Rhythm and meter, counted in fractions

Pitch answers which note. Rhythm answers when, and for how long. It is the half of music that is learned first and studied last.

The note values

Each value is worth half of the one before. There is nothing more to it.

The whole note lasts four beats in a bar of four. From it:

A half note is worth two beats, a quarter note one, an eighth note half, a sixteenth note a quarter. The series goes on for as long as anyone has patience.

The dot

A dot beside a value adds half of its value. A dotted quarter is worth a quarter and an eighth: a beat and a half.

Two dots add a half and then half of that half. In practice, more than one dot is rare outside early music.

The time signature

4/4 is not a fraction to be divided. It is two numbers with different jobs:

• Top: how many beats fit in the bar
• Bottom: which value is worth one beat

So 3/4 is three quarter notes to the bar, and 6/8 is six eighth notes.

Simple and compound

Here is the distinction that separates those who memorised from those who understood.

6/8 and 3/4 have the same total length, six eighth notes. And they are different meters, because they group those eighth notes in different ways:

• 3/4: three groups of two — ONE two, TWO two, THREE two
• 6/8: two groups of three — ONE two three, TWO two three

A meter is simple when the beat divides in two, and compound when it divides in three. The bottom number does not tell that story on its own: in compound meter the value that represents the beat is always dotted; in 6/8 the beat is the dotted quarter, and the eight at the bottom describes the subdivision, not the beat.

Tuplets

Sometimes a beat needs to be divided into a number that does not fit the series of halves. Three eighth notes in the space of two is a triplet, the grouping that appears in almost all Brazilian popular music.

The same goes for five in the space of four, seven in the space of four, and so on. Those cases are the reason this site adds durations with exact fractions instead of decimals: a seventh written as a decimal does not close the bar, and a rounding error that accumulates over a piece becomes an audible one.

What to take from this

Values are worth half of the one before; the dot adds a half. The time signature says how many beats and which value represents them, but it is the grouping that defines how the meter sounds. Two meters with the same total length and different groupings are two different meters, and confusing them is writing the right music with the wrong swing.