Now, I am not asking for the general answer given in band class ("The top number tells how many beats are in a measure; the bottom number tells what note gives the beat"). I'm more asking what it is and by what concept is it defined. My thoughts are:
A time signature is the "feel" of the song. For example, in most songs that are 4/4, there is a drum pattern. It starts with the bass, then the snare, then bass again and snare again. It creates a pulse; that pulse is called a "beat". If someone were to cut a song into pieces, which are, in a sense, equal, the way that makes the most sense is by dividing it into this pattern. Since the pattern consists of 4 parts, in this time, the song would have 4 beats per pattern. Other songs, however, have different patterns and those patterns are what define the measure, what gets the beat, and how many beats each measure has.
Is that correct?