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I've learned that 4/4 means 4 beats with the kind of beat being a crotchet. However, I've seen pieces with that time signature that don't just use crotchets, but minims, quavers, etc. I am still a beginner in music theory, so there's a lot I don't know, and I've not seen anyone ask this question anywhere, which is making me feel dumb.

I know that a semibreve has a time value of 4, minim 2, crotchet 1 etc. I just don't understand the purpose of the bottom number in the time signature. For example, 4/4 is telling me the crotchet is the kind of beat, but crotchets don't need to be used. At this point I'm starting to ignore the bottom number and only rely on the top number (number of beats) as that seems to be the only thing that matters rule-wise.

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  • Has anyone posted an answer where the "bottom number" is not a power of 2 yet? – Judy N. Dec 12 '20 at 21:00
  • upvoted to 19, and it's a duplicate question – Michael Curtis Dec 16 '20 at 22:34
  • @JudyN Adam Neely has a really good video on “irrational” time signatures – Cole Johnson Dec 17 '20 at 18:12
  • @JudyN. In traditional notation it is not possible for the bottom number to be anything other than a power of two. That possibility only arose with the experimental avant guard of the 20th century. – phoog Jan 9 at 23:05
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To put it very simply, the bottom number tells you what the top number is referring to. It is a little clearer to use the fractional way of discussing notes, so:

  • minim = half (1/2) note
  • crotchet = quarter (1/4) note
  • quaver = eighth (1/8) note

So a measure of 4/4 has four quarter notes (4 x 1/4) and a measure of 2/2 has two half notes (2 x 1/2). Technically, the measures both contain the same number of quarter notes, but the measures will be counted differently as ttw described.

But the bottom number does not always equate to the beat. It just tells you what the top number is referring to. So you can have music in 5/4 with five quarter notes per measure and music in 5/8 with five eighth notes per measure, but these measures will each have a different number of beats - usually 5/4 will have five beats and 5/8 will have two beats of unequal length.

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    "the bottom number does not always tell you the number of beats in a measure": in fact, it never tells you that. – phoog Dec 11 '20 at 4:39
  • @phoog Thank you. I have clarified my answer. – Peter Dec 11 '20 at 4:59
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    And I'm not sure that 6/4 will have six beats; it's more likely to be two (like 6/8) albeit a bit slower. What may be worth pointing out is that 6/4 and 3/2 are not the same thing at all. – Andrew Leach Dec 11 '20 at 12:20
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    Okay so I'm as guilty of this as everyone else in this thread (and starting to doubt my position as a result of it), but/so -- can anyone actually turn up an example of 6/4 in the wild? I'm kinda starting to think that this is such a rare time signature that any normative comment about its interpretation is, uh, lacking a real norm. – Esther Dec 11 '20 at 23:16
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    @PeterSmith Brahms Piano Concerto No.1 first movement and Chopin Prelude Op.28 No.13 are also two examples in 6/4. – Divide1918 Dec 12 '20 at 14:06
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You're nowhere near the first, and won't be the last, to be mystified by the numbers shown on time signatures. Maybe they started off rather like fractions - and still look like that, but the numbers are only part of the picture.

As in other answers, the bottom number tells what the denominations are, while the top tells how many of each is contained in each bar. So far, so clear. As in 4/4, the denomination is the crotchet, or quarter note, exactly as it would be in a maths fraction. And the top number (numerator), tells that there are four crotchets per bar. That's perhaps where the confusion starts. There doesn't have to be four crotchets - anything which amounts up to their equivalent is good - two minims, eight quavers, one minim and one crotchet and four semiquavers, or any other of many combinations - as long as they add up to equivalent of those four crotchets.

3/4 works the same way - there are three crothets (1/4 notes) or equivlent in each bar. Often called 'three quarter time', for good reason. Although I've never come to terms with pieces that don't have any full bars in them, if you understand what I mean!

