Transposing means changing the key of a piece of music. This can apply to a scale, a riff, a short melody, or an entire song. The ability to transpose is a very important skill for all musicians to develop.
The easiest way to transpose is to write the scale degrees under the original melody and then work out which notes correspond to those scale degrees in the key you want to transpose to.
The next exercise is a short melody played in the key of C and then transposed to the keys of F and G. Play through them and notice that the melody sounds the same, but the overall pitch may be higher or lower. Transpose this melody to all the remaining major keys found in the key cycle. You should also try this same technique with other tunes you know.
In the previous examples, the melody consists entirely of notes from the major scale. However, many melodies use notes from outside the major scale, particularly in styles such as Rock, Funk, Blues and Jazz.
These "outside notes" relate to the chromatic scale starting on the same note as the major scale of the key the music is written in. Therefore, if you have a piece of music in the key of C which contains notes which are not in the C major scale, you can relate these notes to the C chromatic scale.