24: How to analyze the chord E D A B E?
Question: I am in rehearsal for a setting of "The Cloths of Heaven" in a 5 part choral texture which SEEMS to be in a fairly straightforward dorian mode, at least in the initial motives. As the piece progresses, the dissonance increased so that what you would consider the tonic chord ends up being some permutation of both a d minor and e minor chord at the some time. For instance one cadence figure prepares as (from the bass up) ADFBE, inverts this chord to AEFBD, allows the alto voice to move upward to G while the other voices hold, then "resolves" to EDABE. I notice that the lack of the F in the resolution removes both the half step and tritone dissonance, but it's still far from a major chord, but it certainly SOUNDS settled by this point in the progression. Help? The voice leading is really quite good and the individual parts all make sense, but how would you analyze something like this?

Answer: This could require a cup of coffee. Maybe the piece was not made to be analyzed, but I'd say the composer has written a quintal harmony: a final chord built on fifths instead of thirds: D - A - E - B. And it's in a quintal version of 2nd inversion. If you look at it that way, the penultimate chord is a quintal dominant, making a quintal translation of V - I: A-E-B-F (the upper fifth being diminished), then D-A-E-B.

I don't really believe in quintal harmony, though. That is, while I know some have thought that one might just substitute fifths for thirds as the basis of harmony, a substitution like that doesn't really work in the same way that triadic harmony does. Triadic harmony is not arbitrary; it was as much discovered as it was invented. Triadic harmony derives from the overtone series; we all have heard triadic harmony and tend to mentally fill in a missing third in a sounding fifth. What you end up with in quintal/quartal harmony is something that sounds like triadic harmony with unresolved suspensions.

Which can sound pretty good! But it can't sound resolved; it leaves you with a question. In this case, since the E is the bass of the final chord and "inversion" of a quintal chord really isn't going to work for the listener, I think it will be perceived as an E7 sus 4. Maybe that's what counts. And with A as the bass of the previous two chords, one could even see this conclusion as a sort of plagal cadence, an "amen" cadence of IV- I.

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