NOTATIO

I think that the problem arises because tuplets replace fewer real notes of the same note value: 3:2, 5:4, 7:4 9:8 halves, quarters, eighths etc.

but 2 is special because it is the numerical factor that defines the note values. For this reason, 2:1 can't follow the same value both in duple ( 2 : 1 ?!) and triple meter (2 : 1 ?!) since two quarters can't replace 1 quarter and two dotted quarters can't replace 1 dotted quarter. And 2:3 eighths breaks the fewer rule.

So a compromise must be found for duplets. Some "round" the dotted quarters to eighths and some to quarters.

My vote:

C when there are two beats/measure since 6/8 could be considered an alternate way of writing 2/4 with the tuplet numbers suppressed and dots added to the quarter and half notes.

B when there are six beats/measure since it is perhaps more fitting for 2 quarters to replace 1 dotted quarter.

E is correct for all cases, since tuplets are not involved.

AFAIK, C is the correct version of tuplets.
In simple beats, tuplets are extended upward (toward smaller values), while in compound beats, tuplets are extended downward (toward larger values)---until both meet the regular value.

In his book Modern Rhythmic Notation Gardner Read did a survey of 200 compositions from the late-19th to mid-20th centuries and found a 52% chose my A (his B), 17% chose my B (his A), and 31% wrote it out with dots instead of tuplets (my E after David's suggestion, Read's F).
None of the 200 that he surveyed from that time period used a 4:6 16th note tuplet (his C or E, my C or something else)! Now maybe he overlooked certain composers or cherry-picked the data, but it seems like use of a 4:6 16th note tuplet in 6/8 is a fairly recent case, if it is to be used at all.

Thanks, FredGUnn. That makes compete sense.

All those surveyed are observing the "tuplets replace fewer real notes of the same note value" rule and making the exception only for the duplet, which is the rule followed by Arnstein.

However, I would be very tempted to use C in situations like the following which are analogous to 2/4 (as shown by the first example) and appear more natural to me than B or A:
I was surprised by the number that used E, since it used to be thought esoteric.

Despite the apparent prevalence of A in the literature, a logical problem with this notation occurs to me. Suppose an eighth note quadruplet is used to indicate a whole measure of 6/8 as in Rachmaninoff’s Suite no. 2:
We now have an eighth note quadruplet indicating both a half measure and a whole measure of 6/8!

Fred G. Unn wrote: ↑23 Aug 2025, 19:14 In his book Modern Rhythmic Notation Gardner Read did a survey of 200 compositions from the late-19th to mid-20th centuries and found a 52% chose my A (his B), 17% chose my B (his A), and 31% wrote it out with dots instead of tuplets (my E after David's suggestion, Read's F).

Interesting survey! Good find.