When given any sheet of music without the time signature and you are given the choice of 3/4 and 6/8, how would you know which one would be the appropriate choice?
This question provides a nice complement to Does 3/4 time signature differ from 6/8?. The linked question addresses the "feel" of 3/4 vs. 6/8; the present question addresses the difference in notation.
3/4 as 3 beats per measure; 6/8 as two beats per measure
In terms of single beats, a typical measure of 3/4 time would contain three quarter notes:
X: 1 T: 3/4 time in whole beats M: 3/4 L: 1/4 K: none C C C | C C C |
On the other hand, 6/8 time would contain two dotted quarter notes:
X: 1 T: 6/8 time in whole beats M: 6/8 L: 1/4 K: none C3/2 C3/2 | C3/2 C3/2 |
3/4 has duple subdivisions; 6/8 has triple subdivisions
The expected subdivision of a beat in 3/4 is by the 1/2-beat (i.e., three groups of 1/2-beats)
X: 1 T: 3/4 time subdivided M: 3/4 L: 1/8 K: none CC CC CC | CC CC CC |
The beat is 6/8 time is expected to be divided into 3 (i.e., two groups of three beats)
X: 1 T: 6/8 time subdivided M: 6/8 L: 1/8 K: none CCC CCC | CCC CCC |
In this way, 6/8 is rather more like 2/4 time that 3/4 time. 6/8 contains two beats, like 2/4, but it contains six eighth notes, like 3/4.
3/2 and 6/4 are a bit harder to tell apart, since they contain the same number of quarter notes, so there's no beam to assist in visualizing first-level subdivisions. The better clue is in the use of half notes versus dotted half notes.
X: 1 T: 3/2 vs. 6/4 M: 3/2 L: 1/2 K: none CCC | CCC | [M: 6/4] C3/2C3/2 | C3/2C3/2 |
This question was originally closed but I lobbied for reopening and posted a comment with the info below. Since it was reopened I’m converting my comment to an answer.
It all comes down to grouping of the notes. 3/4 is simply 3 quarter notes but 6/8 is two groups of 3 eighth notes each within an bar and shows an imaginary bar line between beats 3 and 4. In terms of 8th notes 3/4 is 3 groups of 2 and 6/8 is 2 groups of 3.
If you are trying to identify a time signature based on music written with no time signature look for the way the notes are grouped within the bars. If you see quarters and pairs of 8th notes beamed together it’s probably 3/4. If you see groups of three 8th notes and notice that the fourth 8th note of every bar is visible you’re looking at 6/8.
The same basic premise applies to 3/2 and 6/4 except with longer note durations, quarters and halves.
Depends how well it's written!!
I've seen both written wrongly, and it's only when it's performed that the choice is made.
The whole point of the differences has been aired many times - 3/4 is a bar split into 3, 6/8 is a bar split both into 6 and 2 almost simultaneously.
Returning to my opening gambit - if there are six quavers written in a bar, but none of them joined, then it's down to how the emphases are timed. And that in itself may not give an answer. In 3/4 there should be emphases on 1,2,3, whereas in 6/8 they'll come on 1--4--. However, even that isn't enough. 'America' (WSS) is proof of that...