Why did he develop this method? What was his goal? Was it musical, artistic? What was he hoping to achieve? Was he trying to destroy tonality, or create a new kind of music? Did this need to be done? You tell me, I'm here to listen for a while.
millionrainbows
Unity.
Ever since the early 1900s, from around op. 6 or so, he had been focusing more and more intently on motivic and harmonic development out of small cells that generate whole pieces. This meant that the vertical and horizontal directions of music became closer and closer until they were eventually fused nearly completely with the Chamber Symphony.
With the move into music that is not written in the traditional tonal system that began with op. 10 and The Book of the Hanging Gardens, this motivic/harmonic development was freed of its need to fit into standard molds; the pieces that followed in this new style were brief and intensely focused. Often, their structure was tied to ostinati or a reference harmony which could provide stability and form. Just as frequently, they were tied to a text. It was found difficult to create longer movements.
The years of experiment that followed paralleled WWI in Europe and the move away from post-Romanticism in the arts which led to Neoclassicism and "New Objectivity" (Neue Sachlichkeit). Schoenberg's own experiments led him towards a more consistent use of procedures that he had already been using in his earlier works, and he called it "composing with the tones of the motive." These works, including the Serenade and the Five Piano Pieces op. 23, used a proto-serial technique which became the basis for his introduction of the row, or "basic set," as was Schoenberg's term.
This had several advantages:
- It facilitated motivic and harmonic unity, the kind of vertical/horizontal integration which had already been part of Schoenberg's style for two decades
- It allowed one to manipulate the material freely and maintain coherence over longer spans, in contrast to the freer treatment in the previous decade which had been difficult to organize
- This unity is audible to the listener (who is accustomed to a fully chromatic language)
It must be noted that for Schoenberg, this unifying element had an almost religious connotation.
As for whether it needed to be done, I am not sure. It seems unlikely that the method as such is to be consistently employed again by composers in the future. I do believe that serial thinking in terms of the operations and processes of serialism and the integration of vertical and horizontal dimensions of music is here to stay for quite a long time. We should be aware, for example, that even the "tonal" works Schoenberg wrote after the introduction of 12-tone technique (Suite for Strings, Theme and Variations for Band, parts of the Chamber Symphony No. 2, Kol Nidre, etc.) employ serial treatment of non-row materials.
Ever since the early 1900s, from around op. 6 or so, he had been focusing more and more intently on motivic and harmonic development out of small cells that generate whole pieces. This meant that the vertical and horizontal directions of music became closer and closer until they were eventually fused nearly completely with the Chamber Symphony.
With the move into music that is not written in the traditional tonal system that began with op. 10 and The Book of the Hanging Gardens, this motivic/harmonic development was freed of its need to fit into standard molds; the pieces that followed in this new style were brief and intensely focused. Often, their structure was tied to ostinati or a reference harmony which could provide stability and form. Just as frequently, they were tied to a text. It was found difficult to create longer movements.
The years of experiment that followed paralleled WWI in Europe and the move away from post-Romanticism in the arts which led to Neoclassicism and "New Objectivity" (Neue Sachlichkeit). Schoenberg's own experiments led him towards a more consistent use of procedures that he had already been using in his earlier works, and he called it "composing with the tones of the motive." These works, including the Serenade and the Five Piano Pieces op. 23, used a proto-serial technique which became the basis for his introduction of the row, or "basic set," as was Schoenberg's term.
This had several advantages:
- It facilitated motivic and harmonic unity, the kind of vertical/horizontal integration which had already been part of Schoenberg's style for two decades
- It allowed one to manipulate the material freely and maintain coherence over longer spans, in contrast to the freer treatment in the previous decade which had been difficult to organize
- This unity is audible to the listener (who is accustomed to a fully chromatic language)
It must be noted that for Schoenberg, this unifying element had an almost religious connotation.
As for whether it needed to be done, I am not sure. It seems unlikely that the method as such is to be consistently employed again by composers in the future. I do believe that serial thinking in terms of the operations and processes of serialism and the integration of vertical and horizontal dimensions of music is here to stay for quite a long time. We should be aware, for example, that even the "tonal" works Schoenberg wrote after the introduction of 12-tone technique (Suite for Strings, Theme and Variations for Band, parts of the Chamber Symphony No. 2, Kol Nidre, etc.) employ serial treatment of non-row materials.
