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Thread: Chromaticism and Tonality

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    Default Chromaticism and Tonality

    The CP tonal system is based on 7-note scales. Tonality flourishes under this number.

    The more notes that are added, up to 12, the more redundant the index of intervallic possibilities in the scale becomes.

    This is demonstrated empirically by Howard Hanson in his book "Harmonic Materials of Modern Music":
    Quote Originally Posted by Howard Hanson
    p=perfect fifth (or fourth)
    m=major third (minor sixth)

    n=minor third (major sixth)
    s=major second (minor seventh)
    d=minor second (major seventh)
    t=augmented fourth, diminished fifth

    doad (2 notes): p
    triad: p2 s
    tetrad: p3 n s2
    pentad: p4 m n2 s3
    hexad: p5 m2 n3 s4 d
    heptad: p6 m3 n4 s5 d2 t
    octad: p7 m4 n5 s6 d4 t2
    nonad: p8 m6 n6 s7 d6 t3
    decad: p9 m8 n8 s8 d8 t4
    undecad: p10 m10 n10 s10 d10 t5
    duodecad (12 notes): p12 m12 n12 s12 d12 t6

    Each new progression adds one new interval, plus adding one more to those already present; but beyond seven tones, no new intervals can be added. In addition to this loss of new material, there is also a gradual decrease in the difference of the quantitative formation.

    So the sound of a sonority, whether it be harmony or melody, depends on what is present, but also on what is not present. The pentatonic sounds as it does because it contains mainly perfect fifths, and also maj seconds, minor thirds, and one major third, but also because it does not contain the minor second or tritone.

    As sonorities get projected beyond the six-range, they tend to lose their individuality.
    (Hanson generates these scales by projection (stacking) of fifths: doad: C-G, triad C-G-D, tetrad C-G-D-A, pentad C-G-D-A-E, hexad C-G-D-A-E-B, heptad C-G-D-A-E-B-F# (our diatonic G Major scale), etc.



    The actual sound of a scale, if considered empirically as a 'sonority,' contributes to our sense of tonality. The functions of the scale are derived from triads built on the scale steps.

    This is only one aspect of chromaticism, as it affects sonority, or intervallic content formed by cross-relations within the scale collection.

    Next, I'll discuss
    harmonic function, and how it is affected by the addition of notes.

    Why did Schoenberg "order" his tone rows? This insured that all 12 would be stated before any repeats occur; it ensured the constant circulation of all 12 notes.
    Last edited by millionrainbows; Sep-02-2016 at 21:21.

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    "The pentatonic sounds as it does because it contains mainly perfect fifths, and also maj seconds, minor thirds, and one major third, but also because it does not contain the minor second or tritone."

    You could, and should, say that about any melody or passage, not just "scales" (i.e. scale-like passages). Of course, to a certain extent it's possible to find commonalities in pieces of music but, at the end of the day, they are just abstractions, tonality is an illusion.

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    I like your music theory posts, music rainbow. They help one see how an increasing retreat from tonality was a central feature of the romantic era, not just the modern. (And for me is the main appeal of late romantic and impressionist music). Charles Rosen's book has some good examples too. Maybe the next subject to look at is meter: To me, polymeter and metric modulation are the hallmarks of the modern era as much as or even more than atonality (or dissonance, to be more precise). Certainly for those of us performing modern music, metric complexity is a far greater challenge than harmonic complexity.

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    Quote Originally Posted by Chordalrock View Post
    "The pentatonic sounds as it does because it contains mainly perfect fifths, and also maj seconds, minor thirds, and one major third, but also because it does not contain the minor second or tritone."

    You could, and should, say that about any melody or passage, not just "scales" (i.e. scale-like passages).
    Well, we ought to assume that a melody is derived from a scale.

    I see a scale as an unordered index of notes.

    The fact that scales are typically shown as "progressing" from left to right, low to high, is just a convention.

    I do not consider a scale to be a musical "entity" like a melody is.

    A "scale-like passage?" Yes, I see the distinction, but:

    When considering the sonority of a group of notes and intervals, I think the best way is vertically, all at once, as in a chord. Melodies progress through time, and it is harder to hear this. In fact, here is a demonstration of that:

    https://youtu.be/XFYYSq7f6Y8

    Of course, to a certain extent it's possible to find commonalities in pieces of music but, at the end of the day, they are just abstractions, tonality is an illusion.
    Tonality is a perception, this is true. But is also grounded in empirical facts, which are quantifiable data.

    Both perception and empirical data are incomplete, and both are necessary.

