Is this an imperfect authentic cadence in a minor key?

Question

In the case where the chords ending a phrase (in B minor) are:

| D | A | A#m | Bm |

in B minor it would be

III V/III(VII) #vii i

In my opinion the A#m is a passing chord, which leaves me with D A Bm. I understand that in this case the secondary dominant of III also acts as VII being the substitution for V. If I understand correctly the leading tone is E (to F in the passing chord and Bm).

Could this be regarded as an imperfect authentic cadence? Is such a term strictly limited to diminished vii and I in major keys (in relation to the similar movement)?

Answer 1

So, your chord progression is D - A - ^(A♯m) - Bm (b: III - VII - ^(♯vii) - i). Since ♯vii (A♯m) is a passing chord, we skip over it - which means, we get D - A - Bm (b: III - VII - i).

^{(I'm not sure why you are counting the A chord as a secondary dominant if it comes before a passing chord and actually resolves to Bm.)}

Your cadence is a VII - i in B minor, because it is A - Bm. VII - i (or ♭VII - I in major) cadences are extremely common in modern popular music, and is fairly common in late Romantic and Modern classical music.

For example, we have an E minor cadence of VII⁴₃ - I (D7/A - E).

The D7/A chord has dominant function in this case. Its top note, D, is not a leading-tone if you say it is "subtonic". However, it acts more like a leading-tone. Specifically, the ^7 degree note is a whole step below the tonic, but gives us a "pull" back to the tonic. It resolves to E, which is the tonic chord that has tonic function.

Your example is basically the same. The A chord has dominant function and resolves to Bm, which is the tonic.

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Now, the question is basically confusing to answer - The VII chord creates tension and resolves to the stable i chord. However, the root of the VII is a whole step below the tonic, not half. Therefore, it is either a variant of the leading-tone IAC, or "what?". So the answer to your question is: could argued to be a "yes", while it can also be a "no".

Answer 2

An authentic cadence will always have a root-position V moving to a root-position I (or i). In B minor, this means that we'll have an F♯ major chord moving to B minor.

The distinction between perfect and imperfect authentic cadences regards the highest-sounding pitch. If the tonic scale degree (in this case, B) is the highest-sounding pitch, it will be a perfect authentic cadence (or PAC).

But if the highest-sounding pitch is another member of the tonic triad (D or F♯), it will be an imperfect authentic cadence (or IAC).

Your progression of ♯vii to i would be more along the lines of what many call a contrapuntal cadence.

(Is there a text somewhere that told you viio to I was an authentic cadence?)

I'm also not sure what you mean by:

If I understand correctly the leading tone is E (to F in the passing chord and Bm).

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I've never heard of such a leading-tone IAC, but if we're following that definition, it seems that your example would fall under the "subV" category, and therefore fit. IACs are not only limited to major keys, and they do occur in minor keys.

Answer 3

Authentic cadence is always from V -> I.

Imperfect cadence is one that inverts the V or I in some way. So for example vi -> II is an imperfect cadence since vi is the inversion of V and II is the inversion of I.

Reference: https://www.solfej.io/blog/cadences/