Music Theory
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# Dots and Ties

In order to lengthen the duration of a note, ties and dots are used.

You know that

but what is the answer here:

One way to solve this problem is to use a dot.  A dot adds half the value of the note it is attached to.  Here, half the value of a half note is a quarter note, so a dotted half note is equal to three quarter notes.

Here is another question using dots:

The answer is a double dotted whole note.  The duration of the second dot is half of that of the first dot.  Here we begin with a whole note.  The first dots add half its value, or a half note.  The second note adds half the value of the half note, or a quarter note.  All combined, that is equivalent to seven quarter notes.

There is one slight problem with the answers given above.  Each side of the above equations would last the same period of time, but would sound quite different: on one side of the equation there is a single note while on the other side there are several notes.  Ties will help us fix this problem.  Ties extend the duration of the original pitch through that of the tied pitches.  Therefore, to correct the above answers:

Note that ties are always notated in decreasing order of duration.