    As Woodduck said elsewhere (and he's my expert on tonality):

    ...the presence of a tonic or hierarchy of scale degrees...constitute, technically, what tonality is


    If
    someone is hearing "tonal centers," they might at least show us what tones are being called that, where they occur, and how the surrounding harmony functions so as to confer upon them that status. It has to function somehow in relation to a tonic, whether or not that tonic is actually stated; the hallmark of even the most chromatic tonal harmony is the way it plays with, and depends for its effect on, the listener's sense of a harmonic hierarchy, and his expectation that the stability of a tonic, whether or not it ever materializes, is at least possible. Without at least an implied tonic - which in harmonic music means a tonic harmony - there is no tonality.
    Last edited by millionrainbows; Sep-02-2016 at 20:42.

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    Quote Originally Posted by fluteman View Post
    I like your music theory posts, music rainbow. They help one see how an increasing retreat from tonality was a central feature of the romantic era, not just the modern. (And for me is the main appeal of late romantic and impressionist music).
    The issue I want to approach now is this: do we view Schoenberg as a "retreat" or "weakening" or "absence" of tonality, or do we see it as an "expansion" of tonality, with new expanded possibilities?

    I want to combine the empirical evidence of chromaticism (the increasing number of notes from tonality's original 7) with the idea that Schoenberg "expanded" tonality, rather than "weakened" or "destroyed" it.

    This is changing the way I hear this music, as well; I always liked it, and kept listening to it, but now my original "intuition" is combining with my "logical" side, and hearing it as completely "tonal" in every moment.

    This is not quite the same as listening to more obviously tonal music; it is very demanding, from moment to moment; but it finally seems to make sense.

    This new kind of listening also involves a certain detachment from the idea of total clarity; this is chromatic music, and it is sometimes very fleeting. It also requires faith in your "ear" more so, perhaps, than the brain. Sometimes a passage of music is just a "harmonic entity" which exists unto itself, with no apparent reference.

    I also think that Schoenberg changed his way of composing when he entered this chromatic world. He realized that in such an environment, the idea, and presence, of a "tonic" was less and less obvious, and so less and less necessary. The "tonic" could be imagined to be anywhere, and expected to materialize instantly, then disappear.

    Charles Rosen's book has some good examples too.
    I just listened to him play the piano, in Stravinsky's "Movements for Piano and Orchestra."

    https://youtu.be/y0lQUQzmD-8

    Maybe the next subject to look at is meter: To me, polymeter and metric modulation are the hallmarks of the modern era as much as or even more than atonality (or dissonance, to be more precise). Certainly for those of us performing modern music, metric complexity is a far greater challenge than harmonic complexity.
    Elliott Carter come to mind when I hear this.

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    Quote Originally Posted by millionrainbows View Post
    Well, we ought to assume that a melody is derived from a scale.

    I see a scale as an unordered index of notes.

    The fact that scales are typically shown as "progressing" from left to right, low to high, is just a convention.

    I do not consider a scale to be a musical "entity" like a melody is.

    A "scale-like passage?" Yes, I see the distinction, but:

    When considering the sonority of a group of notes and intervals, I think the best way is vertically, all at once, as in a chord. Melodies progress through time, and it is harder to hear this. In fact, here is a demonstration of that:

    https://youtu.be/XFYYSq7f6Y8



    Tonality is a perception, this is true. But is also grounded in empirical facts, which are quantifiable data.

    Both perception and empirical data are incomplete, and both are necessary.

    As Woodduck said elsewhere (and he's my expert on tonality):
    Yes, there is a strong subjective element, approaching the arbitrary, in what intervals one hears as consonant or dissonant. But once your ears, heart and mind accept a system of consonance, I agree that the system necessarily implies a root or tonic. So saying "tonality is an illusion" is probably going too far. All art is based on a system of rules, a logical structure or organization, even subversive art where the idea is to defeat the audience's expectations and break the rules. One could argue generally, "art is an illusion", but only until one learns and accepts its structure. And we humans find beauty in structure. We just don't necessarily agree on which structures are beautiful.

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    Quote Originally Posted by fluteman View Post
    Yes, there is a strong subjective element, approaching the arbitrary, in what intervals one hears as consonant or dissonant. But once your ears, heart and mind accept a system of consonance, I agree that the system necessarily implies a root or tonic. So saying "tonality is an illusion" is probably going too far. All art is based on a system of rules, a logical structure or organization, even subversive art where the idea is to defeat the audience's expectations and break the rules. One could argue generally, "art is an illusion", but only until one learns and accepts its structure. And we humans find beauty in structure. We just don't necessarily agree on which structures are beautiful.
    Yes, we agree on that. Be sure to watch the Pebber Brown video. His voice gets drowned out by the keyboard in parts, but the demonstration is good. There is a part 2 that will come up after that, if you can last through it.

