What can one do to understand time signatures?

Question

I am struggling with the basics of Time Signatures. For one, I see it as more of a 'beat' signature. Notation is old, and time signatures are of an age where there was no clock, or way of keeping time (metronome).

The main reason I can see as to why I do not get it is that:

I fear you have to have a mathematical brain? It would explain why I am struggling to understand and count beats within a bar.

Back to my question, what can one do (what exercises can one do) to understand time signatures?

Resources online are good, but they do not explain it if you are struggling. Instead they continue to then talk about key signatures.

I do understand the following:

• The first number (on top) tells you how many beats there are in a bar.

The second

• What kind of beat is given one note.

This is agreed yes, but if I am still struggling when reading music to understand if there are the correct beats within a measure what else can I do?

Answer 1

True, the top number tells how many beats per bar. The bottom tells what sort of notes each beat is.

In 4/4, for instance, the top 4 says there will be 4 of the bottom 4. That bottom 4 says that each beat, or pulse, will be worth a crotchet, or quarter note. Be aware that nowhere here tells how fast or slow the piece will be played, that's not the purpose. So with no metronome mark or bpm stated, it could be played at whatever speed the player decides.

In 3/4, there will be 3 crotchets per bar, so the count will be 1 2 3 1 2 3, or if there are shorter notes, it may be easier to read counting 1+2+3+1+2+3+, the numbers being counted at the same speed in both cases, but again the speed is not mentioned.

There is no need to struggle to understand if each bar will contain the correct quota - it just will !! It has to . That's why the time sig. is put at the beginning!

If you like, it could be called a 'beat signature', it's not a bad title, although there's no need to change its name, as it does explain the timing, which really has nothing to do with how fast the piece is played.

In 3/8, there will be 3 quavers (1/8 notes) per bar, as the 8 represents quavers. These can be seen as lasting half as long as the aforementioned crotchets, BUT since the actual duration of a crotchet isn't specified within the time sig., it can only be construed that all the notes in the piece will be shorter than in 3/4, thus making it a quicker piece. But no-one can say each beat is half as long, simply because no-one can say how long a crotchet is. I think that's the crux here. Unless we're told how long a beat is (bpm),then we can play the piece at whatever tempo we want, within reason. But - the whole point is that each bar will contain its proper sum of beats, as per time sig., and each bar will be played at the same speed as any other bar in that same piece.

Incidentally, metronomes have been around for over 200 yrs, and clocks a darned sight longer. But neither would be that helpful in explaining time sigs...

Answer 2

Top number: 'how many', bottom number: 'of what?' is half the answer. But it's more complicated than that. When the top number is greater than 4 it will normally be divisible by 3 (6/8, 12/8) and the 'beat count' is the number of '3-groups'. 6/8 is two beats to the bar, each group consists of three 8th notes. 9/8 is three beats, 12/8 is four beats... Then we have time-signatures that indicate a mixture of 3- and 2-groups. 5/8 or 5/4 is a 3-group plus a 2-group (and there's nothing in the time signature to tell us which way round, and it may keep switching! You have to look at the note groupings.)

And none of the above is exhaustive, or immune from exceptions.

Yes, it's complicated. And it's really nothing to do with having a metronome available or not - they just help you keep in time once you've worked out how many beats there are and what the metronome should be set to!

Sit down with your teacher, use music that you are actually working on as examples. This sort of thing is much better demonstrated than explained. Don't worry too much about a Unified Theory of Time Signatures, just learn about the music you're currently reading.

Answer 3

As you have said, the top number tells you how many beats are in each measure. The bottom number tells you the duration of each beat. Multiplying the two numbers in the time signature tells you the total duration of a measure.

To reinforce this, practice translating the time signature into the appropriate music notation. How would you notate the duration of one beat? How would you notate the number of beats? You might find it helpful to make charts like this one:

When I am just beginning to practice something, I like to approach it systematically at first. I would write out the beat duration and number of beats for 2/2, 2/4, 2/8, and 2/16. Then I'd do it again for 3/2, 3/4, 3/8, and 3/16 (see image above). Then I'd do it again for 4/2, 4/4, 4/8, and 4/16. Once you get the hang of this, you can mix up your practice (e.g., do 3/2, 2/4, 5/16, etc.).

