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Originally Posted by Don
Uhuh, I just like showing my intellect, I knew you had some sorta reason. Btw, I think if n = 2 or 4, that's actually not compound time.
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I couldn't resist the urge and just HAD to look it up. Compound time (to quote Wikipedia, which gave the fullest definition... once again) "gets its name by combining two or more simple meter measures to form a compound measure"... and that "Today when we refer to compound meters, we refer only to the 'compounding' of two (or more) simple triple measures." So its only 6/8, 9/8, 12/8 and other multiples of 3/8 which fit the description now.
So yes, you're completely right about n = 2 or 4, and would have been right with a load of other numbers too... 5/8 isn't a compound time now either.
I was always told compound meant quaver-beat based. Its a sad day when you realise that your music teachers were lying the whole time.