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    Diatonic function is based on building triads on each scale step, and ranking them in order of their consonance to the tonic .

    The functions of a major scale are:

    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 is to 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

    If we add more notes, we add more functions. With 12 notes, we have 12 functions.

    With 12 notes, each pitch can be considered in functional relation to 12 key areas. For example, C could function as I in C, viiº in C#, b7 in D, vi in Eb, etc.

    Just as a reference, from WIK:
    The chromatic scale is a musical scale with twelve pitches, each a semitone above or below another. On a modern piano or other equal-temperedinstrument, all the semitones have the same size (100 cents). In other words, the notes of an equal-tempered chromatic scale are equally spaced. An equal-tempered chromatic scale is a nondiatonic scale having no tonic because of the symmetry of its equally spaced notes.
    I post this definition because I have seen Woodduck define it as
    the chromatic scale, which consists of a diatonic scale and the additional five half steps. By that definition the chromatic scale exhibits tonal hierarchy, and one can play with chromatic complexities and so weaken or strengthen the feeling of tonality.
    I've also heard him say
    The 12-tone scale also contains no inherent structure...Schoenberg's 12-tone music is not based on a hierarchically structured scale.


    There is no definitive reason to assume this. In a 12-note scale, any note can be the reference point. E
    ach pitch can be considered in functional relation to 12 key areas, as tonic, or as other.

    Why did Schoenberg order his rows? Firstly, it provides linear, melodic material. But beyond that, why?
    With a chromatic scale, a starting point/end point becomes meaningless in tonal terms. Showing scales linearly, with starting and end points, is a convention which also specifies "key."
    Since key is meaningless in a chromatic field of possibilities, ordering the row is a way of giving meaningful structure without suggesting key.

    The 12 notes are "there" already, before the row is made. Ordering the row keeps it from being a scale, and thus a definer or limiter of sonority/tonality, provides thematic/linear material, and allows the 12 notes to be "stated" in a comprehensible manner.

    It's not necessary for the 12-tone row to function as a scale, because a scale is an inherently "limiting" device which proscribes a key or tonality. Totally chromatic music does not need this.

    Scales are not ordered because they are not really linear (that's just a convention); they are a vertical index of harmonic relations to tonic, all at once, as a sonority (see Pepper Brown video above).(I know I'll get flak for this from the CP camp)

    Since totally chromatic music has no defined sonority as a key area does, it is a field of possibilities which needs no limited, defined sonority or start/end point.

    We see from this that tonality is inherently reductionist. Its scales are limiters. Tonality is defined and separated from the 12-note whole. In chromatic music, this is not necessary.


    Last edited by millionrainbows; Sep-02-2016 at 22:35.

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    Quote Originally Posted by millionrainbows View Post
    The issue I want to approach now is this: do we view Schoenberg as a "retreat" or "weakening" or "absence" of tonality, or do we see it as an "expansion" of tonality, with new expanded possibilities?
    As a concept, I see Schönberg's "atonality" a totally different thing from tonality. I don't see expansion or contraction. Surely Schönberg began expanding tonality with the "free atonality". But when he developed his theory, there was a break point (for me). Like different languages that cannot be translated.

    This is not quite the same as listening to more obviously tonal music; it is very demanding, from moment to moment; but it finally seems to make sense.
    I know that many people need a "training" to appreciate atonality (and most never like it).
    But other people don't. For me atonality is as "natural" as tonality. When I listen atonal music I don't compare to tonal music. I simply listen to it and I like it or not. In fact, I find some styles of tonal music (classicism) boring.
    Well, perhaps this is a different issue about perception.

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    Quote Originally Posted by fluteman View Post
    I like your music theory posts, music rainbow. They help one see how an increasing retreat from tonality was a central feature of the romantic era, not just the modern. (And for me is the main appeal of late romantic and impressionist music). Charles Rosen's book has some good examples too. Maybe the next subject to look at is meter: To me, polymeter and metric modulation are the hallmarks of the modern era as much as or even more than atonality (or dissonance, to be more precise). Certainly for those of us performing modern music, metric complexity is a far greater challenge than harmonic complexity.
    I wouldn't call what happened to harmony in Romantic music a "retreat from tonality," but an expansion of tonality to encompass ever more complex and subtle relationships. So long as the "system" remains basic and implicit - meaning, so long as a tonal center and scale hierarchy are assumed by the listener and composer and those assumptions are primary considerations in the way music is structured - there's been no significant retreat from tonality as such. Nearly all Romantic harmony, and the harmony of much music well into the 20th century, is still rooted in the diatonic major and minor scales (with the increasing addition of modal coloration), despite ambiguities of key which occur in passages where chords can be read as having multiple functions. Ambiguities are only comprehensible with reference to expectations of known tonal relationships and procedures, and no Romantic composer was seeking to abandon comprehensibility. "Nonfunctional" harmonic effects and exotic scales were introduced by Romantic composers primarily for the sake of color and atmosphere; broadly speaking, we can call such effects programmatic.

