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Thread: Harmonic Centricity

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    Senior Member millionrainbows's Avatar
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    Default Harmonic Centricity

    What is "natural" is harmonic centricity, and this should not be exactly equated with Western tonality. Harmonic centricity can loosely and generally be called "tonality," but this tends to confuse the issue, so I'll call it what it is: harmonic centricity, which can be the perception of one note only, or more.

    Western CP tonality is based on harmonic centricity. The C major scale is the given, and triads are built on each of the scale steps. These triads are then ranked in order of their relation to the tonic triad (I), in terms of consonance/dissonance. G major is the next most important triad, being related to the most prominent harmonic, the fifth.

    Each of these triads are harmonic centricities in themselves; each has a fifth, a third, and so on. Thus, triads are the device which creates a centricity on the scale steps, each triad being a small "harmonic model" of the natural overtones which occur in any pitch. Theoretically, and practically, each of these triads can become its own centric/root station, but in Western tonality, all the other triads on the scale steps are subordinated to I (C major), which is the tonic station.
    In jazz, any scale step in any scale can become a main root station, thus "modal" jazz in dorian mode, mixolydian mode, and so on.

    In Western CP tonality, this is not so; unless there is definite modulation to a new root station (scale step triad), all of these other triads are subservient to the home key of C. Thus, when a progression goes from C to, say, G major, G major is heard as a centricity or new station, but there is "expectation" that it will return us to the home key of C. Thus, "expectation" and "anticipation" of the G triad is not based solely on the ear's perception of centricity, but on a cognitive process which occurs over the span of the progression. This system of expectation and anticipation is learned by repetition, by recognizable procedures of resolution and tension, and is based on the style of the music which is produced using this system.

    The fact that all of these subordinate steps "away" from the home key are based on triads, with fifths reinforcing their centric identity, is the way the ear is "convinced" that the subordinate triad might be a new root station; but tension and resolution are the ways the ear's natural tendency to hear harmonic centricity is "overcome;" tension and resolution are the cognitive devices, which require ear/brain perception of progressions and events over spans of time.
    Thus, the 'natural' tendency of the ear to hear harmonic centricity is "overcome" by cognitive, narrative sequences of events which we call "Western tonality."

    So to say atonal music, like Anton Webern's, is "unnatural" because it does not refer every centricity which occurs to a root or key area, is mistaken. All music (using pitch) has tone centricity, even when it is melodic. Centricity becomes more obvious and compelling when there is more than one note occurring, since we tend to hear sequences of pitches as "melody" rather than harmony.
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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by millionrainbows View Post
    When a progression goes from C to, say, G major, G major is heard as a centricity or new station, but there is "expectation" that it will return us to the home key of C. Thus, "expectation" and "anticipation" of the G triad is not based solely on the ear's perception of centricity, but on a cognitive process which occurs over the span of the progression. This system of expectation and anticipation is learned by repetition, by recognizable procedures of resolution and tension, and is based on the style of the music which is produced using this system.

    The fact that all of these subordinate steps "away" from the home key are based on triads, with fifths reinforcing their centric identity, is the way the ear is "convinced" that the subordinate triad might be a new root station; but tension and resolution are the ways the ear's natural tendency to hear harmonic centricity is "overcome;" tension and resolution are the cognitive devices, which require ear/brain perception of progressions and events over spans of time.
    Thus, the 'natural' tendency of the ear to hear harmonic centricity is "overcome" by cognitive, narrative sequences of events
    which we call "Western tonality."

    So to say atonal music, like Anton Webern's, is "unnatural" because it does not refer every centricity which occurs to a root or key area, is mistaken. All music (using pitch) has tone centricity, even when it is melodic. Centricity becomes more obvious and compelling when there is more than one note occurring, since we tend to hear sequences of pitches as "melody" rather than harmony.
    This is a bit of obfuscation, and putting "overcome" in quotes is deceptive.

    The mere fact that the note G is heard as the root of the G major triad has nothing to do with whether or not the G chord as a whole is felt as subordinate to the tonic C. We don't have to "overcome" a perception of a thing seen in isolation to see its relationship to something else. Perceiving tonal progression doesn't require "overcoming" any other perception. We are not tempted by the occurrence of the dominant triad to stop the music and rest content.

    I don't think anyone has called atonality "unnatural" for the reason you give. And the business about all music having "tone centricity" is just not relevant.
    Last edited by Woodduck; Jul-03-2018 at 20:35.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Woodduck View Post
    ...The mere fact that the note G is heard as the root of the G major triad has nothing to do with whether or not the G chord as a whole is felt as subordinate to the tonic C.
    Then the reason the G is felt to be "subordinate" is if it's a G7, and the F (seventh) is perceived as a dissonance which is to resolve to E, third of the C major; but this perception of a dissonance involves comparison to the C, and this is established in memory by comparison or repetition, not by purely harmonic sensation.

