The bottom number in time signatures has always confused me

The top number in a time signature is easy to understand. Is the song in four? Count “one, two, three, four.” Is it in three? Count “one, two, three.” Is it in five? Count “one, two, three, four, five.” That’s all there is to it. However, the bottom number is another story. What is going on down there? I collected various examples of time signatures in this track I made, but I didn’t understand why “Solsbury Hill” by Peter Gabriel is in 7/4 but “One More Night” by Can is in 7/8.

I’m not alone in finding this confusing. My students struggle with it too. They are right to! Every explanation I have ever seen of the bottom number is circular. Say we’re talking about 4/4 time, so a beat is a quarter note long. Okay, so what is a quarter note? Well, four of them make a measure. And what’s a measure? Uh… four quarter notes.

It only gets worse when the bottom number is some number other than four. Let’s say we’re talking about 6/8, so a beat is an eighth note long. And what is an eighth note? It’s half a quarter note, so there should be eight of them in a measure, right? Well, no, because in 6/8 time, there are six eighth notes in a measure. So, what is the quarter note that a beat is half of? I feel like a crazy person just typing this. Imagine being a beginner trying to learn it.

It gets worse. How do you know if you’re hearing 6/4 or 6/8? At some given tempo, you count 6/8 twice as fast as 6/4. But couldn’t you just write 6/4 and double the tempo? You could, but 6/8 feels different. Feels different how? Well, it feels more like two slower beats divided into triplets. But couldn’t 6/4 feel like that too? Logically, yes, it just… doesn’t. But how as a learner are you supposed to know that?

I have read every explanation I could find of the bottom number in time signatures, and asked every music theory teacher I know. Some of them fall back on the same circular logic I described above. Some of them cheerfully admit that the bottom number has no logic to it, that it’s a set of conventions and stylistic associations. You can only develop an intuition for these conventions after you play a lot of classical repertoire. Timothy Chenette says you should internalize them through conducting, even if you never actually conduct an ensemble. That’s probably good advice, but it’s a little late for me, and I don’t know where I would fit conducting practice time into a one-semester theory or aural skills class.

One thing that has helped me is the idea that the bottom number historically conveyed tempo information. For a Baroque or Classical-era musician, the convention went like this:

  • If the bottom number is two, then the tempo is slow.
  • If the bottom number is four, then the tempo is medium.
  • If the bottom number is eight, then the tempo is fast.

To illustrate this idea to myself and my students, I made a song about it.

The track is at a steady 120 beats per minute throughout, and it switches between 2/2, 2/4, 3/2, 3/4, 3/8, 4/2, 4/4, 6/4, 6/8, 9/4 and 9/8 time. The synth plays each beat on the corresponding scale degree from C Dorian mode, so beat one is C, beat two is D, beat three is E-flat, and so on. Here’s an interactive Noteflight score.

My track doesn’t give you the full picture. Baroque-era time signatures weren’t just about metronomic tempo; the different numbers also spoke to the mood and feeling of the piece. A musician in Bach’s time would know that 3/4 implied a minuet or waltz, whereas 3/8 implied a scherzo. Also, “smaller number means slower” is not always true. While 2/2 is supposedly half as fast as 2/4, sometimes composers use 2/2 for uptempo orchestral music. Why? Ask a conductor, I guess.

Ultimately, the best thing we can do is to listen to a lot of real-world examples. Ali Jamieson has a great list. Cadence Hira has a nice list drawn from game scores. And Wenatchee the Hatchet has many more classical examples. Thank you also to my Twitter friends for suggesting some of the examples below.

Examples in 2

2/2

2/4

  • Nursery rhymes like “Pop Goes The Weasel”.
  • European folk and traditional music, like sea shanties, for example “Wellerman“.
  • Zorba’s Dance” by Mikis Theodorakis.
  • Country music is supposedly in 2/4, but I have never in my life heard a country musician count it that way.

Examples in 3

3/2

3/4

3/8

3/16

Examples in 4

4/2

4/4

  • Most Anglo-American popular music: the large majority of  rock songs, almost all top 40 pop songs, just about every rap song, every techno and house track.

