My theory of harmonic functions

Chords, scales, harmony, melody, etc.
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Z1202 wrote: Sun Oct 06, 2019 1:07 pm 1. The strongest and the primary factor is the presence of the 6th or the 7ths degree of the scale in the triad
  • any triad containing the 6th degree has subdominant function (II, IV, VI).
  • any triad containing the leading tone 7th degree has dominant function (III, V, VII), where the III of the major scale is rather weak as the dominant and rather falls into the third group below.
  • any triad containing the natural (Aeolian) 7th degree belongs to the third functional group, the name of which I don't know, if it exists.
  • the raised 6th of the melodic minor could be considered as giving rise to a special flavor of subdominant group (with a questionable member of the diminished root position chord on the 6th degree, thus instead one could rather simply apply the second rule below to the remaining II and IV chords with raised 6th degree of the scale)
  • note that thereby the tonic triad is the only one not belonging to one of the above mentioned groups.
Ideas similar to this do turn up in Christopher Doll's Hearing Harmony, particularly when it comes to VI chords being kinda subdominant.

I think one problem here is the overloading of the word "function", which tends to imply a system that's designed for common-practice tonal music. I don't know the context of your reading or approach to music but I suspect the rules you have been building for yourself are a long way outside the boundaries of common-practice tonal music. Doll's book is about harmony in rock, which often doesn't use the classical cadence structure (and functions) at all.

The big problem with trying to create rules that go outside common-practice tonal is that the terms get muddy real fast. And inventing new terms for "function", "dominant" and "subdominant" isn't very practical. Doll has a go but doesn't go the whole hog, with the result that you wind up wondering what each term really means.

The core problem is that music appreciation and composition is the result of enculturation. There aren't really any rules other than rules of thumb that develop from multiple uses of the same motifs across lots of music that interact with how the brain perceives the harmonic series in individual notes. So, trying to develop a one-size-fits-all set of core rules is, frankly, doomed to failure IMO. All you can really do is say "in this style of music, this tends to happen and some styles insist on certain motifs, such as leading notes for cadences to make it seem cohesive".

You might find work in the psychology of music by people like David Huron more instructive.

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Ploki wrote: Thu Jan 09, 2020 10:24 am
jancivil wrote: Wed Jan 08, 2020 11:03 pm ”Double dominant” is probably a term from some School, but you have one dominant at a time (unless this is supposed to describe bitonality).

“just a flavor of the tonic”? Tonic function, dominant function, two things. I may become V/IV but then it’s the new function. :shrug:
English isn't my native nor the language i studied in, but i think double dominant is referring to "dominant of the dominant" or V/V, which is technically on the II degree (supertonic).
I found the literal translation in one of our papers and it supports this assumption, but it's not a widely used term at all.
Yeah, on reflection I think it may be a lost in translation thing. Double dominant in English indicates duplication, now with some alteration here are two of the things.

All ii has to do is become II to resemble V/V. Best as II7 for *function*. School of St Petersburg has not reinvented the wheel there.

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The slightly irritating thing for me w. EG., vi is subdominant function is there’s just no need for new lingo. It’s too weak. Now ‘iii is subdominant’ is fair game. There is easy to grasp reasoning for these two to be seen as tonic substitution, two of three notes are identical w. I. Hence, “weak progression”. Which is not the pejorative sense of ‘weak’, really, just relative to IV-I or V-I.

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Ploki wrote: Thu Jan 09, 2020 10:24 am
jancivil wrote: Wed Jan 08, 2020 11:03 pm
”Double dominant” is probably a term from some School, but you have one dominant at a time (unless this is supposed to describe bitonality).

“just a flavor of the tonic”? Tonic function, dominant function, two things. I may become V/IV but then it’s the new function. :shrug:
English isn't my native nor the language i studied in, but i think double dominant is referring to "dominant of the dominant" or V/V, which is technically on the II degree (supertonic).
I found the literal translation in one of our papers and it supports this assumption, but it's not a widely used term at all.
I don't think he is referring to secondary dominants or a normal dominant. There's a third concept, but I don't know what it is in english in particular. In Finland, we call it "secondary dominant" whereas what is normally called as secondary dominant is called "mid dominant".

Now I might be incorrect, but I think what might be referred to are dominant seventh chords within a progression that are not based on the fifth degree and do not tonicize the chord that comes after them in the same sense that a secondary dominant would.

