If you have a chord progression like this:
I've seen different websites that have different names for this:
- Non-functioning secondary dominant
- Deceptive secondary dominant
- Secondary deceptive cadence
Are these all the same thing?
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I haven't heard these terms, but if I were to hear them, I would assume the following:
A "non-functioning secondary dominant" is an applied chord that doesn't resolve to its related I or vi. In other words, a V/V should resolve to either V or vi/V. If it somehow resolved to, let's say, IV, that would be a non-functioning secondary dominant.
A "deceptive secondary dominant" is one that resolves deceptively; thus V/V resolves to vi/V. This then shows a broader deceptive resolution of V–vi within the temporary key of V.
And in my view, a "secondary deceptive cadence" is the same as #2 above, because that's all that that is: a deceptive cadence in a secondary key.
They all seem to be plausible labels for a secondary dominant that doesn't resolve as expected. None are, to my knowledge, in general use. So you'd have to ask the person who's using them for his precise definition.
Let's forget about it being a SECONDARY dominant for a moment.
Is a dominant still a dominant even if it doesn't resolve as a Perfect (Authentic in America, I believe) Cadence? We're in C. Is G7 still the dominant when it resolves to Am rather than home to C? I'd say yes, it is.
Is there any reason we can't extend the same latitude to secondary dominants? I'd say no, there isn't.