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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?

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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.

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  • The "statistical" part of this is new and interesting to me. Can you point to a study or theorist I could read?
    – Aaron
    Commented Nov 4, 2021 at 16:59
  • Seems much simpler over here - they're all perfect cadences! (No, not the imperfect ones - they're imperfect...)
    – Tim
    Commented Nov 5, 2021 at 10:23
  • @Aaron Sorry, I forgot about your question here. I can't remember specific research, but William Caplin and William Rothstein are two of the big names in this arena. They don't approach it "statistically" per se, but their corpus studies do suggest the importance of the root-position V.
    – Richard
    Commented Nov 16, 2021 at 11:55
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Simply put...

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)
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    Really need a different word from 'imperfect' - which on the East of the Atlantic means pretty well the opposite.
    – Tim
    Commented Nov 4, 2021 at 8:22
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    I just want to call out, for future visitors, one point that both the question and answer are taking as understood: All "authentic cadences" move from the dominant (V) to the tonic (I). That's the most fundamental defining characteristic of "what an imperfect authentic cadence is," and a perfect as well, as opposed to half or plagal.
    – Andy Bonner
    Commented Nov 4, 2021 at 11:56

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