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Intros where it's hard to find the "1"

9/8 or 9/4 are the same, it's just a question of whether you call the basic pulse an eighth note or a quarter note. The top number is significant, the bottom one really isn't. And neither of them can really tell you how to split things up (although other aspects of notation can give a clue).

John McLaughlin notated Celestial Terrestrial Commuters in 19/8 by the way. He could have used 19/16, not really a scrap of difference. From a notation point of view, there is no absolutely "correct" time signature for any piece of music, it's all down to convenience. You could write out Billie Jean in 11/8 if you wanted, but it would be a bugger to sight read. Your computer would play it perfectly, though.

From a real world point of view, then there is more often than not a definite pattern that should be reflected in the time signature top value, but the bottom value is really a matter of preference and ease of communication in most cases.

Anyway, back on topic...

I must disagree entirely.

The difference between 7/4 and 7/8 is quite noticeable since they are entirely different counts.

Just to write it out, 7/4 is:

1 and 2 and 3 and 4 and 5 and 6 and 7 and 1...

7/8 is:

1 and 2 and 3 and 4 and 5 and 6 and 7 1...
 
Holy crap! 432 bpm! That's insane!
But you could say Billie Jean was 468 bpm if you wrote the time signature 16/16. The numbers and time signature only really tell you how it's been written out and there's some choices involved there, even if the choices are dictated by convenience and musical common sense (as you already mentioned).
 
I must disagree entirely.

The difference between 7/4 and 7/8 is quite noticeable since they are entirely different counts.

Just to write it out, 7/4 is:

1 and 2 and 3 and 4 and 5 and 6 and 7 and 1...

7/8 is:

1 and 2 and 3 and 4 and 5 and 6 and 7 1...
Er... no. Sorry, this is just plain wrong. If something's written in 7, all the beats are the same length, regardless of whether it's 7/4 or 7/8. The way you've written that, the last beat of your 7/8 is a 16th (half as long as all your other 8th notes).
 
Sorry man, but you're the wrong one here.

Try writing Pink Floyd's 'Money' in 7/8 or Rush's 'Tom Sawyer' (the bridge/solo section) in 7/4 and let me know how well that goes for you.

Sorry, man... You are wrong on this one.

If the unit is a quarter note OR and eight note, it's still only counted as 1.

7/4 and 7/8 would be counted exactly the same way. They'd be written using different notation but the count is 100% the same. 7 beats, (x) gets counted as 1.
 
You know what, you're right Bill. Although I would never tell someone the bottom number doesn't matter because the way in which you count something can make a difference on the feel and ease of reading a piece.
 
I must disagree entirely.

The difference between 7/4 and 7/8 is quite noticeable since they are entirely different counts.

Just to write it out, 7/4 is:

1 and 2 and 3 and 4 and 5 and 6 and 7 and 1...

7/8 is:

1 and 2 and 3 and 4 and 5 and 6 and 7 1...

I'm not sure whether you have the right idea in your head or not, but what you have written hear is definitely wrong.

The first example you wrote was 7 beats (not enough info to guess the beat length) and the second is 13 or whatever.

7/4 and 7/8 in the same tempo would compare more like this:

|1 + 2 + 3 + 4 + 5 + 6 + 7 +| 1...
|1 2 3 4 5 6 7 1 2 3 4 5 6 7| 1...
 
I'm not sure whether you have the right idea in your head or not, but what you have written hear is definitely wrong.

The first example you wrote was 7 beats (not enough info to guess the beat length) and the second is 13 or whatever.

7/4 and 7/8 in the same tempo would compare more like this:

|1 + 2 + 3 + 4 + 5 + 6 + 7 +| 1...
|1 2 3 4 5 6 7 1 2 3 4 5 6 7| 1...

That's right.