4/8

  • Exists mainly in arcane music theory discussions and tutorials; I can’t find a single real-world piece of music written in it.

Examples in 5

5/4

5/8

Examples in 6

6/4

6/8

Examples in 7

7/4

7/8

Examples in 8

There is hardly any music that is notated in eight, aside from odd bars of modernist classical works that change meter a lot. But you could argue that most pop music that’s supposedly in four is really in eight. Notice that dancers and choreographers often count in “five, six, seven, eight” rather than “one, two, three, four.” There is plenty of music where everything is organized into groups of eight beats, but we express that idea with hypermeter, not meter. I have seen it argued that the tresillo rhythm should be considered 8/8, but everyone keeps their DAWs set to 4/4.

Examples in 9

9/4

9/8

Examples in 10

10/4

10 /8

Examples in 11

11/4

  • Eleven Four” by Paul Desmond.
  • Whipping Post” by the Allman Brothers, though really it’s 12/4 with the last beat omitted.

11/8

Examples in twelve

12/4

  • 12/4 – I can’t find a single example; it would sound like 4/4 with three-bar hypermeter, like “It’s About That Time” by Miles Davis.

12/8

I am collecting these examples for the specific purpose of teaching music theory in a pop context. How many of these time signatures do pop musicians need to know? They certainly need to know about the top number, but I question the need for them to get familiar with the bottom number. DAW producers use  tempo settings and finer grid subdivisions where composers of notated music would use time signatures. People who are playing and writing by ear tend to count inconsistently in four or eight for duple meter and three or six or twelve for triple meter, and aural communication is enough to keep everyone lined up.

Update: Andrea La Rose has a wonderful history of time signatures that sheds a lot of light on how this whole system came to be in the first place.

9 replies on “The bottom number in time signatures has always confused me”

  1. It’s less confusing if you call it a crotchet instead of a “quarter note”. (a quarter of what?)

    1. Unfortunately, the British system has problems of its own. Why is a “minim” the second-largest note value? Why is the longest note value a “semibreve”? I know that these things make sense in historical context, but without that context, they are just as mysterious as the fractions.

  2. PS – this recent video looking through US chart hits for non-4/4 songs basically emphasises that what you say in that last para is absolutely enough. It’s no kind of spoiler that the exceptions are some 6/8, some 12/8 and I think one or two waltz-feeling songs.

    Oh and ‘Hey Ya’… but when a song just drops beats as part of its hypermetrical structure (is that how you’d put it?) I’d hardly argue it is not “in” whatever main time signature. Um, in other words I’d definitely say ‘Hey Ya’, ‘Jive Talking’, and ‘Heart of Glass’ are all in 4/4 and all just have a fun rhythmical trick in common.

    1. “Hey Ya” is for sure an example of odd hypermeter rather than odd meter. Sometimes these tunes will have meter changes too, bars of 2/4 or 3/4 (that’s what “Heart of Glass” does too).

  3. I really strongly agree with your closing comments that in the context of pop getting a feel for the bottom number is not very important. Not sure how your average musician involved in that 6/8 R&B feel even counts it, but that’s the major split from 4/4 if you think of 12/8 as a 4/4 triplet feel (which I do, living in a DAW since the 90s).

  4. A couple more good examples – “Living In the Past” by Jethro Tull is in groovy, syncopated 5/4, the “Apocalypse In 9/8” section of “Supper’s Ready” by Genesis is in a time signature you’d never guess, “The Eleven” by the Grateful Dead is in…wait for it…11/8, “Starless” by King Crimson is largely in 13/8 (slow in the menacing middle build-up, fast in the ensuing jam), I could go on. Lots of prog rock examples. Good point about the ambiguity of the bottom number.

  5. And I thought I was the only one… A very useful list of samples, thank you

  6. What a brilliant article! My wife comes from a fairly musical family and I’ve got into a fair few happy heated discussions about time signatures with her before, as she tries in vain to explain what on earth that bottom number is referring to!

    I think the last time we waded in we were thinking about Welcome To The Cheap Seats, by The Wonderstuff and featuring the late great Kirsty MColl. Which I think must be (for the most part) in 6/8?

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