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Thread: What determines the function of a chord?

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    Default What determines the function of a chord?

    I’ve been trying to learn about functional harmony and I keep asking myself the above question. Each chord seems to have a general function (with exceptions) within scales, but why is that so? Were scales made with those functions in mind, or were those functions agreed upon or discovered after scales were already determined? Is it a result of having 7 notes in a scale? For example, if you were to choose 7 random notes within an octave...would the 5th chord always serve a dominant function?

    DISCLAIMER: I know I’m asking a simple question that doesn’t have a simple answer and I don’t expect any response to be cut and dry. I also realize I’m making a lot of assumptions about the way music works that may or may not be true, however any insight at all would be helpful! Thanks!

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    Senior Member TalkingHead's Avatar
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    I don't have time to write a detailed answer and I don't like writing reams of text.
    Try this: http://openmusictheory.com/harmonicFunctions.html

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    Quote Originally Posted by TalkingHead View Post
    I don't have time to write a detailed answer and I don't like writing reams of text.
    Try this: http://openmusictheory.com/harmonicFunctions.html
    What a good looking site TalkingH. An excellent resource for anyone interested.
    New website and some new music......www.mikehewer.com

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    Quote Originally Posted by TalkingHead View Post
    I don't have time to write a detailed answer and I don't like writing reams of text.
    Try this: http://openmusictheory.com/harmonicFunctions.html
    I've added it to my theory bookmarks list. It is nice, though, to have a person explain it.

    https://youtu.be/heAcV-kqKrQ
    Last edited by millionrainbows; Apr-02-2020 at 14:08.

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    Senior Member pianozach's Avatar
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    I'll just point out that the "function of a chord" has changed over time.

    If you go from, say, Bach to Beethoven to Mussorgsky, harmonic structure and progression is no longer the same.
    There's even further breakdown of that as the 20th century progressed.

    No, I'd go with an educated explanation, like the one TalkingHead pointed out. It's short, simple, and a good place to start.

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    Quote Originally Posted by pianozach View Post
    No, I'd go with an educated explanation, like the one TalkingHead pointed out. It's short, simple, and a good place to start.
    It is nice, though, to have a person explain it.

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    Quote Originally Posted by pianozach
    I'll just point out that the "function of a chord" has changed over time.
    If you go from, say, Bach to Beethoven to Mussorgsky, harmonic structure and progression is no longer the same.
    There's even further breakdown of that as the 20th century progressed.
    Spot on, Pianozac.
    From the website I posted above:
    Because tendency is style-specific, the same chord can have different functions in different musical styles. For instance, the kinds of functions we find in classical music are different from those we find in pop/rock songs from the Billboard charts. And though there are some general harmonic traits that are common to most eighteenth - and nineteenth-century Western composers (what we call the “common practice”), when we look in closer detail, we find some significant differences in the way Bach, Mozart, Brahms, and others compose their harmonic progressions.

    Quote Originally Posted by pianozach
    No, I'd go with an educated explanation, like the one TalkingHead pointed out. It's short, simple, and a good place to start.
    Thank you, Pianozach.

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    Quote Originally Posted by TalkingHead View Post
    Because tendency is style-specific, the same chord can have different functions in different musical styles. For instance, the kinds of functions we find in classical music are different from those we find in pop/rock songs from the Billboard charts. And though there are some general harmonic traits that are common to most eighteenth - and nineteenth-century Western composers (what we call the “common practice”), when we look in closer detail, we find some significant differences in the way Bach, Mozart, Brahms, and others compose their harmonic progressions.
    I think that chord function is more consistently the same for any era, is based on the same phenomena, and that stylistic practices are much less relevant.

    I think a chord's position in the hierarchy, i.e. what scale step it is built on, has everything to do with its perceived function or possible use.

    You'd have to be a lot more specific than this to convince me otherwise; although it wouldn't surprise me to learn of some archaic practice which took place ages ago, which makes no sense and goes against what our ears tell us is right. It's happened before.