Another way to quiz yourself is with flashcards. Here are two flashcards you might have:

As you can see, this forces you to recognize the time signature even when some of the beats are subdivided.

But if you start subdividing, there's something to watch out for. Imagine taking a measure of 3/4 and subdividing each quarter note into two eighth notes. This gives 6 eighth notes:

How would you distinguish this from a measure of 6/8? After all, they both contain six eighth notes. The answer is in the beat emphasis/grouping. By convention, 6/8 groups the beats this way:

The first beat in each group is stronger (S), meaning we emphasize that beat. The other beats in each group are weaker (W), meaning we don't emphasize them as much. For more on conventions of beat groupings/emphasis, check out this post. The short version is: time signature with 6 beats, 9 beats, 12 beats, or any other higher multiple of 3 are "compound" meter. This means we break up those beats into groups of 3. By contrast, "simple" meters (2/2, 2/4, 3/2, 3/4, 3/8, etc.) generally break up beats into groups of 2.

Answer 4

I think you already understand the theory behind time signatures, but that you are having trouble with all the exceptions that occur in practice. As Laurence Payne writes, "Top number: 'how many', bottom number: 'of what?' is half the answer". The only thing that a time signature denotes with any degree of reliability is the notated length of all the notes in a single bar added together. For example, in a 4/4 you know that all notes in that bar (in a single voice) add up to the same length as 4 quarters (or a whole note). (And even for this seemingly trivial statement there are counterexamples.)

According to the how-many-of-what-system, you should count 4 beats in a 4/4 bar (we would call this "counting in 4"), you should count a 3/4 in 3 and a 6/8 in 6. In practice, however, it doesn't work this way. For starters, 6/8 is virtually always counted in 2 (and a 9/8 in 3, etc). This has a historical justification since these meters are related to time signatures in mensural notation (music notation in the renaissance) and were later used as shorthands for triplets. But this shouldn't have to be a problem; we could call it an exception to the rule (as many theory books do) and be done with it. But the next thing that happens in practice is that some pieces are fast. This means that sometimes it makes more sense to count a 4/4 in 2, or a 3/4 in 1.

When it comes down to it, you should use the time signature to derive the grouping of the notes in a bar (2+2+2 eighths in a 3/4, but 3+3 in a 6/8, for example) and the appropriate downbeats. When you get more comfortable with music notation you will see that at a certain point it doesn't particularly matter how you count internally as long as you preserve the grouping and downbeats; sometimes you need to be aware of all eighth notes in a very slow 3/4 to keep the tempo, sometimes a piece is so fast it doesn't make sense to count as many beats as indicated by the time signature.

To experience this I would advise the following, and I hope this will resolve your doubts about time signatures. Listen to a lot of music, trying to count along, then check the time signature in the sheet music, see if it matches what you thought and if it surprised you listen again, trying to count as the time signature would suggest. Probably, if you were surprised by the notated meter, there is an obvious problem with counting as the meter would suggest (in most cases either too fast or too slow).

If you try my advise, don't expect you will learn to tell the meter of each piece (because, without knowledge of the type of piece, the style of the time the piece was written and the style of the composer it can be impossible to tell). The point of this exercise is for you to see how what you hear relates to what is written (in terms of time signatures). Each time you are surprised by the notated meter is a win.

Answer 5

I think you should distinguish between meter and time signatures. Understand meter first then the time signatures used to represent meters.

Musical meter can be understood as an abstract mathematical idea.

Time signatures are the product of centuries of notation development. As a system they are inconsistent and involve exceptions to rules. But, the good news is that in normal practice there are a small number of common time signatures.

---

Meter

Meter is a regular pattern of accents. Logically it needs at least 2 units so that something is accented while some other thing is not accented. The next larger group of units will be 3. All larger groups can be divided into combinations of just 2 or 3. Sorry for that digression, but it's musically relevant to understand the significance of 2 and 3.

• Meters using a division of 2 are called duple.
• Meters using a division of 3 are called triple.
• Meters using combinations of 2's and 3's are called additive. Example, a meter based on 7 could be broken into groups like 2+2+3, 2+3+2, or 3+2+2. Let's gloss over questions like a count of 7 with only a single accent.