    I don't agree that increasing chromaticism necessarily makes music less tonal; it can do so, but Romantic composers, like composers of earlier times (e.g. Monteverdi, Bach and Mozart) saw chromaticism as an expressive tool, not as an alternative way of structuring music. I think it's interesting that even Wagner, who extended chromaticism farther than anyone else in the 19th century, understood that what he was inspired to do for programmatic purposes (opera being program music writ large) could be abused in other contexts; he said, "For the symphony one writes very differently" - which I take to mean that one takes care to preserve the structural functions of tonality and not indulge in effects which might weaken those functions. Of course Wagner himself had an extraordinary intuitive sense of how to create harmonic effects of extreme expressive power and still maintain comprehensibility (even without the typical forms of absolute music), and his chromatic excursions ultimately and powerfully affirm their diatonic foundations.

    Real retreats from tonality didn't occur until the specific expressive effects of dissonance, tonal uncertainty, and coloristic harmony became overriding objectives, and with Debussy in the vanguard this was really a 20th-century development. In the specific world of post-Wagnerian German expressionism, it was the abrogation of the "tonal contract" between composer and listener which compelled Schoenberg to look for a different structural principle not dependent on a scale possessing an assumed tonal hierarchy. But outside that small (though disproportionately influential) musical subculture, tonality remained alive and well.

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    When I listen to Schoenberg, as I listened to the piano music played by Glenn Gould today, I try to hear tonality. It is becoming easier now, since my intuition and intellect have finally unified into one receptive organ.

    In the Two Piano Pieces Op. 33, I hear a new moment-to moment sense of tonality; I am "hearing in the now," so to speak. Tonality is no longer a drawn-out, linear process of "reading" the music narratively; it is an instantaneous perception of harmonic sonority. Has tonality retreated, or is it in a state of constantly being born anew? I hear "the one note" and I hear it in all places, at all times. It changes; it takes on form, then that form is changed in meaning by the entry of a new note; and it goes on and on. Can I keep up with the kaleidoscope?

    "Tonic" is now in every moment, "scale hierarchy" is everywhere like a radiant wheel which rolls through a field of harmonic possibilities. Ahh, the beauty!
    Last edited by millionrainbows; Sep-02-2016 at 23:00.

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    Quote Originally Posted by millionrainbows View Post
    Do we view Schoenberg as a "retreat" or "weakening" or "absence" of tonality, or do we see it as an "expansion" of tonality, with new expanded possibilities?

    I want to combine the empirical evidence of chromaticism (the increasing number of notes from tonality's original 7) with the idea that Schoenberg "expanded" tonality, rather than "weakened" or "destroyed" it.

    This is changing the way I hear this music, as well; I always liked it, and kept listening to it, but now my original "intuition" is combining with my "logical" side, and hearing it as completely "tonal" in every moment.

    This is not quite the same as listening to more obviously tonal music; it is very demanding, from moment to moment; but it finally seems to make sense.

    This new kind of listening also involves a certain detachment from the idea of total clarity; this is chromatic music, and it is sometimes very fleeting. It also requires faith in your "ear" more so, perhaps, than the brain. Sometimes a passage of music is just a "harmonic entity" which exists unto itself, with no apparent reference.

    I also think that Schoenberg changed his way of composing when he entered this chromatic world. He realized that in such an environment, the idea, and presence, of a "tonic" was less and less obvious, and so less and less necessary. The "tonic" could be imagined to be anywhere, and expected to materialize instantly, then disappear.
    If we know the "language" of (common practice) tonal music, it's inevitable that we will come to hear all sorts of "hints" of tonality in music which, in addition to utilizing the familiar twelve tones of the chromatic scale, preserves as many of the conventions of counterpoint, voice leading, textural and dynamic structure, etc. as Schoenberg's does. But I would dispute that all these "tonics" that fleetingly materialize and disappear, or don't actually materialize at all, ought to be called "tonality" if they don't serve a perceptible structural purpose.

