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Thread: What did Schoenberg have in mind when he invented the 12-tone method?

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    Theory comes after the practice, and this seems to be true with serial music. The Second Viennese School were experimenting with new ways of organizing music, and there wasn't yet a generalized way of using tone rows, especially in the vertical area of 'harmony.' Progress is being made, and now a pre-compositional conception of general principles is developing.
    Some of the techniques and strategies Schoenberg, Berg, and Webern were using, plus some conceptual ideas of Hauer's tropes, are finally giving way to some very valid and justifiable ways of combining rows, and ways of using those to actually compose music in a more controlled and predictable way, rather than groping in the wilderness.

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    Senior Member EDaddy's Avatar
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    What does Schoenberg's music and the Hindenburg have in common?

    Both had a lot of hot air and killed a lot of people.

    (Sorry, I couldn't help myself!)

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    Quote Originally Posted by EDaddy View Post
    What does Schoenberg's music and the Hindenburg have in common?
    Both were structurally unstable.

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    Junior Member Sappho's Avatar
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    Not to forget the existence of a fellow named Josef Hauer, who did it all before Schönberg. Though frankly I wonder why anyone would want to be credited with the "invention" of such an un-musical abomination...

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    Quote Originally Posted by Sappho View Post
    Not to forget the existence of a fellow named Josef Hauer, who did it all before Schönberg. Though frankly I wonder why anyone would want to be credited with the "invention" of such an un-musical abomination...
    The only unmusical thing involved is the critics who have lambasted all of the wonderful 12-tone music that's been written over the years on the basis of nonsense and simplifications.

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    Quote Originally Posted by Sappho View Post
    Not to forget the existence of a fellow named Josef Hauer, who did it all before Schönberg. Though frankly I wonder why anyone would want to be credited with the "invention" of such an un-musical abomination...


    Well, although that seems like a criticism, I will take it with a grain of salt. My example is Schoenberg's String Trio op. 46, which was written in his later period after WWII had ended.

    It's certainly not 'tonal,' so I will assume that's what is meant by 'unmusical'.

    In this work, and in others, Schoenberg seems to have adopted his 'method' and to have completely forgotten about tonality. After all, it is an atonal piece; i.e., it has no tonal center, and is not constructed with a tonal hierarchy.

    In fact, simultaneous soundings of vertical 'chords,' as in discrete homophonic triad-entities, does not seem to be a major concern here. There is as much independent voice movement, and totally independent lines, as there are 'harmonic' entities, like chords.

    Verticality does happen, however, and the rows are planned so that verticalities will occur as 'chords' consisting of 3 different notes; each of the 3 rows is divided into 2 hexads; the first and last notes of each hexad are all different, creating a new row (that's 2 notes per hexad, totaling 12 notes, all different.

    That aside, creating a 'harmonic' effect does not seem to be at the top of Schoenberg's agenda. There are other ways in which he creates meaning and 'musicality.'

    This seems to me to be a work of 'gestures,' and this puts Schoenberg directly in line with traditional uses of music, evolving from 'gestural' music which accompanied drama, as in Wagnerian opera, which eventually existed as pure gestural music without the actual dramatic trappings. This became concert music; music divorced from any specific ceremonial or social occasion or dramatic function, existing as 'pure gesture' expressive of some introspective vision of the artist (Beethoven comes to mind), designed to evoke those same feelings, moods, and emotions in the audience, even though there is no explicit meaning. Music becomes a language of pure gesture and feeling.

    Thus, Schoenberg's music is very 'musical' in this sense.

    Tonally, the work has no meaning. It is atonal, and this fact must be accepted and 'transcended' before one can proceed to accept it as music. There are plenty of brusk, jabbing 'gestures' which are articulated rhythmically. Pitch is often indeterminate or inaudible, as plucked pizzicatos and impossibly high-pitched harmonics, or as muddy lower-register 'clusters' of notes. This is a clear indication that even pitch itself had taken on less importance to Schoenberg, and he was more interested in exploiting other methods of conveying musical meaning.

    So, you see, this is what I would call very 'abstract' music, in the sense that is is primarily gestural, and seeks to create 'events' that do not depend on any overall context, and certainly is not concerned with pitch or 'harmonic entities' being the primary element, focus, or importance.

