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Pitches that determine a chord's harmonic function

Discussion in 'Music Theory [DB]' started by Tom Lane, Feb 4, 2021.


  1. If I would see a maj7b9#11, I would ask first if that is correct, then (if possible) ask the composer for the intended notes to play (to check if he knows what it means or if it has been a writing error). Then if he really wants that. In between maybe checking the score which notes were used for the other players and if they comply with the chord symbol.
    Then maybe (or even earlier) comes the the question to me if I prefer to leave now (before been thrown out).

    Nothing against strange chords, but the composer needs to know what could be played on them and be able to give hints/instructions, since this is far outside of classical and jazz music theory.
    It‘s easier for classical composers since (almost) anything is fixed and the free parts are either completely free or rule based.

    My rule is only halftones (no wholetones) around an augmented second. If that is violated, there is mostly one more note inside the augmented second. Which would make it an eight tone scale (with a dropped note.

    Another rule is no consecutive halftones. The only exception is around the root, fifth or maybe fourth. And this usually only if the root and scale stays constant over a longer time like in Indian classical/traditional music or in Gypsy music with more than one augmented second.

    And that would exclude a major (third) b9#11 for me. And it would put a maj7b9 in the Indian drone category.
     
    Wasnex likes this.
  2. Once we are talking about 13th chords (7 note chords), then the inversion and voicing will change the name of the chords. After all, there are 6 other chords in that scale that have the exact same notes.
     
  3. A Maj7b9#11 in root position or an earlier inversion is just going to create a richer dissonance, the Maj7 is already dissonant, so the role is just expanded a bit. Depending on how it is played and resolved it could be quite beautiful.
    In a root position, you are still going to get the Major 3rd first, and that will soften the blow and keep it from being a cluster.
    The interference with the 5 by the #11 will likely arise as the chord is played. If the voicing drops the 5th, you could get an added unstable quality from the tritone.

    In a II-V-I, it could really be used to hold the tension. Even though the Maj 7 is dissonant, all the internal harmonies are so stable that combined with a return to the tonic, you get a level of resolve.
    You can keep the tension going with such a chord.
    It is the sort of Harmony Mingus would use.

    I don't think it should present any issues or even questions for a bassist. The only real differences are if you want to push the consonance you are going to have a tougher time and you have a few more options if you want to push the dissonance.
     
  4. Harmonic function is understood in context of chord progression, not in chordal isolation. And as posted earlier, harmony, voice-leading and counterpoint are intertwined. Sometimes harmony is given more weight than counterpoint, other times vice-versa.

    Hearing a close-position voice of a Major 7 (b9, #11) in isolation for me the "root" sounds like the foreign non-chord tone..
    ie. on G
    G, B, D, F#, (Ab, C#)
    sounds to me like (G), B, D, F#, G#, C#
    A nice Bm6-9 chord (familiar sound) with a non-chord-tone dissonance below, which wants to resolve to F#
    Bm6-9 / G (Slash chord)
    or in a different voicing.
    (G), G#, B, D, F#, C# (G#ø7add11 / G)

    Without a context, the lowest note won't always sound like a root, or even a chord tone. And counterpoint teaches us that not every note sounding simultaneously with other notes is a chord tone. It could be a melodic dissonance on its way to being resolved.
     
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  5. Tom Lane

    Tom Lane Gold Supporting Member

    I agree with everything in your post but have to quibble with the first sentence. Clearly, everything happens in context; it's unavoidable, but I think there's something to be learned by listening to those "chords in isolation" to see how the pitches affect the chords color. Kind of like looking at a blue square of paint or a green square of paint, each creates its own feeling in isolation, and then when mixed into an entire scene with other colors, present, that feeling is both still present and transformed.
     
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  6. Wasnex

    Wasnex

    Dec 25, 2011

    The point is a chord can totally stand on it's own and sound great without being functional. If this doesn't make perfect sense, I suggest reviewing the definition of functional harmony.
     