    There is nothing inherently dissonant about a G7 chord; it is used all the time as an unresolved root chord, as in blues. Only by comparison in time do we feel a need to resolve.

    (one must understand by this that dissonance and consonance are not absolute states, but exist only comparatively)

    We have to "learn" to hear the G as subordinate, and dissonant, by comparison in the context of a tonal progression in time. The "harmonic centricity" and "harmonic independence" of the G triad is "overcome" in the context of a tonal progression by "learning" that it is subordinate to C, by means of a progression designed to convince us of this.

    So, the reason the G chord is felt to be "subordinate" to C is due solely to cognitive comparison over time, and not to any self-contained harmonic sensation of the chord itself.

    The point of all this is to say: Thus, Western tonality is seen to be a system which is entirely based on cognitive comparisons, not any sort of "natural" sensation of centricity.

    As you yourself said: "The...fact that the note G is heard as the root of the G major triad has nothing to do with whether or not the G chord as a whole is felt as subordinate to the tonic C."
    Last edited by millionrainbows; Jul-03-2018 at 21:34.
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    Senior Member Woodduck's Avatar
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    All tonal systems are learned! In purely melodic music, there is nothing in any single tone that leads us to another tone. So what? Why is this significant?

    You begin this thread by saying, "What is 'natural' is harmonic centricity, and this should not be exactly equated with Western tonality." But who equates them? Who needs to be warned about this? And how do you get to this idea of "overcoming" our supposed sense of "harmonic centricity"? I'm pretty sure that most listeners to music have never struggled with any such problem.

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    Senior Member millionrainbows's Avatar
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    Western tonality is seen to be a system which is not primarily based on cognitive comparisons spread out over time, but an ultimately "natural" sensation of centricity, which all "centric" music is based on.

    I will show that Western tonality, and its comparative functions, can be traced back to vertical factors, and the way we hear harmonics.

    Thus, the "narrative" aspects of Western tonal progressions do not establish tonality; these 'narrative' excursions are based on the original vertical model of harmonics, only assisted by narrative procedures.

    Western tonality is about establishing a key area, and this means we have to "move away" from the tonic chord (C) in order to "return" to it, and establish the tonality, unless we want to drone on in one chord. Western tonality likes to move around, unlike Indian raga music. So how is this "movement" away from, and back to, the key tonic station accomplished?

    The main way that Western tonality establishes key areas is by root movement. These roots are the scale steps, and the functions assigned to them within that scale.
    But why do we hear (in the key of C Major) a G chord as being the "dominant" (V) function, as "subordinate" to I (C)? What is this perception based on, and why does it convince our ear that "G" needs to resolve, and that "C" is our home key?

    Woodduck might say that this perception is based on various factors, which it is, such as repetition, phrasing, etc., but I'm saying that the main way tonality is "played with" is by root movement.

    This "root movement" is really a harmonic interval. The progression from C major to G major is the interval of a fifth, just spread out over time. So all root movement can be traced back to our harmonic intervals, which is the source of all pitched sound.

    What evidence do we have of this? Simply our ears, and the way we hear harmonics.

    Let's say that the root movement from C to G is a fifth up. Harmonically, we hear a fifth with the "root" on the bottom note, so C-G is heard as being rooted on "C." Since Western tonality is largely based on root movements of a fifth, and the 'circle of fifths' is further evidence of this, then this explains much of tonal root movement.

    Conversely, we hear a fourth (the inversion of a fifth) as having its "root" on the top note; so G up to C establishes the root as C.

    This is all based on vertical factors; the way we hear the natural harmonic series. Root movement in Western tonality simply "spreads this out" over spans of time.

    This can also show how the diatonic C major scale, the chosen scale for most of our music, is also inherently unstable as far as being "totally tonal." It's built for movement, for unrest.

    The interval C-F is a fourth; if we hear this as "root on top," then F Major is established, subordinating C, supposedly the "home" key. All this is due to the fact of the tritone F-B in the C major scale.
    In this light, we can see the truth of George Russell's assertion that the Lydian scale is "more tonal" if one wants to establish the scale root as the key. The F lydian scale cycles through all 7 in fifths before it circles back around to F, its key note: F-C-G-D-A-E-B (F).