Regardless of how a meter is notated in written form aurally it will conform to this breakdown into groups of 2 or 3. Of course, music may not conform to a regular meter and it would be called un-metered.

---

Time Signatures

Time signatures are the traditional way to indicate meters in a score and they aren't consistent.

The main inconsistency, however, involves groups of 3. If you get a handle on the time signatures involving 3, the rest should be fairly straight forward.

While meters and time signatures can be classified as duple or triple, they are also classified as simple and compound. Strictly speaking duple/triple tells the number of accents (beats) per measure while simple/compound tell the number of subdivisions of the beat. Subdivision of the beat by 2 is simple and subdivision by 3 is compound.

Regarding the top number of the time signature:

• if it is a power of 2, the meter is duple and simple
• if it is divisible by 3, it is triple, and simple or compound
• if it is prime, it is additive

Notice how the terminology gets jumbled together right at the start of reading the time signature! And the line for "3" more complicated than the other two.

We can untangle the complications by falling back to the abstract metrical concept of 2 and 3 and finding where the accents (beats) are placed and how beat subdivision is handled. The practical way to illustrate it is by comparing the time signatures 3/4 and 6/8.

Numbers like 6 and 12 can be divided by either 2 or 3. From a metrical perspective we could think of them as ambiguous compared to a number like 8 which cannot be divided by 3. Let's examine 6. It could be grouped two ways (angle bracket shows the accent/beat)...

>     >     >
|  |  |  |  |  |

...or...

>        >
|  |  |  |  |  |

I deliberately made abstract figures above and did not indicate the time signatures. Again, the idea is first understand the abstract pattern, then understand the time signature.

The traditional time signature for 3 beats subdivided by two is 3/4...

The traditional time signature for 2 beats subdivided by 3 is 6/8...

The eighth note beaming indicates the beat.

Time signature conventions are...

• Simple and triple is 3/4
• Compound and duple is 6/8

If we wanted to state rules, it would be something like...

• upper numbers that are powers of two or the number 3 are simple
• upper numbers that are greater that 3 and divisible by 3 are compound
• upper numbers divisible by 2 and 3 could be compound or reduced and re-beamed to become simple meters
• upper numbers that are prime are additive meters
• the lower number of a simple meter indicates the note type used for the beat
• the lower number of a compound or additive meter indicates the note type used to subdivide the beat, the number of beats per measure being the upper number divided by 3 for compound meters or some division of the upper number by 2 or 3 for additive meters.

...logical rules get unwieldy, because the time signatures follow conventions not rules.

We could notate rhythms with beaming and accents that contradict those conventions...

...or...

...mathematically we have the correct number of notes, but either we are accidentally contradicting the conventional placement of accents, or technically we are using the rhythmic device called hemiola.

---

In the two sections above the meter part is straight forward while the time signature part is a confusing mess of two counting systems.

Instead of trying to handle time signatures with pure logically, just follow conventions.

When the top number is: 2, 3, or 4 it gives the beats per measure, is simple meter, and and the lower number indicate which note type gets the beat. Subdivide the beat by 2 or 4.

When the top number is: 6, 9, or 12 it gives total subdivisions of the beat per measure, is compound meter, and the lower number is the note type used to subdivide the beat into groups of 3 typically it will be an eighth note.

When the top number is one of the primes: 5, 7, 11, or 13 it gives total subdivisions of the beat per measure, the meter is additive, and the lower number is the note type used subdivide the beat into unequal groups of 2 and 3.

A practical list might be...

Simple

2  3  4  3  2  3
4, 4, 4, 8, 2, 2

Compound

6  9  12 6
8, 8, 8, 4

Additive

5  7  11 13
8, 8, 8, 8

The list above isn't exhaustive and additive or changing time signatures can be written differently. Like this for 7/8...

3+2+2
  8

But, there are only about a dozen common time signatures. It may be easiest to just memorize how they are classified and practice counting them.

...I am still struggling when reading music to understand if there are the correct beats within a measure...

If the score is notated correctly, you don't need to worry about this. Try to focus on counting the time (either out loud or silently in your head.) The only case I can think of to worry about having the correct beats per measure is proof reading a score.