    Yes, there are areas in which voice-leading structure occurs, which to some might evoke some semblance of tonality, but these areas exist unto themselves, as harmonic 'entities' with no tonal meaning as we have ever known it. To grasp at such vestiges of tonal memory is a futile, and ultimately unrewarding activity; I don't think this is what Schoenberg had in mind, as he seemed to be more interested in other aspects of musicality in this piece.

    This work, the String Trio op. 46, is a compendium of 'gestures,' which are evocative, convey emotion and states of being, and could be connected with some inner narrative of the artist. In fact, this is explained in the liner notes, as a narrative of Schoenberg's near-death in the hospital, when he was revived with a direct-to-the-heart injection.

    So, Schoenberg is an Expressionist; he is after the bizarre, the unsettling, the garish colors, and the evocation of near-death experiences. Not exactly a walk in the park, and I admit that the work is challenging; but not "unmusical." This is art of the highest order, regardless of how I may view it.

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    But the String Trio contains explicit references to traditional tonality. Even apart from those sections, it has plenty of tonal meaning, as any collection of notes does, especially one so clearly and cogently formed and related to each other as a piece by Schoenberg.

    It is expressive music, extreme at times, but beautiful at others, and powerfully emotional.

    To say that it does not carry musical meaning is false, as all of this comes directly from the notes, the pitches, and the rhythms employed. Not only was Schoenberg concerned with harmony and harmonic effect, it was second in importance only to motivic and thematic development to him.
    Last edited by Mahlerian; Jun-28-2015 at 21:26.

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    The String Trio op. 46 does contain passages which have oblique references to tonality, but these are not tonal, they only refer to it. These passages are placed alongside passages which have no reference to tonality whatsoever.

    The String Trio op. 46 is Expressionist; Schoenberg had abandoned classical phrase-construction in this work, and replaced it with a kind of "musical prose" reminiscent of the Expressionist period of Erwartung, with fragmentary texture. It is jagged, and the work is one of his most 'abstract' compositions. It's generally regarded as exhibiting rather attenuated tonal motivation, as with the Wind Quintet.

    There is "tonal thought" in this Trio, as in the row-forms and their emphasis on the vertical (harmonic) dimension, instead of his earlier view of the row as a horizontal ordering. The vertical dimension is given priority in this work. Using combinatorial pairs (which I described earlier), these dyads determine both dimensions, and these combinatorial elements are almost as pervasive as the row itself, which in this case is 18 notes, or 3 hexads. This again is a departure from his earlier thinking, creating a sort of 'harmonic source-set' which functions independently of the source-row.

    There are other vestiges of tonal thinking which are always present in Schoenberg's thinking, such as using the T5 or T7 form of the row, to create the IV/V relation.

    There are antecendent and consequent phrases. There are 'cadential' phrases. There is 'developing variation.' There are 'formal prototypes.' However, bear in mind that these are just thought processes, which are idiosyncratic abstractions of late-nineteenth-century musical thought. The presence of "tonal sonorities" is simply a remnant.

    Triads do not imply functional tonality; they only have harmonic color and sonority.

    Is it legitimate to read tonal hierarchies in the String Trio op. 46, where not all elements comply with such hierarchical structuring? Can we say this work is 'tonal' when looking at triadic material which does not have tonal function? I say no. This is modernism.

    The power of Schoenberg's music is in its "classicism," which is not a matter of 'style' or compositional technique, but in its adherence to a particular type of musical logic. I don't think this hidden musical logic translates into the aural content of the work, but is apparent only through analysis. The aural 'content' is modern.

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    Quote Originally Posted by millionrainbows View Post
    The String Trio op. 46 is Expressionist; Schoenberg had abandoned classical phrase-construction in this work, and replaced it with a kind of "musical prose" reminiscent of the Expressionist period of Erwartung, with fragmentary texture. It is jagged, and the work is one of his most 'abstract' compositions. It's generally regarded as exhibiting rather attenuated tonal motivation, as with the Wind Quintet.
    Incidentally, here is an essay pointing out features in the Wind Quintet that link it to traditional tonality.

    http://symposium.music.org/index.php...w=item&id=1962

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    Never mind the word 'atonal.' It's getting to where I don't even know what the word "tonal" means anymore, the way it's used so loosely.

    The T5 or T7 form of the row, to create the IV/V relation; the antecendent and consequent phrases; the 'cadential' phrases; 'developing variation;' 'formal prototypes.' It's all there in the String Trio except for one minor detail: a tonal center.

