In Western musical notation, a dotted note is a note with a small dot written after it. The dot adds a half as much again to the basic note's duration. If the basic note lasts 2 beats, the corresponding dotted note lasts 3 beats. A dotted note is equivalent to writing the basic note tied to a note of half the value, or with more than one dots, tied to notes of progressively halved value.

If the note to be dotted is on a space, the dot also goes on the space, while if the note is on a line, the dot goes on the space above (this also goes for notes on ledger lines).

Theoretically, any note value can be dotted, as can rests of any value. If the rest is in its normal position, are always placed in third staff space from the bottom,

The use of a dot for augmentation of a note dates back at least to the 10th century, although the exact amount of augmentation is disputed; see Neume.

Dots can be used across barlines, such as in H. C. Robbins Landon's edition of Joseph Haydn's Symphony No. 70 in D major, but most writers today regard this usage as "obsolete" and recommend using a tie across the barline instead.

More than one dot may be added; each dot adds half of the duration added by the previous dot, as shown in example 1.

Double dotting

A double-dotted note is a note with two small dots written after it. Its duration is 1¾ times (1 + ½ + ¼) its basic note value.

The double-dotted note is used less frequently than the dotted note. Typically, as in the example below, it is followed by a note whose duration is one-quarter the length of the basic note value, completing the next higher note value.

Example 2 is a fragment of the second movement of Joseph Haydn's String Quartet, Opus 74, No. 2, a theme and variations. The first note is double-dotted.

• Haydn's theme was adapted for piano by an unknown composer; the adapted version can be heard (3.7 kB MIDI file).

In a French overture (and sometimes other Baroque music), notes written as dotted notes are often interpreted to mean double-dotted notes, and the following note is commensurately shortened; see authentic performance.

Triple dotting

A triple-dotted note is a note with three dots written after it; its duration is 1⅞ times (1 + ½ + ¼ + ⅛) its basic note value. Use of a triple-dotted note value is not common in the Baroque and Classical periods, but quite common in the music of Richard Wagner and Anton Bruckner, especially in their brass parts. See example 3.

An example of the use of double- and triple-dotted notes is the Prelude in G Major for piano, op. 28 No. 3, by Frédéric Chopin. The piece, in common time (4/4), contains running semiquavers in the left hand. Several times during the piece Chopin asks for the right hand to play a triple-dotted minim (lasting 15 semiquavers) simultaneously with the first left-hand semiquaver, then one semiquaver simultaneously with the 16th left-hand semiquaver.

Formula

Although notes with more than three dots do not occur often, one can determine the length of any given note a with n dots: $a\_n=aleft(1+tfrac\; 12+tfrac\; 14+\; cdots\; +\; tfrac\; 1\{2^n\}right)=2a-frac\; a\{2^n\}$.

This makes it clear that continuous dotting does give a continuous prolongation of the original note, but it will never get as long as twice the original value.

References