We can extend a note for longer by adding a dot.
A dot increases the duration of a note by another half of the value of the note.
A crotchet with a dot becomes a dotted crotchet and is 1 & 1/2 beats duration.
1 + 1/2 = 1 & 1/2 beats
A minim with a dot becomes a dotted minim and is 3 beats duration.
2 + 1 = 3 beats
A quaver with a dot becomes a dotted quaver and is 3/4 of a beat duration.
1/2 + 1/4 = 3/4 beat
Dotted notes create syncopation as it means that notes get sounded on the off beats of the bar.
Notes can also have their length extended by using a tie.
When using a tie, the first note is sounded and sustained for the duration of the first note plus the note it is tied to. The second note is not replayed. In the above example, there are only two notes played not three, as the final note is just an extension of the second.
A tie can also be used to extend a note across two bars.
This example gives a syncopated feel to the second bar, because the tie means that the note on the first beat in the second bar is not sounded as a new note.