Re: Music Temo Question..
First, tempo and time signature are not the same, at all! You can have a very fast song in 4/2 with 200 BPM or conversely a slow song with 60 BPM in 2/8 timing.
With that said, we will begin with time signature of 4/4. The top number denotes how many beats are in the measure. In this case, 4. The bottom number denotes which note gets the beat. In this case, the quarter note. So, in 4/4 there are 4 beats per measure and the quarter note gets 1 beat. 3/4 timing which has a waltz feel, has 3 notes per measure and the quarter note gets the value of 1 beat. Just to illustrate time signatures here are a few more:
Simple Meter has beats divisible by 2
Simple Duple - 2 beats per measure
2/2 - 2 beats, half note gets one beat
2/4 - 2 beats, quarter note gets one beat
2/8 - 2 beats, eighth note gets one beat
Simple Triple - 3 beats per measure
3/2 - 3 beats, half note gets one beat
3/4 - 3 beats, quarter note gets one beat
3/8 - 3 beats, eighth note gets one beat
Simple Quadruple - 4 beats per measure
4/2 - 4 beats per measure, half note gets one beat
4/4 - 4 beats, quarter note get one beat
4/8 - 4 beats, eighth note gets one beat
Compund Meter - simple meters multiplied by three
Compound Duple - 6 beats per measure
6/2
6/4
6/8
Compound Triple - 9 beats per measure
9/2
9/4
9/8
Compound Quarter - 12 beats per measure
12/2
12/4
12/8
Complex Meter - sums of simple and coumound meter
Quintuple Meter - 5/4
2/4 + 3/4 or 3/4 + 2/4 depending on secondary accents
Septuple Meter - 7/4
3/4 + 4/4 or 4/4 or 3/4
Now, to cover BPM. Beats per minute how fast the aforementioned notes occur.
As I mentioned before, any key signature can be fast or slow depending on the tempo measure in BPM or MM (metronome Marking).
It can get really complicated from here, but I think this should clear it up for ya. If you need to know more, just post your question and I will reply.