Steven Schwartz wrote:

>No. Although there are half-notes and quarter-notes, there's no such
>thing as a "third-note." Think about it.  What's the notational symbol
>for it? If you're talking about the "numerator," however, there are lots
>of examples, some of them quite famous.

Mr. Cooper is referring to the following situation: suppose a piece is
going along in 4/4---four regular quarter notes per measure, and then the
composer wants a measure that lasts the duration of 2 quarter-note triplets
(or 4 eighth-note triplets).  What notational symbol could he/she use for
this? I don't know if the x/3 notation would work, but perhaps something
like the time signatures that Orff and Janacek used, where the numerator is
a digit and the denominator is a note.  In this case the composer could put
2/[quarter-note triplet] then switch back to 4/[quarter note] when desired.
As for precedence of this, I know Stockhausen has done things like this in
Klavierstuck XI and XII (I believe) and in some other pieces.  I think even
Messiaen wrote something about this when talking about non-retrogradable
rhythms, which sometimes become extremely difficult to notate, especially
when several such rhythms are layered on top of one-another.

Thanks,

Marcus Maroney
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