Alternative bass notes
The bass note does not always have to correspond to the root note of the chord, i.e. a C chord can have other bass notes under it besides the C root note. Common alternative bass notes are the third, fifth, seventh, etc. This has a profound effect on the structure of the song as the chord progression is changed.
Alternative bass notes are written after the chord. e.g. C/E is a C chord with an E bass note. Chords with alternative bass notes are also known as slash chords because of the " / " symbol.
The chord progression for this example is:

Notice how the actual chords would have simply been C to D over and over but the bass makes the progression climb.
A pedal bass is when the bass stays on the same note the whole time. Pedals are a suspension device as they create tension. This next example shows how a pedal compares with having the bass follow the changes.