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When trying to find out the time signature, the first thing you do is try to find a strong beat. This beat is often the loudest or something significant will happen on the beat. Next, you count the rest of the beats in a bar before the next bar starts, so if you count 3 beats it might be in 3/4, or it might be in 4/4 if you count 4 beats ect.
You can think of the time signature as describing the length of the bar as a fraction of a whole note. Let's use American (whole note, quarter note etc.) names. It helps in explaining time signatures! 4/4 is 4 X quarter note. A 4/4 bar adds up to a whole note.
For example, in a 120bpm tempo, are note durations of 4/4 time-signature different from 2/4 time-signature? If in both cases the quarter note = 120 bpm, then no - the duration is the same. Time Signatures such as 4/4 are used for notation.
Conducting can go up to 7's, 9's and even 11's. It can sometimes fall to a conductor to conduct in more than one time signature at the same time. So it can be necessary for a conductor to get creative. There are, however, a number of set rules:
A time signature is a device we use when notating music that makes it easy to see where in the meter each note falls. The composer/engraver should choose the time signature that matches up with the music in the cleanest way. People will insist that certain beats will be stronger with certain time signatures.
The note values are relative only (as currently used.) A signature such as 4/2 could have any speed. Often there will be a notation like QN (the symbol) = 120 or the like. The number refers to beats per minute. A few hundred years ago, the time signature did more imply a tempo (or tempo range).
And generally speaking, any time signature is divisible into 2s, 3s and sometimes 4s. 7/4 might be, for example, 12 12 123. One other thought - when these odd ones are written onto sheet music, the better writers will group notes like quavers into their own little 'joined up' bits, like 6/8 should be two lots of 3 quavers.
Sample YouTubes by signature: 2/4. Bamboleo, by Gypsy Kings. 3/4. Bulerias by Paco de Lucia. 4/4. Garrotin. 3/8. Cepa Andaluza by Paco de Lucia, a buleria. 6/8. Percusion Flamenca by Paco de Lucia. Generally, bulerias and sevillanas are 3/4 time; rumbas are 4/4. Disclaimer: my ex was a flamenco dancer and I never throw books out.
It's not a fraction. It's a time signature. Time signatures evolved from fractions. The fractions were applied to the mensuration signs that survive now only as 𝄴 and 𝄵. (No, the symbol 𝄴 does not come from the first letter of "common.") In the French Baroque, time signatures such as 2 and 3 were common.
However as time progressed, it seems the antiquated 3 was replaced by 3/4, which is a sort of one-size-fits-all time signature in that it can accommodate both 'whole' and 'half' time feel. Take four cases (I'm using Bach cello suites as examples because they are based on dances as was the done thing back then, and also because they're awesome ...