Double dotting

A dot after a note lengthens it by half its value. If a second dot follows the first, half of the first lengthening is added once more. A quarter note (one beat) thus becomes first a note one and a half beats long, then one that lasts 1 3/4 beats. You calculate: 1 + 1/2 + 1/4 = 1 3/4.

Why two dots?

A double-dotted note is almost as long as the next larger one. A double-dotted quarter note lasts only one sixteenth note less than a half note. The short note after it merely completes the remainder. That creates a sharp, springy rhythm that occurs especially in marches and solemn music.

How to check the sum

Every further dot is half the size of the one before. For the second dot you therefore take half of the first: the half note is 2 beats long, the first dot adds 1, the second 1/2, together 3 1/2. For the eighth note it is 1/2 + 1/4 + 1/8 = 7/8 beat. If exactly the missing remainder is left in the bar after it, the sum works out.

Counting

Count the subdivision in sixteenth notes: a quarter note has four sixteenth notes, the double-dotted quarter note lasts 4 + 2 + 1, so seven sixteenth notes. The eighth sixteenth note, the single one after it, fills up the bar. What matters is not playing the short note too early. It comes only shortly before the next beat.