I'm sure the subject line alone is fodder for a lively debate.  It has
recently been a source of heated discussion between me and many other
parties online, with there being very few on my side.  I think that 2/3,
4/5 etc.  are all legitimate time signatures, although they are only useful
in mixed time.  A piece written entirely in 2/3 would sound exactly the
same if it were written in 2/2.  However, can't you mix, say, x/3 time
with, say, 4/4 time? For example, if you want to alternate measures of 4/4
time with a measure or measures which have 2/3 the time-value of a whole
note, and there are two beats, each having the value of a triplet half
note.  I can quite clearly hear in my head what this rhythm would sound
like, and I find it rather interesting.  The only other way to notate that
I see would require a change in tempo marking between measures.

Any comments? Can anyone cite specific examples of (preferably classical)
music wherein there is a denominator in the time signature that is not a
power of two (of course, one=two to the zero power).  I heard there are
examples in Varese and Stockhausen, but that's all I've heard.  Clearly
conventional notation is a bit inadequate here, but I don't see why it
can't be bent a little.  2/6 time would have two "triplet" quarter, or
"sixth" notes, in it, so just write them as quarters.

It is interesting that conventional notation has been shown to fall short
in even simpler cases.  Bernstein's "Tonight" ensemble number, in West Side
Story, it seems to me, posed him a tricky problem:  He wanted six beats in
the measure, with the accent on 1, 3, 5.  Using quarter notes as a unit of
measurement, 3/2 has this pattern, but only has three half-note beats; and
in 6/4, the accents go on 1, 4.  As a solution he wrote it 4+2/4, hardly
conventional.

Michael Cooper
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