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  7. Tom Lane

    Tom Lane Gold Supporting Member

    I think we're miscommunicating somehow. I got what you wrote out of Longfinger's response and don't see why you think I didn't based on my post. But, please, tell me what other basic definitions I should review.
     
  8. Wasnex

    Wasnex

    Dec 25, 2011
    Sorry, I don't understand why your are quibbling with @longfinger 's first point and attempted to explain why I think the point is correct, nothing more.

    I agree that there is something to be learned from listening to chords in isolation, but IMHO you cannot deduce harmonic function from an isolated chord (the point I think we are quibbling over). So IMHO the entire premise of this thread is flawed (Edited to add: in the context of an isolated chord anyway).

    AFAIK functional harmony is the Western system of diatonic harmony, and non-functional chords are unrelated in any way to the defined tone center we are working in at a given moment. Most jazz standards have a few chords that I find hard to define as functional, but keep in mind I am semi-literate at best. Also, people with far more of an education than I argue over the harmonic function of various chord passages. AFAIK, there is often enough ambiguity that more than one person can be correct. Perhaps that is what makes jazz great ;)?

    My apologies for being offensive and speaking inartfully :sorry::bag:.
     
    Last edited: Feb 24, 2021
    longfinger likes this.
  9. Tom Lane

    Tom Lane Gold Supporting Member

    No worries. I know that I'm failing to communicate my idea based on the responses. Honestly, I kind of gave up long ago; I mean, TB is full of ideas important to one member that no one else gives a hoot about. But there's still some new thoughts being expressed so I felt compelled to respond. I thought that the "paint square" analogy would be clear, but it's obviously not.
    I'm not sure that I can do better but since there's still some honest, positive engagement, so I'll give it another try.
    As an analogy - maybe that's a logical fallacy, I don't know so but I don't think so - imagine that human language is comprised almost solely by nouns and verbs. No adjectives, adverbs, prepositions, etc, because I'd have to spend a lot of time trying to figure out how those concepts translated to my analogy. In economics or business strategy, we'd refer to that as a "model", which is intended to provide us a framework to consider causes and effects. It's not completely accurate but it still provides some value for prediction of inputs and outcomes. I know that that's an oversimplification but... it's an analogy, go with it, or don't. If your argument is to pick apart the finer details of an analogy, then I don't think you're not really having a conversation, you're just arguing to win.
    In my analogy, dominant chords are verbs - indicating movement - and tonic chords are nouns, indicating something solid with little to no movement; not at ALL the traditional definitions of tonic and dominant. I've redefined them for the point of this discussion.
    If you're still with me, some nouns can become verbs depending on the context, but that doesn't negate the "inherent nature" of the word. Take "effect" and "affect" as an example. In U.S. modern English, they're pronounced pretty much the same way; there's ONE letter difference between the two. But, depending on the context, they take on different roles. The word didn't really change; the context changed the meaning of the word. The word has multiple inherent meanings depending on its context, but it possesses an inherent quality and meaning independent of its context. And that inherent meaning, common to both the noun and the verb is "change".
    So that's my assertion, that chords possess an inherent degree of "movement" or "stillness" that is independent of context, but is very dependent on voicing and instrumentation and once placed in context, the context modifies the innateness of the chord, somewhat regardless of how that vertical set of pitches is realized, but the original nature of the chord still exists; it's modified by context but not typically negated.
    In a nutshell, I agree that chords take on different character based on their context. I reject the idea that they have no character until they have context. So, then, Longfinger's statement: "Harmonic function is understood in context of chord progression, not in chordal isolation" is wrong, because it overstates the value of context, and understates the value of the inherent nature of the pitches in that moment, and that's what I was trying to "quibble" with. If he had written "A chords harmonic function can be significantly determined by its context in its progression and composition." I wouldn't have had a "quibble" but, he didn't and in my view, he overstated his point.
     
