Well, the I-IV
thing is in a sense problem-complete of the question. It shows the relationship of the chords to the tonal center (the key). So we have to do some harmonic analysis just to do this translation.
I'll do House of the Rising Sun because that's the one I know. The Am is the root chord i
(but the proof is really in the second and fourth lines of the progression with the V-i
movements). The next chord C is a mediant III
. The next chord D is a fourth IV
. Then the F is a curveball, because we just heard an F♯ in the D chord. It's called a chromatically-altered mediant ♭VI
, and it produces a little bit of excitement by jumping out of the frame of the scale established so far. Before the F, we're in A Dorian Minor. Then we're in A Natural Minor. But by the time the E7 V7
comes around, we're in Harmonic Minor.
This shifting about of scales is part of the excitement.
Another aspect, exposed by leftaroundabout's answer (with which I entirely agree), is delaying the "cinching" of the tonic. You can't really be sure what the key is until you follow the whole thing with its twists and turns and see where it's driving at.
One rule of thumb which appears to work with both of these examples (and with most Western Tonal Music) is to look for the V-I
or V-i
(if it's minor). The V
chord is often very strong when it enters, and the rules of counterpoint indicate how the trapped tritone wants to resolve. If it resolves "correctly" to I
(or vi
, in a deceptive cadence) then you can be fairly sure you've found the key.