    From the article:
    However, these rules are also related to laws, in as much as they represent one set of practices that mediate the various demands on music from basic principles of human auditory perception and cognition. For instance, the prohibition against parallel fifths is a specific way in which Western tonal composers have mediated the conflict between tonal fusion, goal-directed motion, and independence of line. There are many other similar cases.
    Last edited by millionrainbows; Apr-03-2020 at 16:57.

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    Quote Originally Posted by TalkingHead View Post
    Spot on, Pianozac.
    From the website I posted above:
    Because tendency is style-specific, the same chord can have different functions in different musical styles. For instance, the kinds of functions we find in classical music are different from those we find in pop/rock songs from the Billboard charts. And though there are some general harmonic traits that are common to most eighteenth - and nineteenth-century Western composers (what we call the “common practice”), when we look in closer detail, we find some significant differences in the way Bach, Mozart, Brahms, and others compose their harmonic progressions.


    Thank you, Pianozach.
    But I'd be interested in knowing if there is an underlying principle which is common to all ideas of function. whether they are specific style-related ideas or not; in other words, a "unified field theory" of function.

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    Quote Originally Posted by millionrainbows View Post
    But I'd be interested in knowing if there is an underlying principle which is common to all ideas of function. whether they are specific style-related ideas or not; in other words, a "unified field theory" of function.
    Millionrainbows: I think that's a really interesting question, so interesting, in fact, that it caused me to join this forum. I'm wondering what others may have to say about this. My own experience is that it has been difficult to find a cohesive definition of the term "harmonic function" in the music theory literature, whether it's textbooks, scholarly books, white papers, or whatever. But I am all ears, so to speak, if anyone has come across such a definition that makes sense.

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    Quote Originally Posted by Wes Lachot View Post
    Millionrainbows: I think that's a really interesting question, so interesting, in fact, that it caused me to join this forum. I'm wondering what others may have to say about this. My own experience is that it has been difficult to find a cohesive definition of the term "harmonic function" in the music theory literature, whether it's textbooks, scholarly books, white papers, or whatever. But I am all ears, so to speak, if anyone has come across such a definition that makes sense.
    Thanks, Wes. Here's my view, which is from a blog of mine:

    In a scale, the pull towards a tonic is inherently determined by vertical harmonic factors, not horizontal "emphasis" by repetition or accent. That comes later.

    1. minor seventh (C-Bb) 9:16
    2. major seventh (C-B) 8:15
    3. major second (C-D) 8:9
    4. minor sixth (C-Ab) 5:8
    5. minor third (C-Eb) 5:6
    6. major third (C-E) 4:5
    7. major sixth (C-A) 3:5
    8. perfect fourth (C-F) 3:4
    9. perfect fifth (C-G) 2:3
    10. octave (C-C') 1:2
    11. unison (C-C) 1:1

    So a C major scale's horizontal functions correspond to these harmonic relations; and one can observe how these functions were derived:

    I — 1:1
    ii — 8:9
    iii — 4:5
    IV — 3:4
    V — 2:3
    vi — 3:5
    vii — 8:15

    Their importance in establishing the tonality can be ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

    I — 1:1
    V — 2:3
    IV — 3:4
    vi — 3:5
    iii — 4:5
    ii — 8:9
    vii — 8:15

    Using this model, a "function" hierarchy can be applied to any scale, after the degrees of dissonance are ranked.

    Whole Tone scale: C-D-D-F#-G#-A#

    C — 1:1
    D —8:9
    E —4:5
    F#— 45:32
    G# — 8:5
    A# — 16:9

    Whether or not you attach Roman numerals to the above is optional; but by the numbers, one can see a ranking:

    C — 1:1
    E —4:5
    G# — 8:5
    D —8:9
    A# — 16:9
    F#— 45:32
    Last edited by millionrainbows; Aug-12-2020 at 12:49.