G
Schoenberg, I think, was trying to do away with the concept of a key. I may be completely wrong here but the smallest scale you can have would be the interval of a fifth (or fourth depending on how you look at it). It would be pretty monotonous. To allow those two notes to modulate through keys, we would five more notes--the pentatonic scale. Chinese music is structured something like this--five notes with two more added that allow key change, those two modulators are played like grace notes. Now if you add those two scales together--2+5--you get a seven-note scale or diatonic scale. Now you can modulate the pentatonic scale through seven keys. Add the pentatonic and the diatonic and you get--5+7=12 notes or the chromatic scale. Now you can modulate the diatonic scale through 12 keys. The next in line would be the 7+12 or 19-tone scale.
I think they have made 19-tone instruments but they don't work well. They are cumbersome and some of the intervals are really off but could theoretically play the chromatic scale through 19 keys. So I think Schoenberg may have gotten the idea of 12-tone technique by hitting this brick wall of 12 tones which cannot modulate through key changes because it must have a larger scale to move around in. So the normal interval relationships are changed to get rid of the idea of being in a key. Does that make sense? It's music right at the edge of everything we know about music, as it were.
But don't take that as gospel. I'm not a Schoenberg scholar (or any other kind of scholar) by any stretch and I'm sure someone here will tell I have no idea what I'm talking and unfortunately they could be right.
I think they have made 19-tone instruments but they don't work well. They are cumbersome and some of the intervals are really off but could theoretically play the chromatic scale through 19 keys. So I think Schoenberg may have gotten the idea of 12-tone technique by hitting this brick wall of 12 tones which cannot modulate through key changes because it must have a larger scale to move around in. So the normal interval relationships are changed to get rid of the idea of being in a key. Does that make sense? It's music right at the edge of everything we know about music, as it were.
But don't take that as gospel. I'm not a Schoenberg scholar (or any other kind of scholar) by any stretch and I'm sure someone here will tell I have no idea what I'm talking and unfortunately they could be right.
Forte uses the term 'atonal' because that's what it means: music structured without using a tonal hierarchy, and heard without a sense of 'tonality' or key center, but heard only in terms of sonorities.
As far as actually hearing the effects of 'atonal' music, we can hear it as sonorities, but not as being tone-centric. In atonal theory, unordered pitch class intervals are described and defined as if they were simultaneities. From Ear Training for Twentieth Century Music (Friedman), we see:
"...the same unordered pitch class interval includes the motion from pitch class 1 to pitch class 2, the motion from pitch class 2 to pitch class 1, and the sonority of pitch classes 1 and 2 sounding simultaneously.
Instead of thinking of an unordered pitch class interval as a measurable distance between two notes, it may be more helpful to think of it as a type of sonority, analogous to its "color," or timbre."
We can hear it as a sonority, but NOT as being tonal or tone-centric.
My main point is that in most modern and 'post-tonal' music, music can still be heard as having sonority and having a harmonic dimension, without being structured as, or being heard as, 'tonal' or 'tone-centric.'
Unordered sets are similar to scales and modes, in that they allow free unordered use of the notes as an 'index' of relations, in which every note related to the others. This is similar to tonality, in which every note is related to the key note, except in this case, there is no 'key' note, and therefore no set of 'functions' as in tonality. Every sonority has an equal value, and can be used as the overall basis for a composition.
You could use a 'diatonic set" such as C-D-E-F-G-A-B as the set, but emphasize B-C-G as the main sonority. This is quite dissonant, and in tonality would be considered unusable, too dissonant, or inferior to C-E-G. Nonetheless, this triad has a sonority, and could be the basis of an entire composition, with the use of transposition, inversion, and retrograde procedures.
Additionally, unordered sets can have an 'interval vector,' which is a six-number list of all possible intervals in the set. This is basically a list of what sonorities will be present in using the set.
Ordered sets do not have interval vectors, because they are ordered, and there is no relation among all notes of the set. The ordered row is strictly melodic, and has no sonorous vertical dimension.
