I am new to music theory and I was going through this video on YouTube to understand time signatures. The author mentions that the top number indicates number of beats. I understand what this means. My confusion is with the bottom number (as is rightly pointed out in the video as being most confusing for author's students too). It is mentioned that the bottom number indicates the value of each beat. For example, 4/4 indicates that there are 4 quarter notes per bar. 4/8 indicates that there are 4 eighth notes per bar. Now to my question. Since the terms 'quarter note' and 'eighth note' are relative (in the sense that a quarter note in 120 bpm is exactly as long as eighth note in 60bpm), is there a standard tempo that these are all referenced to?
Please excuse me if my understanding is completely wrong. I will be most happy to correct it from your suggestions.