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The "Andalusian cadence" I-bVII-bVI-V is commonly heard as a repeated figure in Flamenco music as well as many pop songs, e.g. "Hit the Road, Jack":

In trying to think about how this cadence is typically perceived by the listener, classical music theory seems to give (at least?) two possibilities:

  1. It is a perfect cadence: the V-chord at the end is heard to continually resolve into the tonic I at each repetition.

  2. It is a half cadence: the I-chord at the beginning is heard to continually tense into the V-chord at the end, which then hangs there unresolved.

Generally I've been impressed by how much of pop music harmony can be understood by thinking in terms of perfect cadences (a V-I which ends a phrase or section) and half cadences (a phrase or section which ends in an unresolved V, often followed by a new phrase beginning on I). But in this case, I'm not sure I have a strong intuition about which kind of cadence this would be: or perhaps it is "ambiguous", or classical theory doesn't neatly apply here?

(I am aware that this is asserted to be a perfect cadence in the wikipedia article: http://en.wikipedia.org/wiki/Andalusian_cadence But their argument that "[t]he Andalusian is an authentic cadence, because a dominant chord ("V") comes just before the tonic", is completely unconvincing: if a half cadence is followed by a phrase beginning in the tonic, we will also have a dominant followed immediately by a tonic. It seems to me that the relevant distinction is how the harmony interacts with sectional boundaries in the music, i.e. if the phrase or section ends with V-I, or if the V-chord comes as the last element of the phrase.)

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I don't have time to answer right now, but consider that the Andalusian Cadence might not be a cadence at all. In particular, when the chord progression is the entire phrase and is repeated as an ostinato, it is likely not a cadence in its entirety. –  Andrew Jan 2 '13 at 23:04
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2 Answers

My 2 cents: in a perfect Andalusian cadence, (w/ resolution) perhaps the feeling of "incompleteness" or the sense that the cadence, though completed, isn't quite finished is the fact that the leading tone is the third of the V chord, thus giving you the impression that you must return to the tonic.

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It could be the case that the Andalusian cadence is attractive precisely because there is a certain amount of ambiguity to it (i.e., it can't be pinned down as either perfect or half cadence). If I may trust my own instincts on the matter, the cadence exhibits neither the "completeness" of a perfect cadence, nor the "incompleteness" of a half cadence; its semi-completeness is exactly what makes it musically satisfying but also what causes it to be perpetually driven forward. As we reach the V chord, we are compelled to expect the return of the i chord (prompting us to suspect that we are nearing the end of a perfect cadence), but as soon as we reach the i chord, we realize that the music's momentum is still driving us forward towards the V chord again (causing us to suspect that the real goal is the dominant chord, as in a half cadence). In short, the Andalusian cadence would probably be known as an "elided" or "dovetailed" cadence since the last chord of the progression becomes the first chord of the next iteration. This elision is what simultaneously causes the feeling of necessary return to tonic at the end of a phrase and also the feeling of momentum pushing us forward from the beginning of the next phrase.

To some, this may appear as a non-answer, but I think that there's nothing wrong with accepting, as your question implies, that it is neither obviously perfect nor obviously half cadence, but rather some mix of the two.

(Updated for concision.)

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The progression moves diatonically stepwise to a V chord at which point it turns around to I. There isn't a shred of ambiguity there, and that is why it is popular. –  Kaz Jun 14 '13 at 16:40
    
It appears that you read neither the question nor my answer. The question was not what the CHORDS were, but what the CADENCE was. We can all agree that "the progression moves diatonically stepwise to a V chord at which point it turns around to i." What we don't all agree on is whether (as the questioner asked) the cadence is a perfect cadence or a half cadence. I have indicated in my response that there's not a straightforward answer because of the fact that the momentum of the cadence drives us forward even after we have reached the i chord. Please re-read the question and response. –  jrc03c Jun 15 '13 at 13:44
    
I do not see it that way. We both agree that it is "musically satisfactory", yet you claim that it is due to incompleteness, wheres musical satisfaction in a cadence, to me, is evidence of (nearly tantamount to) completeness. I believe that any sense forward drive from the tonic is only the expectation that, having heard several rounds of the same thing, there will be another round. The music can easily stop on the I without any strangeness. The listener will expect it if there is another ending hint, such as a ritardanto or if he or she simply knows where the song ends from the lyrics. –  Kaz Jun 15 '13 at 15:46
    
You said that musical satisfaction in a cadence is evidence of completeness; what did you mean by "completeness"? That a cadence is "complete" if it resolves dissonances? Or that a cadence is "complete" if it fulfills its structural role? In my answer, I used "completeness" to mean the resolution of dissonances; perhaps that was the wrong word to use. But the way you used "completeness" in your last comment isn't the way I used the word. By your usage, "complete" must mean that a chord fulfills its structural role; in which case it would be right to equate completion with musical satisfaction. –  jrc03c Jun 16 '13 at 2:00
    
If you can offer a straightforward answer as to whether the Andalusian cadence is a perfect cadence or a half cadence, then feel free to submit it as an alternative to my answer. I can't see that it is very straightforward, but that's just my take on it. I'm not saying that the chords themselves are complex or difficult to understand, but rather that the cadences are elided one after another in a way that nearly (or perhaps completely) erases the seams between cadences. –  jrc03c Jun 17 '13 at 20:10
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