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  10. Wasnex

    Wasnex

    Dec 25, 2011
    As far as I can follow it, I agree with you up until the quibble begins. Much of what you are writing is very abstract so understanding your exact meaning is not possible, but I think I get much of what you are trying to say. But I think you are talking about a different idea.

    AFAIK @longfinger 's statement is actually very precise and limited.

    If you were to give a chord and specify the tensions out to the 13th...in other words specify the quality of all 7 tones, you can't say how the chord is functioning until you put it into the context of the surrounding chords and possibly the melody. I believe the very same chord and tensions can function in different ways, or the chord may be nonfunctional. Here is a simple example, we normally assume a D7 will be a V chord, but it could also be a diatonic IV chord in Jazz/Melodic minor.​

    Keep in mind, with jazz you have to deal with altered extensions. AFAIK some altered chords can still be considered functional even though they are not 100% diatonic--I.E. we kind of fudge the definition of functional harmony somewhat in jazz, sorry :atoz:. So if the full chord symbol does not fit into a key center for a Major, or one of the three Minor forms, how do you know for sure how a single isolated chord functions. AFAIK, you can't until you put the chord into the context of the surrounding chords and melody.

    In other words, we only see if the chord is functional and how it functions in the full context of the harmony and melody.

    This is really getting over my head but AFAIK, once you start getting up into extended chords it's fairly easy to get new chords by simply using an inversion. In other words, if you invert the chord you get another chord. This posses the question, which chord is actually the functional chord? Hopefully this little quirk helps you see why I am challenging your point.

    In my experience, this can make analysis very complicated because the chord written on the page may not actually be the functional chord, so you have a bit of a riddle to solve before you can complete the harmonic analysis. Not certain, but I believe all of the following are possibilities: 1. The functional chord may be an inversion of the written chord, 2. the functional chord may be extensions of the written chord, or 3. the written chord may actually be extensions of the inferred functional chord. Sorry if any of this is wrong...like I said, we are getting over my head.
     
    Last edited: Feb 25, 2021
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  11. I'm enjoying this discussion.

    TLDR version: isolated sonority absolutely has character. Character is not harmonic function. An isolated sonority with the character of dissonant-movement, (or dissonant-stillness, consonant-movement, consonant-stillness) does not mean it has "harmonic function", because common use of the term harmonic function is a smaller label that depends on a parent scale, and a chord scale tonal relationship. (eg. I, ii, iii, IV, V, vi, vii)

    A sonority may have an intrinsic quality of dissonant-movement, that you may want to associate with a dominant function, but that is an expansion beyond the common use of the term in tonal harmony. (Ditto "Stillness" sounds that you may want to associate with a "tonic" function.)

    It is a good exercise to do. Listen to sounds that we imagine want to go somewhere, vs. sounds that we imagine want to stay as they are. Expand our imagination regarding sounds. Perhaps even create new language to describe those sounds.

    As music creators, we can do whatever we want with the music. If the music sticks in the culture, the theory will catch up.
    -----

    Long version:

    * An isolated sonority absolutely has character. Character is not harmonic function. *

    To expand on that...

    Take this lovely isolated sonority.
    0,1,6,7
    in the names.. C , Db, F#,G
    Sound really nice right? Go to the keyboard and play around with the voicing options, inversions. Each one has a sound and a character. The character is there without context.

    Harmonic function is not there. Not in those 4 notes by themselves.
    This isolated sonority of 4 pitch classes, has its origin in set theory which nothing to do with 7 note scales and tonal harmony. There is no chord progression, no key, no 7 note scale, no harmonic function.

    To use your terms above of "movement" or "Stillness"... the 0167 while dissonant, it is somewhat equal in dissonance so perhaps there is not much "movement" Would "Dissonant stillness" apply? Even if an isolated sonority had a character of "dissonant movement", by itself, that would not really mean it has harmonic function. I think this is the quibble point between us on this topic: The definition of harmonic function.