As far as actually hearing the effects of 'atonal' music, we can hear it as sonorities, but not as being tone-centric. In atonal theory, unordered pitch class intervals are described and defined as if they were simultaneities. From Ear Training for Twentieth Century Music (Friedman), we see:
"...the same unordered pitch class interval includes the motion from pitch class 1 to pitch class 2, the motion from pitch class 2 to pitch class 1, and the sonority of pitch classes 1 and 2 sounding simultaneously.
Instead of thinking of an unordered pitch class interval as a measurable distance between two notes, it may be more helpful to think of it as a type of sonority, analogous to its "color," or timbre."
We can hear it as a sonority, but NOT as being tonal or tone-centric.
My main point is that in most modern and 'post-tonal' music, music can still be heard as having sonority and having a harmonic dimension, without being structured as, or being heard as, 'tonal' or 'tone-centric.'
Unordered sets are similar to scales and modes, in that they allow free unordered use of the notes as an 'index' of relations, in which every note related to the others. This is similar to tonality, in which every note is related to the key note, except in this case, there is no 'key' note, and therefore no set of 'functions' as in tonality. Every sonority has an equal value, and can be used as the overall basis for a composition.
You could use a 'diatonic set" such as C-D-E-F-G-A-B as the set, but emphasize B-C-G as the main sonority. This is quite dissonant, and in tonality would be considered unusable, too dissonant, or inferior to C-E-G. Nonetheless, this triad has a sonority, and could be the basis of an entire composition, with the use of transposition, inversion, and retrograde procedures.
Additionally, unordered sets can have an 'interval vector,' which is a six-number list of all possible intervals in the set. This is basically a list of what sonorities will be present in using the set.
Ordered sets do not have interval vectors, because they are ordered, and there is no relation among all notes of the set. The ordered row is strictly melodic, and has no sonorous vertical dimension.
At this point, I'm not sure how original or innovative Schoenberg's 12-tone method was, if all it did was 'order' the notes. Other 'atonal' ideas were in the air at the time. By 'atonal ideas,' I mean ideas which create musical structure without using the tonal hierarchy.
Josef Matthias Hauer (March 19, 1883 - September 22, 1959) developed a system of 'tropes' which used the entire chromatic scale for composing, before Schoenberg came up with his 12-tone system.
From WIK:
In certain types of atonal and serial music, a trope is an unordered collection of different pitches, most often of cardinality six (now usually called an unordered hexachord, of which there are two complementary ones in twelve-tone equal temperament). Tropes in this sense were devised and named by Josef Matthias Hauer in connection with his own twelve-tone technique, developed simultaneously with but overshadowed by Arnold Schoenberg's.
Hauer discovered the 44 tropes, pairs of complementary hexachords, in 1921 allowing him to classify any of the 479,001,600 twelve-tone melodies into one of forty-four types.
The primary purpose of the tropes is not analysis (although it can be used for it) but composition. A trope is neither a hexatonic scale nor a chord. Likewise, it is neither a pitch-class set nor an interval-class set. A trope is a framework of contextual interval relations. Therefore, the key information a trope contains is not the set of intervals it consists of (and by no means any set of pitch-classes), it is the relational structure of its intervals.
Each trope contains different types of symmetries and significant structural intervallic relations on varying levels, namely within its hexachords, between the two halves of an hexachord and with relation to whole other tropes.
Based on the knowledge one has about the intervallic properties of a trope, one can make precise statements about any twelve-tone row that can be created from it. A composer can utilize this knowledge in many ways in order to gain full control over the musical material in terms of form, harmony and melody.
The depicted example trope (no. 3) indicates that one hexachord of this trope is an inversion of the other. Trope 3 is therefore suitable for the creation of inversional and retrograde inversional structures. Moreover, its primary formative intervals are the minor second and the major third/minor sixth. This trope contains [0,2,6] twice inside its first hexachord (e.g. F-G-B and Gâ™-Aâ™-C and [0,4,6] in the second one (e.g. A-C♯-D♯ and Bâ™-D-E).
Its multiplications M[SUB]5[/SUB] and M[SUB]7[/SUB] will result in trope 30 (and vice versa). Trope 3 also allows the creation of an intertwined retrograde transposition by a major second and therefore of trope 17 (e.g., G-Aâ™-C-B-F-F♯-|-E-Eâ™-C♯-D-Bâ™-A → Bold pitches represent a hexachord of trope 17)
(end of quote)
So you can see, this type of 'atonal' thinking was already in the air. Yes, it is 'atonal thinking' because it sees notes in terms of their internal symmetries, not according to the 'tonal hierarchy.' It is non-tonal thinking and structuring.
