Under what circumstances can a V be followed by a vi6?
My music theory textbook says:
A good rule to remember is that V in root position should not be followed by vi6...The V-vi sounds fine—a good example of a deceptive progression—but the vi6 sounds like a mistake.
But then says later that:
The vi6 will also occur occasionally as part of a sequential pattern...
I6 V vi6 iii IV6 I
So is the second example not truly a deceptive progression? What makes this acceptable and other cases not acceptable?
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You have to think critically about this. The third of the six chord is the tonic note of the scale. You have to double the third of the six chord when it is after the dominant but when you have that six chord in first-inversion you make it very much harder to resolve the leading tone in a satisfactory manner(Because one of the notes that can resolve that leading tone is already used.).
When you keep the six chord in root position you open your voice leading to more possibilities which simply makes it better.
I guess if the Dominant chord is in first-inversion then you have no choice but to have the six chord in first-inversion but at that stage, I wonder if it would not simply be better to use the tonic chord.
As for cadences, they will typically be in root position. Triads become more unstable as the inversions go up. This is less so in four note chords but for triads, it is very much true.
That is why second inversion triads are only used in a very specific manner. For cadences you don't want unstable chords, you want stable chords to add to the feeling of finality.
Richard's answer is correct, but I would add one more thing: A Deceptive Cadence usually occurs at the point where you expect an Authentic Cadence. That is, at the end of a phrase. In the example you give, the sequence in question occurs very early in the phrase and that is very likely why the author of the textbook does not consider it Deceptive and therefore believes it to be "acceptable."
Sequences and sequential patterns often break more traditional "rules" of voice leading. Within a sequence, for instance, you'll often find doubled leading tones, which is a cardinal sin outside of a sequence! This is because the pattern of the sequence overrides such individual errors. (But note that something like a chordal seventh must still resolve down by step in a sequence, since otherwise this mistake will just keep happening when it's sequenced down!)
Thus the latter example is really overridden by the larger sequential pattern and not a true "deceptive progression."
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