An authentic cadence (also called a full cadence) is a cadence based on an authentic cadential progression i.e. the chord progression from the fifth or the seventh scale degree to the first scale degree.
We already said that not every cadential progression is a cadence. It is a cadence only if it feels like the ending of a complete thought. For instance, chord progressions from the fifth to the first scale degree often occur at the beginning of thoughts (as a way to prolongate the tonic harmony). Such chord progressions are not cadences.
An authentic cadence can be perfect or imperfect.
A perfect authentic cadence is called so because it follows a certain set of rules. The perfect authentic cadence is an authentic cadence that:
Uses a chord progression from the fifth scale degree (not the seventh scale degree)
Uses root positions of the chords
Has the final chord whose highest pitch is the tonic (the tonic is in melody)
As an example, we can examine the ending of Chopin’s Prelude No. 9 in E major. We see the chord progression from the fifth to the first scale degree. After examining the bass tones of the chords, we see that the chords are in a root position. Also, the final chord has the tonic as its highest pitch.
A perfect authentic cadence is usually annotated using the abbreviation PAC.
Figure: The perfect authentic cadence at the end of Chopin’s Prelude No. 9 in E major
An imperfect authentic cadence is an authentic cadence that is not perfect.
As an example, we can examine the ending of Bach’s Prelude No. 8 in Eb minor from Well Tempered Clavier, Book I. We see the chord progression from the seventh to the first scale degree. Thus, this authentic cadence is not perfect.
An imperfect authentic cadence is usually annotated using the abbreviation IAC.