Pedal point, and the harmony that moves over a note standing still
A sustained note while the chords change above it, creating dissonance without losing the centre; the dominant pedal builds tension, the tonic pedal settles, and both are everywhere.
One note stays. Above it, the chords change, and some of them do not contain it: for a moment, the note that stays is dissonant with what sounds above, and then it belongs again. That note is the pedal, the name comes from the organ pedal, and it is the simplest device there is for creating tension without leaving the spot.
The tonic pedal
The tonic sustained in the bass while the harmony passes through other degrees. The ear never loses the centre, because it is sounding the whole time, and the chords above sound like colours over a fixed floor.
C in the bass throughout; above it, C major, F major, G major, C major. In the second and third chords the bass C does not belong to the chord above, and the dissonance that creates is gentle, because the ear knows the C is home.
The chart writes the pedal with a slash: F with C in the bass, G with C in the bass. It is the beginning of countless introductions and the end of countless codas: a passage that has already concluded, settled by a note that does not leave.
The dominant pedal
The dominant sustained in the bass while the chords change above. The effect is the opposite: instead of settling, it builds tension, because the note that stays is the one that most wants to resolve, and it does not resolve while the pedal lasts.
G in the bass; above it, C major, G seventh, C major, G seventh. The tonic appears above, but over a G that contradicts it, and the ear waits for the real arrival, with the bass on C, which only comes when the pedal ends. It is the "preparing the return" gesture of every classical form, and of most song bridges: a dominant that lasts eight bars and does not resolve, until it does.
Where the pedal lives
The bass is the commonest place, but not the only one. An internal pedal sits in a middle voice; an upper, or inverted, pedal sits in the top voice, and it is what makes a repeated high note sound over changing chords, a bell-like effect. The rule is the same in any register: the note is fixed, the harmony moves, and the momentary dissonance is accepted because the fixed note has a function.
How analysis treats the pedal
The pedal is a note foreign to the chords that do not contain it, classified by how it arrives and leaves: it arrives belonging, it stays, and it leaves belonging. In analysis by degree, the chords are read by what sounds above the pedal, and the pedal is noted separately, as "tonic pedal" or "dominant pedal", without becoming each chord's bass. An F major over a C pedal is still the IV, not a strange chord with C in the bass.
What to take from here
The pedal is a note that stays while the harmony moves, dissonant for moments and always with a function. The tonic pedal settles a passage that has already concluded; the dominant pedal builds tension until it resolves; in any voice, the mechanism is the same. Analysis reads the chords above it and notes it separately, because it is not a bass: it is a floor.