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    Quote Originally Posted by Wes Lachot View Post
    Millionrainbows: I think that's a really interesting question, so interesting, in fact, that it caused me to join this forum. I'm wondering what others may have to say about this. My own experience is that it has been difficult to find a cohesive definition of the term "harmonic function" in the music theory literature, whether it's textbooks, scholarly books, white papers, or whatever. But I am all ears, so to speak, if anyone has come across such a definition that makes sense.
    https://en.wikipedia.org/wiki/Function_(music)

    Read the whole article. Btw, it assumes meantone temperament.
    Pythagorean tuning is schismic (until 665 edo when schisma becomes a step), so the theory is different (diminished and augmented intervals are the 5-limit consonances = 317.595 cents, which is almost pure min3rd is Pythagorean augmented second and 384.360 cents, almost major third is Pythagorean diminished fourth).
    Schismic, meantone and their difference (diashismic) and their sum (pythagorean comma) meet in 12 equal only (this can lead to potentially confusing or wrong notation systems)

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    million rainbows; Thanks, interesting and logical stuff. The hierarchy method for determining which scale degrees, are "functional" would tend to support only calling the I, IV, and V functional degrees, since the next one, 3:5, is way out of tune compared to ET, around 14 cents (I'm sure Babygiraffe could tell us precisely in less than a nanosecond). Then the next one, the III or 4:5 is off by a similar amount. Only after those two in the hierarchy do we get to the II, which is more in tune with ET and is the one some theorists let into the "functional" club right after the I, IV, and V.

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    Quote Originally Posted by BabyGiraffe View Post
    https://en.wikipedia.org/wiki/Function_(music)

    Read the whole article. Btw, it assumes meantone temperament.
    Pythagorean tuning is schismic (until 665 edo when schisma becomes a step), so the theory is different (diminished and augmented intervals are the 5-limit consonances = 317.595 cents, which is almost pure min3rd is Pythagorean augmented second and 384.360 cents, almost major third is Pythagorean diminished fourth).
    Schismic, meantone and their difference (diashismic) and their sum (pythagorean comma) meet in 12 equal only (this can lead to potentially confusing or wrong notation systems)
    Thanks, interesting article. It does sum up pretty succinctly some of the differences in terminology, and one can infer the differences in the conception of what is meant by the term "function" within the various schools of thought. The term seems to mean different things to different people.

    For instance, theorists will sometimes state that because a chord "stands in" for another chord in a chord progression, it must have the same "function" as the chord it replaced. An example would be the III occurring in a place where the I could be in the progression. Or lets say a N6 chord in place of a IV chord. The term "pre-dominant" seems shaky to me for this reason, as even the name itself seems to lock in the position in the chord progression--this in an art form that's all about defying expectations. Secondary (applied) dominants are also referred to as "functional" and "non-functional" depending on where they resolve to, and so on. And so began the search for clarity.
    Last edited by Wes Lachot; Aug-13-2020 at 07:34. Reason: spelling

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    Quote Originally Posted by Wes Lachot View Post
    Thanks, interesting article. It does sum up pretty succinctly some of the differences in terminology, and one can infer the differences in the conception of what is meant by the term "function" within the various schools of thought. The term seems to mean different things to different people.

    For instance, theorists will sometimes state that because a chord "stands in" for another chord in a chord progression, it must have the same "function" as the chord it replaced. An example would be the III occurring in a place where the I could be in the progression. Or lets say a N6 chord in place of a IV chord. The term "pre-dominant" seems shaky to me for this reason, as even the name itself seems to lock in the position in the chord progression--this in an art form that's all about defying expectations. Secondary (applied) dominants are also referred to as "functional" and "non-functional" depending on where they resolve to, and so on. And so began the search for clarity.
    There will never be clarity, because there are no universal functions even in the same tuning or even in the same musical scale, if we change the modes... And meantone theory fails in other temperaments, supported by 12 equal like modes of limited transposition (which can be described as diminished, augmented, diaschismic) and pythagorean/schismic tuning - they have their own logic of chord changes.
    Classical function theory assumes heptatonic diatonic in meantone temperament.

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