So, for example, Imaj7 | II7 | ii7 | V7. And possibly also something like VI7 -> V7 in major. Of course, this shouldn't include augmented sixth chords since they're analyzed as subdominants anyway.

All in all, this is just a guess as to what it could mean and yes, if it is this, it's probably too obscure to be using just like that. I've never heard of it in English and besides knowing that something like this exists, I've never really seen any proper theory on it.

EDIT: Oh I found it. Apparently it's just substituting a chord in a progression with a dominant seventh chord that is a fifth below the chord you'd substitute. Still don't know if that is what they meant by this

2nd edit: And after reading that particular bit, I do not think this is what was meant. Probably mistranslation.

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jancivil wrote: Wed Jan 08, 2020 10:37 pm I’m not into theory at the level of caring a lot about eg., Riemann, or Schenker, really at all. Schenker is interesting and deep, but who has time for one individual’s takes. Except maybe Schoenberg, Structural Functions of Harmony. IE., what did Riemann write we care a lot about?
Riemann wrote on many topics, but is mainly famous for his take on harmony (basically invented "functional" harmony, also the name; but music theory in Anglo-American parts of the world uses the Austrian take on these theories - the German take is more complicated - https://pdfs.semanticscholar.org/673f/5 ... b680ff.pdf). Also, is the godfather of modern "post-tonal" chromatic theories, based on voice leading/compositional spaces (Lewin, Tymoczko and other modern theorist work on this).


https://en.wikipedia.org/wiki/Hugo_Riemann
https://en.wikipedia.org/wiki/Riemannian_theory
https://en.wikipedia.org/wiki/Neo-Riemannian_theory

Schenker/Schoenberg's take on harmony is better suited for 12 equal and is certainly more readable.
But, like I said, today exist better resources for studying harmony both for the practical student (any modern textbook) or theoretically inclined student(many specialized academic monographs and articles that really get into the deep - not or only from acoustic or mathematical viewpoint, but also don't forget facts from human psychology and our hearing apparatus).

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Sorry, I meant compare Schoenberg, the composer, what music did Riemann write.

Seems interesting, but I’m not intellectual enough for it I’m afraid.

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Gamma-UT wrote: Thu Jan 09, 2020 11:30 am Ideas similar to this do turn up in Christopher Doll's Hearing Harmony, particularly when it comes to VI chords being kinda subdominant.
Actually I learned this idea literally from Piston's book on harmony, and I think it totally makes sense. Especially in the minor key, while in the major key the perception of vi as subdominant can be easily offset by its function as a tonic of the relative minor.
I think one problem here is the overloading of the word "function", which tends to imply a system that's designed for common-practice tonal music. I don't know the context of your reading or approach to music but I suspect the rules you have been building for yourself are a long way outside the boundaries of common-practice tonal music. Doll's book is about harmony in rock, which often doesn't use the classical cadence structure (and functions) at all.
Maybe my use of the word "function" is not 100% standard. This is the system I developed for my own, based on common practice tonal theory but with purpose of application to something more like modern pop. I found that most of the common practice rules still do apply, it's more that one can more easily abandon them.
The big problem with trying to create rules that go outside common-practice tonal is that the terms get muddy real fast. And inventing new terms for "function", "dominant" and "subdominant" isn't very practical. Doll has a go but doesn't go the whole hog, with the result that you wind up wondering what each term really means.
Well, the terminology I'm using is essentially the one used by Piston, just from a different angle (using the presence of 6/7 degrees as a key feature rather than listing the chords explicitly).
The core problem is that music appreciation and composition is the result of enculturation. There aren't really any rules other than rules of thumb that develop from multiple uses of the same motifs across lots of music that interact with how the brain perceives the harmonic series in individual notes. So, trying to develop a one-size-fits-all set of core rules is, frankly, doomed to failure IMO. All you can really do is say "in this style of music, this tends to happen and some styles insist on certain motifs, such as leading notes for cadences to make it seem cohesive".
Yes, I probably didn't clearly enough state the context. My fault, I was assuming this would be implicitly understood. Actually the set of rules I'm proposing are not any kind of rules to follow. Maybe the word "rules" is a misnomer. Their purpose for me is rather "macro controls". Rather than thinking about individual notes, I want to have some macro features, identifying the harmony. What I found is that rather than asking myself "which chord do I want here" I tend to ask the questions: "do I want something of a tonic, or something of a subdominant or something of a dominant feel" and "which bass note do I want to have here". The other notes in the chord are decided later. E.g. I'd start with the idea to have a subdominant type of chord on the 4th scale degree in bass. Whether it's gonna be ii6 or IV is a detail (maybe it's gonna be none of those, as I might put some other notes in). Similarly, I tend to see augmented sixth chords as a particular form of V/V, it doesn't matter that the secondary leading tone is not in the bass, it is still there in the chord, and for me it defines the chord's function. So there "rules" are more a description of the way of thinking. But they are nothing to be strictly followed, rather to be used as one sees fit ;)