So far, so good. Then it starts to go awry. Most beginners consider that 3/4 and 6/8 are the same. Yes, and no! True, they work out exactly the same mathematically, but music is more than maths. There had to be a way in which to signify a particular rhythm that went 1 2 3 4 5 6. It couldn't be counted like 3/4 time, as there were six 'beats', or 'sub-beats'. So the top number would be 6. 6 what? Quavers, which then made the bottom 8. Hence 6/8. To me (and my students), it's more of a code that says 'think Humpty Dumpty' (an English nursery rhyme in that rhythm). 12/8 has a similar problem/solution.

So, that bottom number simply tells what sort of notes each bar is going to contain, the top one telling how many of them there will be (or equivalent). There aren't that many different time signatures used regularly, so it may be a good idea just to treat each as its own case, and work from there. Then when 5/4, or 7/4, or 9/8 come along, work them out individually too.

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  • haha, I more consider 3/4 to be the same as 3/8 and not 6/8. Once I realized that this is true (after seeing some songs written e.g. in both 2/4 and 2/2), I finally understood what the time signature really is. – yo' Dec 11 '20 at 13:22
  • @yo' - that is a good way to regard it! – Tim Dec 11 '20 at 13:23
  • Please write a book, Tim! – cmp Dec 11 '20 at 14:10
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    @ColeJohnson - if it ain't broke, don't mend it. But if it's music, go with the flow. We're powerless...I stopped looking for complete logic decades ago. Thus I'm only half insane - at the moment! – Tim Dec 17 '20 at 18:37
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    @ColeJohnson in fact, as this answer implies, time signatures did originate as fractions describing the relationship between the note values and the tactus, so 3/2 was 50% faster. Faster than what? The fraction was applied to the mensuration sign, which could be a full circle or a broken circle (which looked like a C, giving rise to the symbol that many believe incorrectly to denote "common time"), and which could have a dot inside it or a slash through it (giving rise to the symbol that people associate these days with "cut time"). The logic we use today developed during the early baroque. – phoog Dec 17 '20 at 18:42
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The denominator represents the note that would get a single beat. In 4/4 time, there are 4 quarter-notes (or crochets) worth of time in a single measure. Although the measure is 4 crochets long, any notes that add up to the correct length are fine. The measure could have 8 eighth notes (8 quavers) or 2 minims or 1 semi-breve or 3 quavers plus a crochet and three more quavers.

In simple time signatures (4/4, 3/4, 3/2, 2/4, 3/8...) the lower number gives the pulse-unit and the upper number gives the number of such units in a measure. It helps to organize the music (it's easier to think of 4 objects than 47 objects, usually). There is an implied accent on the first beat of 2/4 and 3/4 and an implied light accent on the beat 3 of a 3/4 measure. This becomes important with other time signatures. All this is has been historically developed. For example, 6/8 not only means 6 quavers in a measure but also signifies that these are grouped into two groups of three. (Mostly I mention this to show that 3/4 is not equivalent to 6/8.)

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    A bit concerned about 4/4 having '3 quavers, a crotchet and 3 more quavers'. True, a lot is written like that now, but it's better if 4/4 bars can be seen to have two halves. A lot of us understand what you meant, but a beginner? Just being pedantic! – Tim Dec 11 '20 at 8:44
  • When using the word denominator for the number below, I think one can use the word numerator for the number above. In fact, a time signature with 3 as upper number and 4 as lower number means a 3/4 measure, which literally means that each bar fits notes and pauses which sum up to 3/4, as in a fraction. – rexkogitans Dec 11 '20 at 9:16
  • Your 1st para.: in 6/8, the 8 doesn't really represent a single beat. It could, but often a dotted crotchet does instead. Trouble is, there's no denominator for dotted crotchet... – Tim Dec 11 '20 at 13:26
  • @rexkogitans - those terms can be used, although the numbers don't really mean those words as it's not maths. Although funnily enough, here we all are, typing them as fractions! – Tim Dec 11 '20 at 13:28
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The bottom number may be thought of as the unit of measure, while the top is the measurement. Changing the bottom number (for example from 3/4 to 3/2) is analogous to changing a distance from 3 mm to 3 cm. The number of units is the same, but the size of the unit is different. With time signatures, however, it is a factor of two rather than a factor of ten.

for example 4/4 is telling me the crotchet is the kind of beat, and yet crotchets don't need to be used.

