In a time signature of 3/4 (three by four), what is the name given to the
3 and the
4? I know it in my own language, but can't find the answer for the English equivalent.
The entire symbol that defines the meter of a measure of music is called a time signature.
To my knowledge, English does not have specific words to refer to the top and bottom numbers, though some people may use the words 'numerator' and 'denominator', respectively, as if it were a mathematical fraction. I do not recommend this (since time signatures have nothing to do with fractions).
If I needed to give names to the top and bottom numbers I would call them 'measure length' and 'subdivision quantifier,' but usually it's not necessary to do this--or at least, we have enough other ways in English to talk about musical meter and the time signature that it's not necessary to refer to those numbers directly.
If you really need single words, I'd recommend 'count' and 'quantum'. If it isn't obvious which is which, then this is a bad suggestion.
There are no specific names, although that would be nice. The numerator is beats per bar. The denominator is the note duration of a beat. So 3/4 means 3 beats per bar, where quarter note is a beat.
Also, although tempo is specificed in beats per minute, it actually means QUARTER notes per minute. Even if the beat is not a quarter note per the time signature.