[limey]

SN - you're looking at only one half of the information which defines "time" in written music. The time signature (3/4, for example) tells you how many beats there are in a bar. 3/4 is a waltz time so you'd count, giving each beat an equal length in time, but stressing the first beat
ONE two three ONE two three ONE two three ONE two three ...
The "tempo mark" for this waltz example would be shown as the symbol for a quarter-note = 180. This means that there are 180 quarter-notes in a minute, or (coincidentally) one bar is one second long.
You could play the music much more slowly, but then it would be difficult to dance to . It might become a lovely lyrical tune, instead ...

Originally Posted by squirell nutkin

So can a measure be empty of notes?

Yes. This would represent a set period of time (defined by the time signature and the tempo mark) in which that voice or instrument does not make a noise.

Originally Posted by squirell nutkin

Wait, let's say we're singing "do re mi fa so la ti do" That's eight notes.
How many measures is that? or Bars?

The eight notes you have named are the names of note pitches, how high or low they sound. They do not in your example given above have any rhythm or time value assigned to them.

Originally Posted by squirell nutkin

So, if in 4/4 time, there'd be 1,2,3,4 1,2,3,4 1,2,3,4 and in those four beats how many of the notes get sung?
And in 8/4 time there'd be 1,2,3,4,5,6,7,8 1,2,3,4,5,6,7,8 and the same number of notes get sung as in 4/4 time, just more beats?

The emphasis would be slightly (ever so slightly) different in the two examples you have given
1,2,3,4,1,2,3,4,1,2,3,4
vs
1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8
I've taken the spaces out as the beats are regularly spaced in time. The time signature shows where the emphasis should fall.
I have no idea if this is helpful at all ...