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I'm starting to learn Music Theory and I don't really understand time signatures.

Let's say we have time sig 3/4, so one beat is 1/4, means one 1/4 note is a beat, or a 128th of a Minute at 128 BPM.

So now let's say we have time sig 6/8, so one beat is 6/8, means one 1/8 note is a beat, or a 128th of a Minute at 128 BPM, right?

So is the denominator of the time signature really purely notational? Because in booth examples the timing is exactly the same, as long as you change all the Notes to have half the value. So why would you even bother to change the denominator if the timing stay exactly the same, but just the notation of the notes change?

  • The thing throwing off your understanding is mistaking a time signature for a fraction. 6/8 is a compound signature and compound signatures is where you learn time signatures aren't fractions. – Michael Curtis Dec 30 '19 at 14:34
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There have been many questions here concerning the compound time signature of 6/8. It's not an easy one to explain simply (it's compound..!) and even harder to understand.

Let's get back to your 3/4. Yes, straightforwardly, it's a bar with 3 beats in, each worth a quarter (one crotchet), so is called simple time. Try not to get bogged down with how many seconds a beat is going to last for - it's unhelpful and pretty well impractical from a playing point of view. Better to set your metronome and play along with one click per beat (crotchet).

Now 6/8 can be seen as 6 mini-beats of quavers, but that's only one way of regarding it. And because it's called compound, it has another angle. Two beats of a dotted crotchet - which makes up the same amount of time, note-wise and in reality.

If you really want to stick with timing in seconds, usually, the tempo for 6/8 is given as the time for one dotted crotchet - of which there are two in each bar. So if the bpm is 120, then one whole bar will last one second. It's more simple to look at the timing this way. But the only folk who use a stopwatch for music are film makers, who need the music to sync with the images. Players tend to count, and keep to a prescribed tempo - as in bpm.

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As Tim said, 6/8 is complicated, and there are more questions on it here. I would note that in general a tempo indication should indicate what durational value in the notation that it is referencing. In 6/8, that's usually a dotted quarter (or dotted crotchet, for those outside the U.S.). However, I've definitely seen tempo indications for 6/8 given for the eighth note or even (very rarely) for the dotted half.

That is, at the top of your score, there should be some indication saying, "Dotted quarter = 128" (usually a little version of a dotted quarter note, rather than writing the name out). Or "eighth note = 128" or whatever.

As for the reason that the dotted quarter is almost always seen as the primary "beat" in 6/8, it's because of a whole history of music notation that we don't need to get into right now. Suffice it to say that in music, from the earliest days of rhythmic notation, it seems groupings of beats into 2s and 3s were most popular. And subdivisions of beats into 2s and 3s were also the most popular. (4s could also be seen as twice 2, but 5s and higher numbers weren't part of the groupings.)

Hence, we have a system of time signatures where the beats are divided into two parts (so-called "simple time"), like 2/4, 3/4, and 4/4, which have 2, 3, and 4 beats per measure, and where each quarter note beat can be broken into two eighth notes.

And we have a system where the beats are divided into three parts (so-called "compound time"), like 6/8, 9/8, and 12/8, which have 2, 3, and 4 beats per measure, and each dotted quarter note beat can be broken into THREE eighth notes.

All other standard time signatures generally contain only these six numerators (2, 3, 4 or 6, 9, 12), with a different denominator to indicate the relative size of the pulses.

In sum, please do NOT think of a time signature as "the top number is the number of beats and the bottom number is the note that gets the beat." That's wrong, despite the fact that many music beginners are taught that, due to teachers attempting to oversimplify things. For time signatures with a top number of 5 or bigger (particularly the standard numbers of 6, 9, and 12), there are usually some other groupings of smaller note values that are felt as the "beat."

So why would you even bother to change the denominator if the timing stay exactly the same, but just the notation of the notes change?

That's a separate question: why would you write 2/4 with quarter note tempo at 128, but you could also write 2/2 with half note at 128 or 2/8 with eighth note at 128? The brief answer is that yes, they are all basically equivalent notations, so there's some redundancy. (The longer answer has to do with historical practice: certain styles of music tended to be notated in 2/2, while others were in 2/4 or 4/4, etc. But most of those distinctions are less important in modern music.)

As for the difference between 3/4 and 6/8, the basic difference is explained above, but there are a bunch of other questions here on that exact topic. It has to do with whether you group the eighth notes into 3 beats of 2 eighths, or group them into 2 beats of 3 eighth notes.

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  • I think of 6/8 more as a triplet 2/4 than an eighth note 3/4. Then it makes total sense to think of 9/8 as a triplet 3/4 and 12/8 as a triplet 4/4. In fact, when I play Chopin's Nocturne in Eb Op. 9 no. 2, I subconsciously count it as triplets in 4/4 instead of eighth notes. – Caters Nov 30 '19 at 22:26
  • @Caters - I'm not sure I see the difference in counting in groups of three eighth notes, whether they are "triplets" or not -- they are still three eighth notes to a group. The only difference is that if you think of them as "triplets" they don't accord with the rest of the notation, as three triplet eighth notes add up to a quarter note, not a dotted quarter as they do in 6/8, 9/8, or 12/8. – Athanasius Dec 1 '19 at 17:25
  • But, think of it this way, Chopin could have easily written his Nocturne in Eb Op. 9 no. 2 to be in 4/4 and the dotted quarters would turn into quarters and the eighths would turn into eighth note triplets. The tempo in BPM wouldn't change at all if Chopin wrote it in 4/4 instead of 12/8. This, this is where I get the 12/8 = Triplet 4/4. And thinking of 12/8 as a Triplet 4/4 saves me having to count eighth notes individually as beats for those time signatures that are prime(in other words can't be equivalent to any quarter note time signature) such as 5/8 and 7/8. – Caters Dec 1 '19 at 17:54
  • @Caters - I understood your comparison. But the key thing is that the eighth note are NOT beats; that was part of the main point of my answer here. In 6/8, the primary "beat" is on the dotted quarter note. Textbooks that say the eighth note is the "beat" in 6/8 are wrong (to explain why, I'd have to go into a long historical discussion of how meters like 6/8 and 6/4 evolved): you should be counting only four beats in the Chopin piece, as that is the number of beats in a 12/8 bar. – Athanasius Dec 1 '19 at 18:11
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You've been offered explanations of Simple Time (beats split easily into 2) and Compound Time (beats divide easily into 3). A rather complex topic! I suggest you don't look for TOO much logic in it, just, for now learn that 4/4 is four quarter beats, 6/8 is two dotted-quarter beats etc. Worry about 5/8 and 7/8 when you encounter a piece that uses them.

You actually asked about durations. And the simple answer is - yes by choosing a suitable BPM any note can have any duration. And composers HAVE written music where a 16th was a pretty slow note, or a whole note pretty brisk.

But there's more to music than durations. There's where the barline comes, where the BIG beats occur. After two beats, after three...? Is it a waltz or a march?

I suggest, as always, that you don't try to get 'theory' all sorted out in the abstract. Play music, read music. When something arises that you don't understand, THAT'S when that bit of 'theory' will be useful. Otherwise you'll be like all those beginners who learn about the notes in the C major scale and the chords that can be formed from them, then think those are the ONLY notes and chords that are 'allowed' without changing key.

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