    This is also why piano tuners start on F and tune by fifths. If we try to "stack fifths" starting on C, we get C-G-D-A-E-B-(F#?). It doesn't work for a C major scale, as it has an "F."
    As the Pebber Brown video on Youtube shows, when he sustains all the notes C-G-D-A-E-B, the consonance of perfect fifths falls apart when the clunker "F" is added on top.

    The C major scale is structured so that there is a "leading tone" E-F (establishing F), as well as B-C (establishing C).
    The C lydian scale has a leading tone F#-G (establishing the more closely related V step of G) and B-C (establishing the scale key).

    I'm not criticizing the C major scale; it's perfectly suited for what it is used for: to travel to other key areas.
    Last edited by millionrainbows; Jul-07-2018 at 22:45.
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    Quote Originally Posted by Woodduck View Post

    The mere fact that the note G is heard as the root of the G major triad has nothing to do with whether or not the G chord as a whole is felt as subordinate to the tonic C.
    If we see G is subordinate in a "fifth" relationship to C (C-G), then G's subordinate role is easily demonstrated. We hear fifths with the "dominating note" on bottom.
    "The way out is through the door. Why is it that no one will use this method?"
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    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

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    Quote Originally Posted by Woodduck View Post
    All In purely melodic music, there is nothing in any single tone that leads us to another tone.
    There exist universal cadence like melodic gestures involving semitones (in scales with leading-notes; also flamenco/arabic type scales resolve 1 semitone down). And this is not something exclusive to Western music scale and tempered system.


    Millionrainbows: "Thus, Western tonality is seen to be a system which is entirely based on cognitive comparisons, not any sort of "natural" sensation of centricity."


    Not really, I suggest reading some papers on modern scale theory and diatonic set theory. Current research in mathematical music theory offers surprisingly deep connections to algebraic topology, graph theory, word combinatorics, group theory, projective geometry.

    https://en.wikipedia.org/wiki/Diatonic_set_theory

    This guy did some really interesting research (imo).

    https://www.researchgate.net/profile/Marek_Zabka
    Last edited by BabyGiraffe; Jul-09-2018 at 07:38.

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    The fact that C-G root movement in Western tonality establishes G as subordinate to C (in the key of C) is based on the vertical factor derived from harmonic hearing; the fact that the C-G is spread out over time is dependent on the "memory" of that C-G vertical relationship. So the fact that the C-G is spread out as a "narrative" device really in itself has nothing to do with establishing the relationships in tonality; only vertical factors, which we cognitively remember.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Woodduck View Post
    All tonal systems are learned!
    That's misleading. The harmonic nature of any fundamental pitch is heard, and requires no learning to intuitively understand.

    Quote Originally Posted by Woodduck View Post
    In purely melodic music, there is nothing in any single tone that leads us to another tone. So what? Why is this significant?
    The harmonic series, which is the model we base our other models on, is a simultaneity, not a melodic interval. So the reason G is sensed as subordinate to C is because of this.

    Quote Originally Posted by Woodduck View Post
    You begin this thread by saying, "What is 'natural' is harmonic centricity, and this should not be exactly equated with Western tonality." But who equates them? Who needs to be warned about this?
    Any "tonality" is based on a harmonic model. This is vertical in nature, and is 'modeled' by different scales.

    This should not be confused with the Western tonal system, which elaborates and 'plays' with this verticality by spreading it out over "progressions" of chords (root centers). This 'elaboration" and narrative 'playing with' is what makes Western tonality unique, and very advanced. But other than this, Western tonality is just a tonality based on harmonic centricity, like all other 'tonalities.'

    Who equates "tonality" with harmonic centricity? You do, all the time, in all your statements about it. You make statements which confuse basic, primal "tonality" (harmonic centricity), which is ubiquitous in most musics of the world, with our particular Western form of 'harmonic elaboration' which plays narratively with the notion of subordinate functions, moving to new key areas, and 'functions' of triads. All of these methods and practices are dependent on long narratives or progressions of chords, and comparatively long-term goals.

    Quote Originally Posted by Woodduck View Post
    And how do you get to this idea of "overcoming" our supposed sense of "harmonic centricity"? I'm pretty sure that most listeners to music have never struggled with any such problem.
    We have to listen to music with our memory. A fifth is heard with the root on bottom, as a harmonic interval. When this interval gets translated into a horizontal movement of a fifth, we hear the first area as the "root" area, with the move a fifth away from it as a 'secondary' area or function, by using our memory of the interval of a fifth. This takes it out of the vertical 'now'into the horizontal world of time. This is like 'reading' a sequence of events. This has to be learned.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

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