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    Quote Originally Posted by millionrainbows View Post
    The T5 or T7 form of the row, to create the IV/V relation; the antecendent and consequent phrases; the 'cadential' phrases; 'developing variation;' 'formal prototypes.' It's all there in the String Trio except for one minor detail: a tonal center.
    But I don't understand what you mean by tonal center. I hear centers in Schoenberg, including the String Trio, like I do in Debussy and Bartok and Stravinsky. I hear him moving from center to center, weighting this one at one point and that one at another.

    I don't hear in terms of rows, and Schoenberg doesn't expect us to. He just wants us to listen to his music as music.
    Last edited by Mahlerian; Jul-01-2015 at 20:34.

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    Tone centricity is a feature of chromatic tonality, as it begins to use all twelve notes and geometric divisions of the octave.

    Localized tone-centricities do not qualify as tone centers, which is a more pervasive and far-reaching term.

    Tonality governs an entire octave, and the scale functions built on those scale steps.

    Tone-centricities are not octave-based in the same sense; they divide the octave into smaller autonomous segments, and this may create several points of centricity. This is a fragmented form by comparison.

    I hear Schoenberg largely in terms of musical gestures, not as tone rows. I think musical gesture is a form largely derived from traditional tonality (as in antecedent and subsequent phrases, cadences, etc).

    I also hear The String Trio in more modern terms, in the form of sound "events" which are not meant to be heard as definite 'musical' pitch or harmonic events, but as gestures of pure sound. Thus, the super-high harmonics, low bass clusters, plucked notes. This is the "abstract" Schoenberg.

    When, in the String Trio, Schoenberg creates a sustained verticality or 'chord,' my ears hear it harmonically as a 'chord,', as is their nature, with low notes seeming to be a 'root' or 'center' and higher notes as being component parts which create color, just like harmonics. I don't call this 'tonality' or even a tone-centricity; it's just a passing harmonic moment.

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    What is the difference between a tone centricity and a tonal center? How long is long enough for a tonal center to have significant definition?

    It is true that I do not hear Schoenberg's music in terms of functional tonality, but this is also true of the composers I mentioned, as well as music before 1600 and the music of other non-European countries.

    I hear Schoenberg as music, working with themes, motifs, harmonies, and timbres to create coherence. The separation of one of these elements from the others makes no more sense here than in any other piece of music. I don't hear Schoenberg's musical gestures as essentially different in any way than those in music by Beethoven or Mahler.

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    Quote Originally Posted by Mahlerian View Post
    What is the difference between a tone centricity and a tonal center? How long is long enough for a tonal center to have significant definition?
    I explained that difference above. If you mean in terms of your perception of it in time, I can't define that.

    I can only say that serial and 12-tone music uses all 12 notes, rather than tonality's 7, so this makes it automatically 'less tonal.' Tonality is a matter of degree, not an absolute.

    Tonality becomes less defined as more notes are added to a scale. This can be demonstrated mathematically; the more notes, the less variety of intervals, therefore it becomes 'harmonically less defined' as we approach 12 notes. In the following post is an excerpt from another thread on another site that I made which shows this.

    Quote Originally Posted by Mahlerian View Post
    It is true that I do not hear Schoenberg's music in terms of functional tonality, but this is also true of the composers I mentioned, as well as music before 1600 and the music of other non-European countries.

    I hear Schoenberg as music, working with themes, motifs, harmonies, and timbres to create coherence. The separation of one of these elements from the others makes no more sense here than in any other piece of music. I don't hear Schoenberg's musical gestures as essentially different in any way than those in music by Beethoven or Mahler.
    If that were the case, there would be no need for the 12-tone method, which is basically what that article you linked to is stating. I'll have to print that out in order to fully understand, assess, and comment on it, which may take a week or longer.

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    The material being discussed here is from Howard Hanson's "Harmonic Materials of Modern Music".

    The Projection of the Fifth

    As we all know, going around the circle of fifths yields all twelve notes before repeating. Therefore, there is a progression into chromaticism that is visible in this process.

    First, some nomenclature:
    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

    "Projection": the building of sonorities or scales by superimposing a series of similar intervals one above the other.

    Beginning with C, we add G, then D, to produce the triad C-G-D, or reduced to an octave, or its "melodic projection", C-D-G. Numerically, in terms of 1/2 steps, 2-5. In terms of total interval content, using the nomenclature above: p2 s.

