I don't really fully understand what an imperfect authentic cadence is. I was told that if the chords are inverted, then it's considered an IAC. Or maybe the melody can be 4–3, etc. I just need an explanation that's easy to understand. What are the requirements to make an IAC?
There are two opposing schools of thought. Aaron has offered one, so I'll offer the other:
In order to be an authentic cadence—perfect or imperfect—both the V and the I must be in root position. This is deduced from large-scale studies of both prolongation in tonal music as well as phrase structure. And music of the common-practice period is incredibly consistent in this regard: inverted V chords prolong tonic, whereas cadences at the ends of phrases exclusively use root-position V chords.
As such, a V6–I (an imperfect authentic cadence in the other school of thought) is best understood as just prolonging tonic. It's not until you get a root-position V that we have a true cadence.
With this out of the way, the only different between an IAC and a PAC is the soprano scale degree: in a PAC, it's scale-degree 1 in the I chord. In the IAC, it's either 3 or 5.
Perfect authentic cadence
- Both chords in root position, and
- Tonic in the highest voice for the final chord
Imperfect authentic cadence
- Everything else (meaning, chords are in root position, but final chord does not have the tonic in the highest voice; one or both chords is inverted; V chord is replaced by viio chord)