    For most: Standard harmonic function, to exist, needs a parent key. A 7 note scale to build all the chords out of stacking 3rds to create a chord scale. Then the chords from that chord scale relate to each other in a functional way (I, ii, iii, IV, V, Vi, vii) We can borrow chords from adjacent scales as heard fit to do so.

    Those 7 chords are then grouped in 2 main functions.
    1- Tonic,
    2 - Dominant

    and 2 smaller functions
    3 - pre-dominant
    4 - tonic prolongation

    Without that whole system, the term "harmonic function" doesn't really mean much. Within the system, a chord that "wants to resolve" can be called a type of Dominant function, if it's built right. But once we pick notes that are outside of the system, a chord that "wants to resolve" isn't really any kind of Dominant. It is just a sound that we imagine wants to go somewhere. The sounds have outgrown the tonal harmony box.

    ----
    (side tangent)
    @DoubleMIDI brought up some really good points about the scale, no consecutive half-notes, no whole notes around an Aug2nd. Why? Well, to stack up chords using ONLY Major 3rds and Minor 3rds we simple can't make those combinations up. Stacking only Major and Minor 3rds we get the following 4 scales.
    - Major
    - Melodic minor (asc)
    - Harmonic minor
    - Harmonic major
    Each of those has 6 other "modes" or "scale inversions", each with their own character.

    Without a diminished 3rd in the scale, we cannot make a Dominant 7(b5) or a Major 7(b9).

    So when we have a Major 7(b9)#11 chord, what is the parent scale?
    1,b2 3,#4, 5, (6), 7. (using the lowest note as 1. There are 7 options)

    If we use that scale, and make up the 7 chord scales, and relate those scales to each other, we will have tonal progressions and harmonic function and one of the chords will be a Maj7(b9)#11. Without that, it is not a diatonic chord in a chord scale. In the regular scales we use, that chord has to have one non-chord tone, or one chromatic alteration that makes one note a foreign tone to the scale of the moment.

    Another side tangent:
    We can also listen to early 4 part renaissance music. Each 4 note simultaneity has a character and can be appreciated "vertically", and many, but not all, may be spelled out as a chord built of thirds. However, there is no formal harmonic function, nor chord progressions at work. It's all counterpoint in that era. A sound that wants to resolve or move forward, which the music has, should not be given a Dominant label, if wanting to be true to the music of that era.
     
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  12. Tom Lane

    Tom Lane Gold Supporting Member

    Thanks for your comments. I didn't quote them because they're so long, but I thought @Wasnex did a great job explaining the complexities of harmonic analysis of Eurocentric music, if not others cultures too, and I think @longfinger has put his finger on the crux of the discussion - namely, whether a chord that "wants to move" is inherently dominant. If I understood him correctly, he said "No", and, I agree with him. His 0167 chord does an excellent job pointing that out because it's pleasingly dissonant without a sense of movement. An aside: I don't think I've seen that nomenclature before, 0167, where is that common?

    And, I think we're all agreeing that chords have innate characteristics and that it's worthwhile to listen to them in isolation - without a key or tune in your mind's ear - and then see how they behave "in the wild". Considering @Wasnex 's comment made me think of these three scenarios. I won't bother to TL;DR them because I know you guys are already nerding out with me beyond normal reason and I'm glad that I managed to find this discussion after all. I don't think I'm saying anything below that you don't already know; on the contrary, you're probably ahead of me and I'm catching up to you, but maybe the illustration will be worthwhile.

    First, consider a nice, pleasant DbMajor6 chord. Played on a digital piano just above middle C, contained within that octave. A digital piano because I want to be able to reliably recreate the sound without concern for how well tuned my piano is. At least a digital piano will be consistent. Spelled Db F Ab Bb. And, of course, the specific voicing is significant because a different voicing will sound different. I know you guys can hear that in your minds so I won't bother to notate it or record it; for a student I probably would have.

