Basics of Rhythm Theory
Count, measure, phrase, meter and time signature.
Model songs
A couple of songs will guide us to the heart of counting theory.
Song #1 - We Shall Overcome
| 1 2 3 4 | 1 2 3 4 |
| We shall o- ver | come, |
| 1 2 3 4 | 1 2 3 4 |
| We shall o- ver | come, |
| 1 2 3 4 | 1 2 3 4 |
| We shall o- ver | come, some |
| 1 2 3 4 | 1 2 3 4 |
| day | |This is a phrase of eight measures, each with four beats or counts. We say the count of the song is four, and that it is “in four.”
Now, while imagining, humming or singing the song, tap your foot along to the beat. These are the pulses.
In this song, there is one pulse per count. But in other songs, like the next one, only some of the counts will get a pulse.
Song #2 - The Bear Went Over the Mountain
| Pulse Pulse |
6 | 1 2 3 4 5 6 |
The | bear went o- ver the |
| Pulse Pulse
| 1 2 3 4 5 6 |
| moun- tain |Here we have six counts per measure, but only the counts one and four get a pulse. Each of the pulses can be felt as a group of three counts.
Meter and Time Signature - first approach
The meter for a song is the structure of counts and pulses inside the measures, and its time time signature is a symbolic, written representation for the meter.
There is a standard notation for time signatures, which is shown as a couple of numbers at the top of every written score. And we are free to create our notation for time signatures as well.
Here is a first cut at the time signature for our sample songs:
Song #1: (count 4, pulse 4) # i.e. four counts and four pulses per measure.
Song #2: (count 6, pulse 2) # i.e. six counts and two pulses per measure.
This is almost a complete description of the meter - just one more bit of information is needed.
Beat size
The concept of beat size is an elusive but real thing. It is a qualitative notion, having to do with the subjective sense of how “big” the beats are, in relation to the other contents of the music, such the flow of melody notes and words. So the qualitative beat size is assessed only in the context of an individual song.
The most basic beat size is shown by the counts in Song #1, each of which feels like a single step while walking. So let’s call them single beats.
On the other hand, in Song #2, where there are six counts but only two pulses per measure, the counts happen rather fast. They are perceptually smaller than single beats; they are fractions, or subdivisions of a single beat. Let’s call them mini-beats.
A simple language for time signatures
To complete our vanilla language for time signature, we only need to extend what we wrote above by adding the size of the counts as well:
Song #1: (count 4, count-size single, pulse 4)
Song #2: (count 6, count-size mini, pulse 2)
Unpacking the notation, it says:
We Shall Overcome has measures with four single-beat counts and four pulses.
Bear Went Over the Mountain has measures with six mini-beat counts and two pulses.
Once you process this, it’s pretty straightforward.
General principles for translating to the standard language for time signatures
Now we just need to explain how to go back and forth between our simple notation and the standard language for time signatures.
There are two principles involved:
In standard notation, pulse is not mentioned in the time signature. This makes it less informative. However, in practice this is okay, as the pulse value can be inferred from the count, using additional contextual assumptions. More on this later.
Beat size is described by other terms than the ones introduced here.
Two key standard names for beat sizes
Here are two of the main standard terms for beat sizes:
Single beat = quarter note
Mini beat = eighth note
Recommendation: whenever you see the term “quarter note” think “single beat”, and when you see “eighth note” think “mini-beat”.
Conventional time signature notation
A conventional time signature is a pair (count,size) = “count/size”, where count is the number of counts per measure, and size is a symbol indicating the size of the count beat:
‘2’ - half-note - two single beats
‘4’ - quarter-note - single beat
‘8’ - eighth-note - mini beat
Now let’s apply this to get the standard time signatures for our sample songs.
Song #2. We analyzed the time signature as (count 6, size mini, pulse 2). To convert to standard notation, first drop the pulse, giving (count six, size mini), then convert “mini” to “8” (as per the above), giving (6,8) or “6/8”.
Song #1. We analyzed the time signature as (count 4, size single, pulse 4). To convert to standard notation, first drop the pulse, giving (count four, size single), then convert “single” to “4” (as per the above), giving (4,4) or “4/4”.
