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I've been getting a lot into microtonality/xenharmony recently. However, I've been struggling when composing, since the theory of functional harmony I usually rely on is now deemed useless. I understand that songs don't necessarily have to be functional, but I wanted to ask the question:

Is there some way to generalize the concept of chord function to arbitrary systems of notes?

In other words, is there something that could tell me what the functions of each chord withing an arbitrary, microtonal scale were, without having to depend on trial and error? (Or maybe something that works for a general enough family of cases?)

Anonymous Pi
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    I don't know enough for an answer but you might start with looking a tension and release in melody and think about how leading tones work. Like if you play a regular diatonic major scale and just stop on the seventh degree, that will create tension until you move on to the octave to "resolve" it. I expect there is a microtonal equivalent to that. From there you might find chords that contain leading tones to the notes in other related chords. – Todd Wilcox Feb 12 '18 at 20:06
  • @ToddWilcox I've heard that one of the main reasons some chords such as the usual V or vii° sound tense is because of the 4th and 7th degree, clashing with the much more consonant and near 3rd and 8th. This isn't that easily generalized since it requires a well defined tonic chord to base upon, and notes on the scale near some of them. But I'm guessing that after some experimentation, something like this might just work out. – Anonymous Pi Feb 12 '18 at 22:02
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    Good question. I'm afraid it may not be answerable – many microtonal composers seem to struggle finding proper functional harmonies, and even great Ben Johnston's pieces often lack a clear finality in cadence-analogues. In most systems, there's just such a vast space of possibilities that it's hard to establish anything like resolution-familiarity. [Elaine Walker has a lecture on some possibilities of functional harmony in Bohlen-Pierce](https://www.youtube.com/watch?v=noBPeHMorVI&list=PLE3C3C9E2284F993A), that's the closest I'm aware of. – leftaroundabout Feb 12 '18 at 22:34
  • You may find some guidance in the articles posted in answer to [Microtonal theorists who go beyond describing temperament and scale construction](https://music.stackexchange.com/questions/75208/microtonal-theorists-who-go-beyond-describing-temperament-and-scale-construction/104759#104759). – Aaron Sep 12 '20 at 04:27

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To me it sounds like you’re looking for a way to extend some fundamental concepts of functional harmony while compensating for the use of microtones. Unfortunately, to my knowledge, such a guidebook doesn’t exist. It is likely because microtonality is still not standard practice - it’s use and application typically being pretty specific and situational. However, there is good news, we can puzzle our way through it. Since the application for your purposes is different, in order to figure out chord function on a micro-scale, we have to actually widen the scope of our lenses and look at general chord functions through a very wide lens.

Tension / Release: As others have mentioned, this is a biggie. Triads built diatonically from scale degrees exist on a continuum of tension. However, it’s important to remember that the chords in of themselves do not contain much tension, but it is rather the context through which the chord operates. A major chord in one context may provide a peaceful resolution while that same chord in another context may provide a strong pull somewhere. How are you creating tension / resolution through context? How are you creating that context?

Progression / Regression: In traditionally functional contexts, certain chord relationships result in “progression” or the sense of moving “forward” in a piece while other chord relationships yield a sense of “regression” or the sense of holding back perhaps with a slight feeling of repose. How could you create these same experiences with microtones?

Frequency: No, not talking about individual pitches or Hz, but rather, how often something happens. In traditional harmony, we hear tonic sounds the most, or at least are the most heavily emphasized. In the absence of traditional function, how might you emphasize certain notes over others to establish hierarchy?

Harmonic Pacing: Beyond how often you hear something or how you got there, it also matters when you hear it. In traditional harmony, cadences typically signal the completion of a musical thought, idea, or section. How are you placing your chords to establish function through harmonic pacing? How are you signaling the completion of a musical thought, idea, or section?

In sum, by widening our scope on the role of traditional chords, we’re able to see their application to microtonality. Though by no means comprehensive, this should at least get the ball rolling in terms of creative thinking.

Hope that helps.

jjmusicnotes
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  • Seems like a pretty fine answer to me. Just one question: How do you determine (as in your first point) where does a chord lead to? I mean, we probably have no objective way of doing this, but is there something I can guide myself upon apart from pure trial and error? – Anonymous Pi Feb 14 '18 at 19:58
  • Well, if chords are important to your music, you’ll need to figure out where they’re going and why they’re going there. You figure out where they’re going based on the music you write. Having a large-scale tonal plan is a great way to give yourself a framework to work from - even if you eventually abandon it entirely. From there you can use your brain to see if it makes sense and your ears to see if it sounds right. This act of checking is a very necessary part of the creative process. Writing music is mostly trial-and-error as everybody has different answers for themselves. – jjmusicnotes Feb 15 '18 at 03:00