Suppose you're covering a tear in a sheet of paper with adhesive tape. The total length of the tear is 4 cm. That doesn't mean that you need to use four 1-cm pieces of tape to cover the tear! You can use any combination of different lengths of tape as long as the sum of all the lengths is 4 cm. Similarly, when the time signature says that a measure has a total duration of a 4 crotchets, that means that the notes (and rests) in the measure must sum to the same duration as four crotchets.

It may be that time signatures are a bit more intuitive if you use the American system (which we got from German music teachers) wherein a semibreve isn't worth 4 but 1 (a "whole note"), and a crotchet isn't worth 1 but 1/4 (a "quarter note"). You can still ascribe these values to the notes even if you continue to call them by their traditional English names.

At this point I'm starting to ignore the bottom number and only rely on the top number (number of beats) as that seems to be the only thing that matters rule-wise.

That is a fairly reasonable way to approach it, but the bottom number does have useful information. Time signatures that are mathematically equivalent when considered as fractions do specify the same total duration of each measure, but they are not equivalent because they also give information about how the measure is organized.

The clearest example of this is 3/4 vs 6/8. In both cases, a measure filled with quavers would contain 6, but in the first case, they would normally be grouped in three groups of two, while in the latter case they would be in two groups of three.

Another example is 4/4 (often given as C) as opposed to 2/2 (often given as C with a vertical line). In both cases, a measure full of quavers has 8 of them, but in the first case, if you're tapping along with the music you'd tap four times in each measure, on every other quaver, and in the second case you'd tap at half the rate, twice in each measure, on every fourth quaver.

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  • So why not call it the German system? – mirabilos Dec 14 '20 at 2:13
  • @mirabilos I suppose it is because English speakers are most commonly exposed to the system through its use by Americans. – phoog Dec 17 '20 at 18:45
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The textbook answer I always received was, "The top number tells you how many beats per measure, and the bottom number tells you what value note receives one beat." So 3/4 time means "three beats per measure, and a quarter-note receives one beat." That tells you that each measure will contain three quarter-notes or the equivalent thereof.

From my point of view as a hobby musician (I don't read music very well), I look at it this way: The top number gives you the rhythmic feel of the song, which is generally the most important thing to know. The top number can (theoretically) be any integer, but the most common ones are 2, 3, 4, 6, 8, and 12. Occasionally you'll see other numbers, such as 5, 7, and 9. There's a Wikipedia article that lists lots of songs with unusual time signatures, with "unusual" most often defined in terms of the top number.

The bottom number is more about how the composer chose to write the actual sheet music, in conjunction with the feel given by the top number. If the composer found it easier (or more explanatory) to write most passages using quarter-notes, the bottom number will more likely be a 4. If eighth-notes better suit the composition, the bottom note will be an 8. It's largely a judgement call. Sometimes composers will write in unusual time signatures as an exercise, and sometimes an unusual time signature will be used to add an extra beat (or two or more) to a phrase. Both of these cases can be seen in the above-linked Wikipedia article.

Often I will try to reverse-engineer a song without referring to the original sheet music. The most frequent variable I've encountered when doing so is whether the bottom number is a 2 or a 4, but I've also found some variability between 4 and 8. There can also be ambiguity about the top number: I've sometimes thought a song was in 2/4 when it turns out to have been written in 4/4. I've also sometimes thought a song was in 3/4, 6/8, or 12/8, only to find that it's written in X/4 time, with lots of triplets. (A triplet is when a note's time is divided into three notes, usually written as three barred eighth-notes with a small number 3 above or below the bar. Think of the "merrily, merrily, merrily, merrily" part of "Row, Row, Row Your Boat.")

But another very important factor is something the OP didn't ask about: the tempo notation. On sheet music you'll often see, at the top of the piece, a quarter-note followed by an equal sign followed by a number, as shown here:

enter image description here
This gives us very firm guidance on the tempo of the song: 90 quarter-notes (or 90 beats) per minute. You can set that number on a metronome and you'll know that you're at the tempo the composer wanted. But nearly as often, you'll just see a verbal description of the tempo, such as "Moderately," "Brightly," "Quickly," or some such. Most classical compositions use Italin words to describe the tempo, such as "Andante," "Presto," "Lento," and so forth. Classically trained musicians develop a feel for what each of these means, but there are also guidelines available through a simple online search.