Josef Matthias Hauer (March 19, 1883 - September 22, 1959) developed a system of 'tropes' which used the entire chromatic scale for composing, before Schoenberg came up with his 12-tone system.
From WIK:
In certain types of atonal and serial music, a trope is an unordered collection of different pitches, most often of cardinality six (now usually called an unordered hexachord, of which there are two complementary ones in twelve-tone equal temperament). Tropes in this sense were devised and named by Josef Matthias Hauer in connection with his own twelve-tone technique, developed simultaneously with but overshadowed by Arnold Schoenberg's.
Hauer discovered the 44 tropes, pairs of complementary hexachords, in 1921 allowing him to classify any of the 479,001,600 twelve-tone melodies into one of forty-four types.
The primary purpose of the tropes is not analysis (although it can be used for it) but composition. A trope is neither a hexatonic scale nor a chord. Likewise, it is neither a pitch-class set nor an interval-class set. A trope is a framework of contextual interval relations. Therefore, the key information a trope contains is not the set of intervals it consists of (and by no means any set of pitch-classes), it is the relational structure of its intervals.
Each trope contains different types of symmetries and significant structural intervallic relations on varying levels, namely within its hexachords, between the two halves of an hexachord and with relation to whole other tropes.
Based on the knowledge one has about the intervallic properties of a trope, one can make precise statements about any twelve-tone row that can be created from it. A composer can utilize this knowledge in many ways in order to gain full control over the musical material in terms of form, harmony and melody.
The depicted example trope (no. 3) indicates that one hexachord of this trope is an inversion of the other. Trope 3 is therefore suitable for the creation of inversional and retrograde inversional structures. Moreover, its primary formative intervals are the minor second and the major third/minor sixth. This trope contains [0,2,6] twice inside its first hexachord (e.g. F-G-B and Gâ™-Aâ™-C and [0,4,6] in the second one (e.g. A-C♯-D♯ and Bâ™-D-E).
Its multiplications M[SUB]5[/SUB] and M[SUB]7[/SUB] will result in trope 30 (and vice versa). Trope 3 also allows the creation of an intertwined retrograde transposition by a major second and therefore of trope 17 (e.g., G-Aâ™-C-B-F-F♯-|-E-Eâ™-C♯-D-Bâ™-A → Bold pitches represent a hexachord of trope 17)
(end of quote)
So you can see, this type of 'atonal' thinking was already in the air. Yes, it is 'atonal thinking' because it sees notes in terms of their internal symmetries, not according to the 'tonal hierarchy.' It is non-tonal thinking and structuring.
I think Schoenberg 'ordered' the rows so he could make horizontal melodic constructs: themes, and motives, and contrapuntal lines which are melodic in nature. Since Debussy and Bartok were already expanding the harmonic aspects, there was really nothing left to do.
Schoenberg's ordered 12-tone system is limited in this respect; he makes no consideration for harmony, or vertical chordal aspects. He didn't have to, either; harmonically, Debussy, Stravinsky, and Bartok (and Hauer) were already using unordered sets, which were not tonally derived, to create new harmonic, vertical sonorities.
So, big deal. Schoenberg's 12-tone method is only a half-solution. It's only melodic. The unordered, harmonic set thinking was already taking place.
I think Schoenberg was to a degree, grandstanding, and trying to ensure his place in history. His method, and the way he used it, was never codified very strictly, and he seems to have bent an awful lot of rules in creating any kind of "harmony' out of the system itself, since it is inherently melodic and un-harmonic.
I think he used it to create themes and motives, like Brahms, but the rest of it was using unordered rows. Even within each composition, I think he was 'winging it' and fudging on the strict adherence to ordered rows.
Schoenberg's ordered 12-tone system is limited in this respect; he makes no consideration for harmony, or vertical chordal aspects. He didn't have to, either; harmonically, Debussy, Stravinsky, and Bartok (and Hauer) were already using unordered sets, which were not tonally derived, to create new harmonic, vertical sonorities.
So, big deal. Schoenberg's 12-tone method is only a half-solution. It's only melodic. The unordered, harmonic set thinking was already taking place.
