On the difference between 4/4 and 4/2 time signatures [duplicate]

Question

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.

Answer 1

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).

Answer 2

The difference is more academic. A long time ago, 4/2 was more prevalent, perhaps in slower pieces, but the /2 doesn't have to signify slow. It will all depend on the tempo of the piece, obviously.

4/4 has become the mainstay for pieces in 4 time, but occasionally it's easier to write and read if 4/2 is used - it saves writing very small value notes, as those will be twice as big in 4/2 as in 4/4.

By doubling or halving the tempo marks, 4/2 and 4/4 could be played at the same speed, so there's an easy solution there.

Answer 3

Simple answer: You can't hear the difference. The only difference would be how the music looks on the page.

To elaborate phoog's comment: tempo indications are given not just as a number but also as a note value, like "quarter note equals 120." So in fact a quarter note—at "quarter = 120"—is exactly equal to an eighth note at "eighth = 120"... and to a half note at "half = 120." You can "call" the beat whatever kind of note value you want. The listener just hears the pulse; unless they're also reading along in the score, they have no way of knowing what note value it represents (aside from a few educated guesses).

So why might a composer choose one value or another? Well, those educated guesses are about what's most common. The quarter note is most often the beat. For meters that divide the beat into three subdivisions, it's most common to use the eighth note to indicate these subdivisions, giving time signatures like 6/8 or 9/8 (even though the real "pulse" is then a dotted quarter). If you're listening to music from the Renaissance or very early Baroque, there's a good chance the beat (tactus) is represented by a half note because of the way rhythmic notation was still changing. In modern practice, it would be rare to choose the half note, but conceivably if you had a whole lot of very short notes, it could make the music more readable to print fewer "beams" on them (e.g. for notes that divide the beat into 8 parts, they could be printed as 16th notes instead of 32nd notes). This would probably be more confusing than helpful, though.

Answer 4

No, there isn't any information such as 'a quarter note normally takes X seconds' and so on. That's why there are metronome marks or tempo expressions (Andante, Allegro etc.) written on scores. You 'split' a given time into equal sub-parts. Imagine splitting a cake. So 4/4 means you split a given time period into 4 quarter notes and the metronome mark or the tempo expression on the score determines how much time a quarter note should/must ('must' if there is a metronome mark on the score) take. If the metronome mark is 'quarter note=90' then the time lapse between two metronome pulses which are in '90 bpm' speed is the answer for the question 'how long a quarter note must be in this piece/song?'. Subsequently, an 8th note will be 2 times faster and so on.