting issue - what is the relationship between how we notate something and how performers conceptualize it - how they count something. I’ve heard about a pianist who totally re-barred the Boulez 2nd Sonata so as to make it more “countable”. When I played Crumb’s Music for a Summer Evening in grad school, the professor conducting it had us draw in barlines everywhere. Could anyone hear a difference in performances working from scores where the notation had been altered in these ways? Music is a three-way dialog among composer, performer and listener, but when the performer and listener are one (arguably the case in much of Bach’s keyboard music) is changing the notation of greater significance? (Are you ready to play the WTC in the original clefs?)
I wish I had asked Don Martino what he meant when he wrote a pair of tied sixteenths instead of an eighth note in the midst of a quintuplet of eighth notes on the first page of the Fantasies and Impromptus. (The quintuplet is not over a barline, which would require ties from one measure to the next). However, the tied sixteenths are marked with a marcato and a staccatissimo wedge, in contrast to the marcato and tenuto on the preceding and following notes. He wants you to get off the tied sixteenths early - yet sustain the chord? Of course, this is happening at high speed, with five quintuplet eighths to a half note = 40 beat. It’s perhaps like those spots in Schumann where he writes staccato dots, but with pedal - perhaps a performance indication more than a sonic one?
I tried to reply to this but I think it didn’t go through, perhaps because it had links in it, so I’ll try again without them:
Morton Feldman’s “Triadic Memories” is a good example of a piece that is perversely tupletted. I don’t have the score on me so I don’t remember if it lasts the whole piece or just for one section, but you can see the first page if you do an image search for “triadic memories score” - it’s all 4-in-the-time-of-3 where the underlying 3 pulse is completely virtual; it serves no function other than to make the pianist’s life more difficult. (Of course there are many pieces whose time signature’s “pulse” isn’t audible because the rhythms are so complicated or abstract, but this example strikes me as particularly perverse because it’s so unnecessary.) I wonder whether pianists who perform it try to keep that “virtual 3” in their heads or effectively renotate it from 3/8 to 4/8.
I once had to renotate a part of Evan Ziporyn’s to make sense of it for performance. It two competing simultaneous pulses in a 3:2 ratio. He wrote the more fundamental pulse of dotted quarters so that his counter-pulse could be in regular quarters, but when the pulse got subdivided down to things like dotted 32nd notes I just couldn’t take it anymore, and rewrote it to be in quarters with the counter-pulse in triplets (even though they didn’t always come in multiples of 3). You can hear it by searching for “ziporyn amok” and going to the artofthestates page (the section I’m talking about is Part 2).
My recollection is that the particular perverse notation to which you refer at the beginning of Triadic Memories only goes on for a few pages - but then there are other issues…
If anyone reading this has played Triadic Memories, please comment on how you approached the piece.