    Now, try to describe that sound. For me, I'd probably start with it's kind of bland. Pleasant, friendly enough, really no tension or dissonance; no deep dramatic bass note, no piercing high note; not a cluster chord but not spread across three octaves either. If it were a color, I'd say beige. If it were a car, I'd say it's a Toyota Avalon because it's not as rich as a Lexus nor as sporty as a Camry, but nice, comfortable, kinda boring, but solid. If it were a food, maybe oatmeal? Or a hearty slice of sandwich white bread? Not Wonderbread, but the more homemade kind you'd find in a deli that prides itself on its breads. Wonderbread would probably just be the triad in root position. Fair enough? I know some people associate sounds with colors and other people colors with people's names. It's usually very personal to them in that no one else shares their associations in the same way. It's probably worth noting that while the descriptions are culturally bound, the overall feeling is roughly the same for most people. If you're in Texas, you might think it'd be an white Ford F-150 and unadulterated grits, but the majority of people would hear it roughly the same way.

    By the terminology I was trying to apply earlier in the discussion, this chord would be "still" rather than "moving". But, to put the scalpel on the points you've been making, if I use that chord in a progression, I can change its harmonic function despite its innate nature. If I use it as the last chord in a ii V I progression, it will sound like the tonic, perhaps a little bland, but solid. If I drop it as the penultimate chord in: C69 E-7 A-7 D-7 G7 Db^6 C6 it takes on a dominant function despite it's "feeling" in isolation.

    And, the opposite extreme, a dominant chord that serves a tonic function. Coltrane's Blue Train exemplifies the idea; every chord is a 7#9 chord. But it's really worth noting how weak the resolution is between the V7#9 to the I7#9 chord is. The nature of the 7#9 chord itself makes it less effective as a tonic chord in terms of producing that satisfying cadence we can get.

    So, I think that we're agreeing that chord voicings have an innate character and that character is independent of the harmony it's used in, but, the context can alter or not, the "behavior" or function of the chord.
     
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  13. My point is that in many cases, such a complex chord is not a 'challenge' to the bass player (trying to make sense of what is essentially shorthand for sheet music) but the other way around, it is the notation of what a celebrity bass player chose to play in a seminal recording of a piece. Our choice is to either copy that (and then a transcription would be far easier) or to create our own bass line, in which case we have as good as no business with maj7b9#11-like additions. And if these occur in the melody of the tune, that gives us all the more reason to avoid them.
     
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  14. Wasnex

    Wasnex

    Dec 25, 2011
    In my experience, such a unique and complex chords can definitely complicate the bass line. They may make it difficult to improvise a nice line on the spot that leads smoothly through the changes with the proper motion and energy. The chord is definitely helpful, but figuring which tones to play, and which beats to play them on on can be quite the challenge.

    Usually I have enough skill to play pretty freely over written changes, but with chords like that I may have to figure out one or two lines that work well in advance.

    There's only one chart in about a 25-year career where I remember dealing with chords like that where it was essential to integrate the altered extensions into the bass line, and it was only in the very last few bars of the tune.
     
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  15. Oops, I missed this request.

    I learned these in music ear training class, and theory class. They are common in 12-tone serial music (Dodecaphonic).
    Each note is given a number C = 0, C#/Db = 1, D = 2 etc... Bb = t, B = e

    The common tri-chord and tetra-chord structures are transposable, so 0 here can be any note.
    012
    013
    014
    015
    016
    024
    etc Just list "prime" form. A 023 is an inverted 013, so the convention is to stick with 013.

    tetra-chords
    0123
    0246
    etc

    0167 is nice sound as it has large and small intervals. It is also a dissonant but stable sound. It is also inversionally symmetrical. It is sometimes called a Z-cell.

    I looked around, and found this link. It is a nice refresher.

    Analyzing atonal music – Open Music Theory
     
  16. Tom Lane

    Tom Lane Gold Supporting Member

    Thanks for the explanation and the link. I read the link. I'm familiar with much of it, but it was a good read, thanks!
     
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