Remarks:
Time signatures are not ratios or fractions!! Do not be mislead by the misleading syntax like “6/8”, which merely looks like a fraction. Rather, the standard time signature consists of two separate numbers, and is more clearly written as a pair like (6,8).
We haven’t yet seen songs where the size indicator would be ‘2’, indicating counts that are half notes. This is called cut-time, and will be covered at the end of the article.
Inferring the pulse indicator
Conventional time signature omits the pulse descriptor, which is central to the description of the meter.
But as there are not that many time signatures commonly used in practice, it turns out to be easy to infer the pulse value using a couple of rules:
(6,8) has two pulses per measure.
(12,8) has four pulses per measure.
Otherwise, there is one pulse for each count.
Remark: for odd meters, where the pulses are not evenly spaced throughout the measure, a grouping indicator is absolutely needed as part of the time signature. And this is more than just a number. For example, for 7/8 time, it could be the expression 3+2+2, which means three pulses, with the first pulse taking three counts, and the second and third pulses each taking two counts.
Why is a single beat called a “quarter note”?
As mentioned, a single beat is called a quarter note. Where does this curious term come from?
The root of it is that - purely as a matter of convention - a duration of four single beats is called a “whole note.” Once you take that convention as a premise, then it of course follows that a single beat will be called a quarter note.
But what is “whole” in terms of the music is the measure, which may or may not contain four beats. So the definition of a whole note as four beats is one-sided and biased towards songs that have four beats per measure.
As a thought experiment, one could imagine a culture where all the songs were waltzes, and so the people decided to call three beats a whole note, and then naturally a single beat would be a one-third note. Then a measure of four would consist of four one third notes, and the connotation would be made that the measure contains one note too many.
That said, there is a redeeming aspect for the bias towards the number four. A large number of songs are in four time, and four seems well connected with our walking patterns involving two feet. So there is a naturality to it, and indeed, the time signature is called common time.
So if you had to arbitrarily and misleadingly choose one count for the whole note, four would not a bad choice.
Catalog of conventional names for beat sizes
Now that we have analyzed and comprehended the quirks and limits of the standard terms for beat sizes, we can engage with them, as they are ubiquitous and useful.
Quarter note - single beat
Eighth note - mini beat - subdivision of single beat into 2 or 3 parts
Sixteenth note - tier-2 mini beat - subdivision of single beat into 4, 5, 6 or 7 parts
Half note - two single beats
Whole note - four single beats
Sidenote. the British naming system for beat sizes uses manifestly arbitrary names for the beat sizes. For example, a quarter note is called a “crotchet”, and an eighth note is called a “quaver.” This avoids any pseudo-mathematical connotations. On the other hand, it loses the qualitative ranking provide by the names: Whole note > half note > quarter note etc.
Cut time
A noteworthy meter is cut time, also known as cut common time. This is given by the time signature (2,2) or “2/2”. (With an implied two pulses per measure.)
Here, the counts is a half-note, which consists of two single beats - we could call them double beats.
An example of a song in cut time is Yankee Doodle.
Interestingly, the pulses are felt as half notes, even though the song is up-tempo and they happen very quickly. It’s enigmatic, but that’s how we feel it.
Names and symbols for particular time signatures
‘4/4’ is called common time, and is designated by the symbol C
‘2/2’ is called cut common time, or just cut time, and is designated by a C with a vertical slash through it.
‘3/4’ is waltz time.
Songs with mixed meter
All along we’ve tacitly been assuming that all of the measures of a song have the same number of counts.
Only then can we talk about the meter as a property of the song itself, rather than its individual measures.
If the meter of the measures varies over the course of a song, then we say that it has mixed meter.
Example: Across the Universe
In this Beatles song most of the measures have four beats, but the measures for this part of the lyrics “way A-cross The Un-ni-verse (rest)” have five beats. (There’s a rest on beat 5). And the seventh measure has only two beats. Here are the beat counts for the first eight bars:
4 4 4 5 4 4 2 4Because the majority of the bars have four beats, the departures from four are perceived as a variation from the general flow, and the song is still treated as ‘4/4’.