    Next, we add A to the stack, forming the tetrad C-G-D-A, reduced melodically to C-D-G-A. Numerically, 2-5-2. Interval content: p3 n s2.
    The minor third appears for the first time.

    Next, pentad C-G-D-A-E, reduced to C-D-E-G-A, recognizable as the pentatonic scale. The major third appears for the first time. Numerically, 2-2-3-2. Interval analysis: p4 m n2 s3.

    The hexad adds B, forming C-G-D-A-E-B, reduced to C-D-E-G-A-B. Numerically: 2-2-3-2-2. Interval content: p5 m2 n3 s4 d.
    For the first time, the dissonant minor second (or major seventh) appears.

    Continuing, we add F# to get the heptad C-G-D-A-E-B-F#, reduced as C-D-E-F#-G-A-B. Here the tritone appears; also, this is the first scale which in its melodic projection contains no interval larger than a major second; i.e., look, ma, no gaps. It contains all six basic intervals for the first time in our series.
    Numerically: 1-1-2-2-1-2-2. Intervals: p6 m3 n4 s5 d2 t.

    Octad: Add C#, yielding C-C#-D-E-F#-G-A-B. Numerically, 1-1-2-2-1-2-2. Intervals: p7 m4 n5 s6 d4 t2.

    Nonad: Add G#: C-C#-D-E-F#-G-G#-A-B. Numerically, 1-1-2-2-1-1-1-2. Intervals: p8 m6 n6 s7 d6 t3.

    The Decad adds D#, yielding C-C#-D-D#-E-F#-G-G#-A-B.
    Numerically, 1-1-1-1-2-1-1-1-2. Intervals: p9 m8 n8 s8 d8 t4.

    Undecad: Add A#. C-C#-D-D#-E-F#-G-G#-A-A#-B. In 1/2 steps, numerically, it is 1-1-1-1-2-1-1-1-1-1. Interval content: p10 m10 n10 s10 d10 t5.

    The last one, the duodecad, adds the last note, E#. C-C#-D-D#-E-E#-F#-G-G#-A-A#-B.
    Numerically: 1-1-1-1-1-1-1-1-1-1-1.
    Interval content: p12 m12 n12 s12 d12 t6.

    Note the overall progression:
    doad: 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: p12 m12 n12 s12 d12 t6

    What can be noted is the affinity of the perfect fifth and the major second, since the projection of one fifth upon another always produces the concomitant interval of a major second;
    The relatively greater importance of the minor third over the major third; the late arrival of the minor second, and lastly, the tritone.

    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.
    In the octad, the same number of major thirds & minor seconds; In the nonad, same number of maj thirds, min thirds, and min seconds. In the decad, an equal number of maj/min thirds and seconds.
    When 11 and 12 are reached, the only difference is the number of tritones.

    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.

    Mahlerian will love this next paraphrase/quote from Hanson:

    This is probably the greatest argument against the rigorous use of atonal theory in which all 12 notes are used in a single melodic or harmonic pattern. These constructs begin to lose contrast, and a monochromatic effect emerges.

    Each scale discussed here can have as many versions as there are notes in the scale. The seven-tone scale has seven versions, beginning on C, D, E, and so forth. These "versions" should not be confused with involutions of the same scale.

    What has the projection of a fifth revealed to us?

    Quoting Hanson: "Since, as has been previously stated, all seven-tone scales contain all of the six basic intervals, and since, as additional tones are added, the resulting scales become increasingly similar in their component parts, the student's best opportunity for the study of different types of tone relationship lies in the six-tone combinations, which offer the greatest number of scale types."


    -------------------------------------------------------------------------------------
    Actually, this could be used to defend 12-tone theory, by the use of hexads (six-note sets), but note this crucial difference, seen by examining the interval content:

    hexad: p5 m2 n3 s4 d

    These intervals are based on the cross-relations of unordered scale-sets; NOT ordered tone rows.

    Maybe Mahlerian, and that article he posted, are correct: maybe the 12-tone method is not really any different from tonality, since Schoenberg hardly ever used the row in its ordered form except as thematic, melodic material. He always "cheated" and used hexads in their unordered forms!

    So really, what's the big deal? What did he invent? Is the 12-tone method just a sham?
    Last edited by millionrainbows; Jul-02-2015 at 18:03.

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