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So, it's just about the two key-factors defining the harmony (from my POV): the bass note and the flavor (being mainly defined by the presence of 6th or 7th degrees, although other factors may offset that). So I might start with the idea that I want to have a subdominant flavor of the harmony, which means I need to have a chord whose primary triad contains the 6th degree, and generally I need to have the 6th degree somewhere in the chord. Then I can decide on the strength of the subdominant, giving me a choice between 6, 4 and 2nd degrees as the bass note (unless I want to have a higher factor in the bass, which is a special case, since the bass note in this case is usually more like a passing one). Then I can decide which other notes I want to add to the chord. Some of these notes may completely offset the original idea, but some others won't. E.g., given the 4th degree in the bass and the 6th degree somewhere else, I might simply add the 1st degree, giving me the IV, or just add the 2nd degree, giving me ii6 or add both, giving me added sixth chord. OTOH, adding the leading tone is likely to offset the whole into the dominant area, but now I'm having both 7th and 6th degrees in the chord and the 7 degree simply "wins".
Conversely, I might have an idea of having the 4th degree in the bass. Then I can decide on the flavor. Using the 6th degree somewhere would tend to give me the subdominant, using the 7th creates the dominant tritone. In minor I could also add the secondary leading tone at 4+ degree, giving me the augmented sixth chord (V of V). Then I could choose other factors (in particular I can construct different augmented 6th chords at will).
Of course there are exceptions. E.g. I might have 4th degree in the bass and have the fifth of the chord, but completely omit the third of the chord (the 6th degree). But that's a special case which is judged in relation to the "normal ones". Specifically, I don't want to define which of the two subdominant flavors (the one with natural or raised 6 degree) I'm using.

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Blablablablabla listen to the expert from 19:30

https://m.youtube.com/watch?v=KAHY7jNGT9c&t=83s

Maybe you guys'll learn something. I highly doubt it, though. But that's another part of the story. Not too bothered here :)

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jancivil wrote: Thu Jan 09, 2020 5:31 pm The slightly irritating thing for me w. EG., vi is subdominant function is there’s just no need for new lingo. It’s too weak.
The OP gives all Roman numerals in capital letters. You cannot sufficiently convey this kind of concept to others being unclear like that.

I apparently looked at this and corrected VI (unclear, since VI occurs in minor) in my mind to vi. Not buying vi as subdominant at all. However, VI in minor to V can be secondary dominant; confer flat five substitute principle (also seen as French sixth construction). In C minor: Ab C D F# to G B D F.

Augmented Sixth chord is secondary dominant functionally. I would not conflate subdominant w. secondary dominant. Subdominant does not have a particular tension fulfilled by a subsequent dominant harmony, as secondary dominant does; except that Augmented Sixth chord alters iv6. In C minor: Ab C F to Ab C F#.
Last edited by jancivil on Mon Jun 22, 2020 1:49 pm, edited 1 time in total.

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Interesting, but let's hear it from a real expert (starting at 18:10):

https://m.youtube.com/watch?v=KAHY7jNGT9c

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So, you’re unable to say anything at all about the matter in your own words. I’m not worried about what you believe to be expertise. IME you’ve shown your ass quite enough here.

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jancivil wrote: Mon Jun 22, 2020 1:51 pm So, you’re unable to say anything at all about the matter in your own words. I’m not worried about what you believe to be expertise. IME you’ve shown your ass quite enough here.
I have no clue what you are trying to state.

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You’re the guy who tried to argue a straightforward Am7 in first inversion (or Cadd6) was really E minor sus4 #5 (and at least one other equally hilarious construction) FFS, and proceeded to explain the lack of agreement with this crap as everyone else had a reading comprehension problem. You’re an absolute joke here.

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@jancivil
Obviously, I was kidding. Sorry, I won't do it again :)

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