    Tonality, by traditional definition, is systemic; the notes of a scale relate to a tonic in particular, limited ways, and those relationships have constancy beyond the musical moment, give coherence to the music's progress, and can do these things because they are known and expected by the listener. Hearing "tonality" in Schoenberg's (or anybody's) nontonal music seems to me analogous to looking at a white object and seeing colors; light is refracted, and the eye sees, in ways that produce this effect, but the tints perceived have no constructive potential from which an artist can create a picture.

    Redefining tonality this way simply defines it out of existence.
    Last edited by Woodduck; Sep-02-2016 at 23:31.

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    Quote Originally Posted by Woodduck View Post
    If we know the "language" of (common practice) tonal music, it's inevitable that we will come to hear all sorts of "hints" of tonality in music which, in addition to utilizing the familiar twelve tones of the chromatic scale, preserves as many of the conventions of counterpoint, voice leading, textural and dynamic structure, etc. as Schoenberg's does. But I would dispute that all these "tonics" that fleetingly materialize and disappear, or don't actually materialize at all, ought to be called "tonality" if they don't serve a perceptible structural purpose.
    The perceptible structural purpose is within my total focus. Its "nowness" is its purpose, manifest in every fleeting moment. The tonic is not a still reference point; I have entered a new realm, in which the tonic is a moving point, like a cursor, going across fields of meaning.

    Tonality, by traditional definition, is systemic; the notes of a scale relate to a tonic in particular, limited ways…
    Yes, I have said this. Tonality at its clearest is also at its most limited.

    ...and those relationships have constancy beyond the musical moment…
    Yes, in their most limited form...

    ...and are known and expected by the listener.
    Yes, in their most stable and predictable form, this is true.

    Hearing "tonality" in Schoenberg's (or anybody's) nontonal music seems to me analogous to looking at a white object and seeing colors; light is refracted, and the eye sees, in ways that produce this effect, but the tints perceived have no structural functions from which an artist can create a picture.
    It is possible to hear this way. The tonal perceptions are fleeting, and change constantly, but they are as real as any other tonality I have heard. Not as defined or lasting, but there.

    Redefining tonality this way simply defines it out of existence.
    Not for me; I'm listening to Schoenberg, Elliott Carter, and Roger Sessions in this way now. What you say may be true for 12-note chromatic music which has other goals other than "pitch-meaning," but for these composers, I find that tonality is there in a very subtle, rarefied way. I see them as connected to tonality via their art.

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    Quote Originally Posted by Woodduck View Post
    I wouldn't call what happened to harmony in Romantic music a "retreat from tonality," but an expansion of tonality to encompass ever more complex and subtle relationships.

    ....

    Real retreats from tonality didn't occur until the specific expressive effects of dissonance, tonal uncertainty, and coloristic harmony became overriding objectives, and with Debussy in the vanguard this was really a 20th-century development. In the specific world of post-Wagnerian German expressionism, it was the abrogation of the "tonal contract" between composer and listener which compelled Schoenberg to look for a different structural principle not dependent on a scale possessing an assumed tonal hierarchy. But outside that small (though disproportionately influential) musical subculture, tonality remained alive and well.
    But "more complex and subtle relationships" and "more uncertain relationships" or "more ambiguous relationships" aren't so far apart in meaning, are they? It's all a matter of degree. As music becomes more harmonically remote from one key, or tonal center, and the relationship becomes more complex or subtle, or uncertain, or ambiguous, it nears another key. Will there be a modulation into the new key? Or, a return to the original? Or, an extended period of ambiguity, as in, say, the music of Philip Glass? And if, after a very lengthy period of ambiguity, Glass finally and triumphantly resolves on the original key, or on the new one, as he often does, is that conventionally tonal music? To me these are all semantic questions, and I don't worry much about them.

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    Quote Originally Posted by millionrainbows View Post
    The perceptible structural purpose is within my total focus. Its "nowness" is its purpose, manifest in every fleeting moment. The tonic is not a still reference point; I have entered a new realm, in which the tonic is a moving point, like a cursor, going across fields of meaning.

    The tonal perceptions are fleeting, and change constantly, but they are as real as any other tonality I have heard. Not as defined or lasting, but there.

    Not for me; I'm listening to Schoenberg, Elliott Carter, and Roger Sessions in this way now. What you say may be true for 12-note chromatic music which has other goals other than "pitch-meaning," but for these composers, I find that tonality is there in a very subtle, rarefied way. I see them as connected to tonality via their art.
    "Nowness" is not a structural principle. Not in music, the art of time, in which something comes next, and that something is either related or unrelated to "now." If it's unrelated, there's no tonality.

    You have indeed entered a new realm, and it isn't a realm of clear concepts. I think you may have reached your million and first rainbow.


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