Dots and ties

A dot adds half: a dotted half note lasts 3 beats and a dotted quarter lasts 1.5, the long-short step in the fourth bar of Ode to Joy.

Lengths the halving system cannot make

Halving gives you 4, 2, 1, one half and one quarter beats, but music constantly needs lengths in between, such as three beats or one and a half. Notation solves this with two tools. The first is the dot, a small point written just to the right of a note head. A dot makes the note half again as long as it was. A half note is two beats, so a dotted half note is 2 + 1 = 3 beats. A quarter note is one beat, so a dotted quarter is 1 + 0.5 = 1.5 beats. A dotted eighth is 0.5 + 0.25 = 0.75 of a beat. The same rule works for rests: a dotted quarter rest is a beat and a half of silence.

A handy way to think of it: a dotted value equals three of the next smaller value. A dotted half is three quarters, a dotted quarter is three eighths, a dotted eighth is three sixteenths. That "three" will matter a great deal in compound meter, two units from now, where every beat is a dotted note split into three.

Ties join notes of the same pitch

The second tool is the tie, a curved line connecting two notes of the same pitch. You play the first note and hold it through the second without striking again, so the lengths add. A quarter tied to an eighth sounds exactly like a dotted quarter. Ties can join any two values: a half tied to an eighth lasts 2.5 beats, a length no single note shape can show. Do not confuse a tie with a slur, which looks similar but connects notes of different pitches and means play them smoothly. If the two notes under the curve have the same pitch, it is a tie.

Ties are also the only way to hold a note across a bar line. A dot cannot reach past the end of a bar, because each bar must add up on its own. So if a melody holds a note from beat 4 of one bar into beat 1 of the next, it is written as two notes, one at the end of each bar, joined by a tie. The note blocks show this: any block that crosses a bar line turns orange, and the panel reminds you that written music would split it and tie the halves.

The long-short step in Ode to Joy

The theme from the last movement of Beethoven’s Ninth Symphony, first performed in 1824, is one of the best-known public domain melodies. Its first three bars are plain quarter notes. The fourth bar is the interesting one: a dotted quarter, an eighth and a half note. The dotted quarter leans across the middle of beat 2, the eighth slips in on the "and" of beat 2, and the half note settles the phrase. Count it as "1, (2) & 3, (4)". In the Tap along tab below, tap the whole four-bar phrase. Most people play the eighth too early the first time, cutting the dotted quarter short.