Imperfect authentic cadence

In Classical music, an imperfect authentic cadence (IAC) is a cadence comprised of 2 factors¹:

1. An authentic cadential progression
2. The mediant (3rd) scale degree in the soprano (highest) voice

Others may more loosely define it, though do not claim this definition to be for Classical music only: for example, Hutchinson² says that an IAC occurs if a perfect authentic cadence (PAC) has any of the following changes:

• Inversions of the dominant or tonic chords are used
• The highest voice uses any scale degree that isn't the tonic
• $VII°$ occurs in place of $V$

Kostka goes far so as to define subcategories of IACs, such as:

1. Root-position IAC: a PAC but with $\hat{3}$ or $\hat{5}$ "in the melody"³
2. Inverted IAC: a PAC but either or both chords inverted³
3. Leading-tone IAC: $VII°$ substitutes for $V$ (inversions allowed)⁴