Assessing the time signature of a single measure
Is it possible to tell the difference between a single measure written in 3/2 time vs 6/4 time, when looking solely at what is written, with no audio available?
For example, consider a measure which consists of the following notes:
halfnote, halfnote, quarternote, quarternote
If I'm asked to fill in a time signature, are both answers correct? And if so, are they equally correct? or should I be looking for clues as to which answer is better?
Edit: Thanks to the editor for fixing my errors. I still had intervals on my mind when typing the question. :)
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Summary
In your example, the notes create a rhythmic grouping of 2+2+[1+1]. Fundamentally, these notes divide the measure into three primary beats. That quality is sufficient to qualify the rhythm as 3/2 and not 6/4, because the convention is that 6/4 divides the meter into two primary beats of 3+3 whereas 3/2 divides the meter into three primary beats of 2+2+2.
Meter in General
A song written with 6 beats could be broken into different groupings. You could group the beats 2+2+2 or 3+3. The groupings tell us where the strong/primary beats lie. 2+2+2 implies that there are three primary beats (occurring on 1, 2, and 3), and each primary beat has 2 sub-beats (1 & 2 & 3 &). A grouping of 3+3 implies that there are two primary beats (occurring on 1 and 4), and each primary beat has 3 sub-beats (1 2 3 4 5 6). (In fact, when counting 6/4 time, many feel it like this: "1 and uh, 2 and uh.")
This difference has a name: simple meter vs. compound meter. Simple meter divides the primary beats into two sub-beats. Compound meter divides the primary beats into three sub-beats. This difference is how we will determine what the meter is in your example.
But there's a second important characteristic of any meter: how many primary beats the song has.
duple refers to meter made up from two primary beats
triple refers to meter made up from three primary beats
quadruple refers to meter made up from four primary beats
We can combine these two qualities of the meter:
As you can see by looking at the table above, meters written as 6, 9, 12 (and any other higher multiple of 3) are, by convention, compound meter. Meters written in 2, 3, or 4 are, by convention, simple meter. We need a way to distinguish the two, and this is the convention we've created to achieve that goal.
Your Meter Is Probably 3/2
Music tends to emphasize the primary beats. This is evident in how the music appears, sounds, and feels. So in 3/2 time we would expect notes to fall on beats 1, 2, and 3 because those are the primary beats. But in 6/4 time, we would expect notes to fall on beats 1 and 4 because those are the primary beats.
As the top picture shows, your notes line up perfectly with the primary beats of 3/2. By contrast, as the bottom picture shows, your notes barely line up at all with the primary beats of 6/4. This suggests that the rhythm is probably in 3/2, because music tends to emphasize the primary beats. It's not impossible for music to emphasize the upbeats--it's just less common in many forms of music.
To summarize, here's the first big consideration we've just looked at: which beats does the rhythm emphasize? But there's a second consideration: how the music is actually notated. Music is often notated so that the primary beats aren't hidden. Technically, there are actually two ways to annotate your example:
The top picture shows where beats 1, 2, and 3 are, whereas the bottom picture is written to specifically show where beat 4 is. If we saw the bottom notation, we would think "oh, beat 4 is being shown, so it must be a primary beat. This music is probably in 6/4." So the fact that your rhythm is notated like the top picture (and not like the bottom picture) suggests 3/2 rather than 6/4.
Your example is clearly in 3/2. It is grouped as three half-note beats. 6/4 would be grouped as two dotted-half beats. (The first naming is intuitive, the second just a convention.)
As with so much of music theory this is a framework, not a 'rule'. If it's established that the pulse is 'three-in-the-bar' (3/2) it's perfectly allowable to notate a syncopated 'two-in-the-bar' against it. Playing a 6/4 rhythm against an underlying 3/2 is a very different effect to changing into 3/2 completely.
But, if this is a 'theory exercise question', don't get too clever. It's 3/2.
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