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You can think of the time signature as describing the length of the bar as a fraction of a whole note.

Let's use American (whole note, quarter note etc.) names. It helps in explaining time signatures!

4/4 is 4 X quarter note. A 4/4 bar adds up to a whole note. Fill it with any combination of whole, half, quarter, eighth notes (or rests) that you like, as long as it all adds up to a whole note.

3/4 will add up to 3 X quarter note. 6/8 will add up to 6 X eighth notes. But remember, that doesn't mean there MUST be 6 X eighth notes in each bar, just notes and rests that add up to that. Remember those 'how many ways can you make up a dollar from coins' questions at school? Same idea. And yes, I'm sure you just noticed that 3 X quarter notes and 6 X eighth notes add up to the same thing. Read on...

Now, it can get more complicated than a simple count-up. We use both 4/4 and 2/2 time signatures. Both add up the same. Two halves or four quarters both add up to one whole. And you'll see both 3/4 and 6/8. Both add up the same. And I'd love to be able to tell you that 3/4 means three quarter-note beats in the bar, 6/8 means six eighth-note ones. But 6/8 is actually TWO beats in the bar, two groups of three eighth-notes each.

I can't throw this all at you in one post and expect you to understand. Get a music rudiments textbook and work through it from the beginning. Most of all, PLAY music written in different time signatures. You can't learn notation apart from playing it. Would be like learning the letters but never reading a book!

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The bottom number is a naming convention: in n/4 you decided to consider the "basic note" (not an official term!) to be a 4th note (crochet), in n/8 you decided that to be an 8th note (beaver). But other than that, 4/4 and 4/8 are basically the same thing.

The only information the composer gives in the bottom number is some (rough) idea about how heavy the "basic note" is: you'll hardly have all 8th notes heavy even if it's the basic note, but it's completely expected for a half note (minim) to be heavy. But that's already a feeling you might have.

The top number is how many of the "basic notes" you count in each bar. And there are some common conventions (non-strict conventions!) considering how "basic notes" and "beats" compare:

  • 2/d and 6/d is commonly 2 equally long beats (unless 2/d has only one beat per bar)
  • 3/d is 1 or 3 (or two, first one twice as long as the second one, 2+1)
  • 4/d and 12/d is 4 (or three as 1+2+1)
  • 8/d could be e.g. 3+3+2, but also 8*1, it really depends.

The bottom line: When looking at music, consider 3/4 to be closer to 3/8 with doubled notes than to 6/8.

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The number below the time signature or bottom number of a time signature indicates which note gets the beat that is equivalent to one beat by which the length or value of notes like; Whole note,Half note, Quarter note etc will be decided(except compound time).Since no note has a set duration, the value of all notes without the bottom number or beat unit is zero.So bottom number of a time signature plays a very important roll in a music piece that says how a music will be counted and played.

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  • 'No note has a set duration'? That kind of confuses me. A semibreve has a time value of 4 beats right? And it's still confusing how people describe the bottom number of a time signature as indicating 'which note gets the beat'. This is one thing in music theory that I don't get, no matter how many times people explain it the exact same way. I need an adult to explain it to me like I am a toddler at this rate. – Jessica Cunningham Jan 4 at 1:07
  • I'd like to tell you that a whole note or semibreve would be equal to 4 beats only when the quarter note or crochet becomes the beat unit which is equivalent to one beat,such as; in 4/4, 3/4, 2/4 etc time signatures quarter note gets the beat because bottom 4 represents quarter notes as whole notes relative value. As we know the quarter note is 1/4 of a whole note and for the same reason a whole note's value is equal to 4 beats.If half note becomes the bottom number of the time signature like 4/2, 2/2 ...then whole note is 2 beats long. To know more you can contact me at 91 7980292419(India). – Gopen DeSarkar May 31 at 20:48

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