I think Schoenberg was to a degree, grandstanding, and trying to ensure his place in history. His method, and the way he used it, was never codified very strictly, and he seems to have bent an awful lot of rules in creating any kind of "harmony' out of the system itself, since it is inherently melodic and un-harmonic.
I think he used it to create themes and motives, like Brahms, but the rest of it was using unordered rows. Even within each composition, I think he was 'winging it' and fudging on the strict adherence to ordered rows.
I think Schoenberg was much more worried about harmony. After all he wrote a harmony book that's richer in thought than his 'contrapuntal exercises' and his melodies tend to fit together in fixed harmonies that drive on the music, often compressing the rhythms in the line for the sake of it. Berg on the other hand wrote much more fluid polyphony.
But the more I think about it, the more possibilities arise from using different forms of the row, and also by breaking it down into smaller groups of 6, 4, 3, and 2 notes. Three notes can become almost as flexible as an unordered scale! 1-2-3/3-2-1. You can't get 2-1-3. though. And it gets less flexible as you add notes.
Still, though, what a system! It's like being in the Marines! :lol:
Still, though, what a system! It's like being in the Marines! :lol:
Schoenberg, Elliott Carter, Milton Babbitt, and George Perle were all interested in certain rows which had symmetry under transformation; in other words, rows which gave the same intervals when inverted or reversed.
Why was this? It was because they were searching for some form of consistency in the row, so that when combined with other forms, they at least had some control over the materials, and could predict what the results might be.
Why was this? It was because they were searching for some form of consistency in the row, so that when combined with other forms, they at least had some control over the materials, and could predict what the results might be.
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.
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.
What does Schoenberg's music and the Hindenburg have in common?
Both had a lot of hot air and killed a lot of people. :lol:
(Sorry, I couldn't help myself!)
Both had a lot of hot air and killed a lot of people. :lol:
(Sorry, I couldn't help myself!)
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...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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?
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?
Sorry for my late reply, I only just noticed this thread. I have not read any of it before.
In my opinion, Schoenberg was pushing the boundary of the tonality with atonal music. He saw it as the theoretical means to push the evolution of dissonance. He also wanted to make a name for himself in music and the arts in general.
In my opinion, Schoenberg was pushing the boundary of the tonality with atonal music. He saw it as the theoretical means to push the evolution of dissonance. He also wanted to make a name for himself in music and the arts in general.
Schoenberg called his music "pantonal", which could mean "all tones are tone-centres", which is basically the same thing as none of them being a tone-centre - atonality, in other words. It's like everyone being the leader. And he did consider the technique historically important:
From Wikipedia
Schoenberg announced it characteristically, during a walk with his friend Josef Rufer, when he said, "I have made a discovery which will ensure the supremacy of German music for the next hundred years" (Stuckenschmidt 1977, 277)
From Wikipedia
Schoenberg announced it characteristically, during a walk with his friend Josef Rufer, when he said, "I have made a discovery which will ensure the supremacy of German music for the next hundred years" (Stuckenschmidt 1977, 277)
I actually find the scores very interesting! Just as interesting as how it sounds. Understanding a Schoenberg score, for me, is like understanding a Schumann score. There are fascinating ideas on the paper; they are the closest we can really get to the thought process of any composer and that's what makes score analysis really invigorating. One thing which I find exciting is reading a score and looking at the fine details, how they fit together and imagining everything being played in my head. Most often, there is no interpretation quite like it when I try to find one closest to how I would play it!
Berg's and early Webern scores, full of variety and detail of all kinds, parallel the beauty of the sound they code. In contrast, most of Messiaen's scores are the most boring great things I've looked at.
Yes, the quote means that those musics are not tonal.
It says that the definition of atonality "being in the Western tradition and not being tonal" does not apply to those kinds of music in spite the fact that, like the music called atonal, they are within the Western tradition and they are not tonal. There is no other way in which this sentence can be understood.
Atonality never has been opposed to tonality. Any attempt to define it as such runs into contradictions.
It says that the definition of atonality "being in the Western tradition and not being tonal" does not apply to those kinds of music in spite the fact that, like the music called atonal, they are within the Western tradition and they are not tonal. There is no other way in which this sentence can be understood.
Atonality never has been opposed to tonality. Any attempt to define it as such runs into contradictions.
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
