Originally Posted by: dlwalkeBut in 3/4 time, 3 quarter notes don't add up to 1 even though they also take up 1 measure.[/quote]

Right, but that's because the 4 indicates the type of note that gets one count. It indicates what type of graphic symbol to be read as 1 count in the measure.

Originally Posted by: dlwalkeSo is the choice of the lower number (if its not a fraction I guess its not really a denominator) at least a little bit arbitrary?

Not really. Certain choices might be interchangable. There might 2 different time sigs that give the same aural result.

But this is more about the composer (or transcriber, the person writing the music notation) trying to capture the rhythmic pulse of the music. As a rough linguistic analogy, you could say basically the same things 2 different ways.

1. The guitarist struggled to understand the difference between 2 time signatures.

2. The guitarist had a hard time comprehending how 2 different time signatures were different.

Both sentences convey the same meaning, but using slightly different words & orders, & possibly stress points.

[quote=dlwalke]What i mean by that is if you had a piece of music that specified 80 bpm and it was in 4/4 time and another piece of music that specified 80 bpm and it was in 4/8 time, wouldn't they sound exactly the same (assuming that all the note values were halved in the 2nd piece of music).

Yes, they could sound exactly the same. But a piece of music might be written one way or the other in order to indicate how the performer should be counting the notes, or thinking of them as they phrase the music.

4/4 has 1/4 notes counted 1-2-3-4. This leaves a lot of subdivision space for 1/8th & 1/16th notes.

4/8 has 1/8th notes counted 1-2-3-4 with less space for subdivisions!

A practical example would be a song in which the music is in 4/4 for a while & the melody might have some 1/4 notes mixed with 1/8th notes. But then mixed in the middle of a phrase or at the end of phrase, there might be a series of 4 1/8th notes that add up to 2 beats of music that have to get indicated in order to make a seamless whole. So the perform knows how to play right through all those changes & make it sound smooth & connected.

So, the composer or transcriber uses 4/4, but then switches to 1 measure of 4/8 to indicate this change, then back to 4/4 again. Makes sense?

Most pop & rock music doesn't have to consider these factors. The tunes are in one sig & just keep trucking right through to the end in the same sig. But some music is more complex & makes wider use of time sigs. Some classical, jazz, & in my personal experience, Broadway musicals do this often. That's because there is frequently the need of matching music to dialogue or choreography. So other time sigs really help make difficult things or complex rhythmic ideas easy to indicate, understand & play.

Hope this helps!