A question on 12-tone Schoenberg

[SeptimalTritone]

Hi guys,

I have been thinking about the cadences in Schoenberg's 12 tone music. Some of Schoenberg's final resolutions are very traditional in rhythm and evocative of a clear, cadential finish chord -> chord, while others are a lot less clear to me! I.e., to take a favorite example out of many, the fourth quartet https://www.youtube.com/watch?v=L85XTLr5eBE has emphatic cadences... I think... at measure 6 beat 2*, measure 16 beat 2.5, measure 62, mm. 238 beat 4, mm. 257 beat 4, mm. 284... there are also quite a few phrase endings, pretty much whenever the upper square symbol ] is marked in the score, a few of those might be weak cadences but the majority are just phrase endings. The chordal simultaneity cadences I mentioned above are probably the stronger onces.

Anyway... I was looking at the chordal set of some of those final chords, as well as where in the tone row these are, and I don't see an obvious pattern. From the standpoint of "what set" as in set theory, there seems to be variety, and form the standpoint of "which notes in the tone row", there is also variety. Yes, the final cadence is the prime tone row's hexachord h2 -> hexachord h1 with the C# held on top in the first violin, and ending on the prime hexachord seems to be standard as a big ending in Schoenberg's other pieces like op 33a, op 31, op 26's first movement, and probably many more examples than that. But the other cadences, it's not obvious, the set is different, and the tone row position is not conjunct. There's a clear melodic drive to cadence helped by the motion of the voices, but a rule for why it sounds so stable is a mystery to me. Actually, forget the tone row, because you can play these examples in isolation so that the tone row doesn't matter, and they still sound cadential!

One possible answer I had in mind was suggested in Charles Rosen's Schoenberg book, where he says that there's a strong tendency in highly chromatic non-tertian/diatonic music for the 12 notes of chromatic space to want to fill it out. If one plays one hexachord simultaneity, the complementary hexachord played afterward will sound like a resolution. But if notes are held between so that the complementary hexachord doesn't get fleshed out, it won't sound as resolved.

I tried this here: https://musescore.com/user/4084206/scores/2687666 In the first example, the two hexachords are complete complements. But in the other examples, one by one, I leave a note there without moving it. In the fourth example, three notes are held. It sounds like each time I keep a note not moving, it sounds less and less satisfying.

This sort of resolution doesn't depend on a tone row of course and sounds good on its own. Such resolutions are natural to incorporate in a tone row composition with a naturally defined h1 and h2, but it's not required to have a tone row to do this. It also clearly depends on the notes chosen, it's not arbitrary. I would imagine that resolutions with tetrachords or trichords would be governed by a similar rule: have the three tetrachords or four trichords "fill out" chromatic space, although I haven't systematically tested this in detail.

So... is it possible that, while in common practice music a chromatic hexachord, or even a chromatic tetrachord or chromatic trichord would be a tense dissonance, that such chords could be the most stable ones in 12-tone music, provided that the voice leading uses these chords to fill out chromatic space?

* Actually, I'm not entirely sure about this one either. Schoenberg has the ] marked at the end of beat 1, not the end of beat 2. I hear the second beat as the ending, and so does my book, but I'm not sure.

[Karl Henning]

[...]

One possible answer I had in mind was suggested in Charles Rosen's Schoenberg book, where he says that there's a strong tendency in highly chromatic non-tertian/diatonic music for the 12 notes of chromatic space to want to fill it out. If one plays one hexachord simultaneity, the complementary hexachord played afterward will sound like a resolution. But if notes are held between so that the complementary hexachord doesn't get fleshed out, it won't sound as resolved.

[...]

So... is it possible that, while in common practice music a chromatic hexachord, or even a chromatic tetrachord or chromatic trichord would be a tense dissonance, that such chords could be the most stable ones in 12-tone music, provided that the voice leading uses these chords to fill out chromatic space?

This seems to accord (!) with a "discovery" I made in my own work some time ago (casting discovery in quotes because I know I am not the first to discover it, Rosen e.g., but it was a Eureka! moment for me when I found this) that, much as in tonal music (duh ) the harmonic flow feels different whether one goes from one harmonic unit to another with no shared pitch content, or when there are common tones.


Good post.

[Cato]

Hi guys,

I have been thinking about the cadences in Schoenberg's 12 tone music. Some of Schoenberg's final resolutions are very traditional in rhythm and evocative of a clear, cadential finish chord -> chord, while others are a lot less clear to me!

There's a clear melodic drive to cadence helped by the motion of the voices, but a rule for why it sounds so stable is a mystery to me. Actually, forget the tone row, because you can play these examples in isolation so that the tone row doesn't matter, and they still sound cadential!

One possible answer I had in mind was suggested in Charles Rosen's Schoenberg book, where he says that there's a strong tendency in highly chromatic non-tertian/diatonic music for the 12 notes of chromatic space to want to fill it out.


So... is it possible that, while in common practice music a chromatic hexachord, or even a chromatic tetrachord or chromatic trichord would be a tense dissonance, that such chords could be the most stable ones in 12-tone music, provided that the voice leading uses these chords to fill out chromatic space?

Your musings have led you to the correct solution: the answer to your final question is simply "yes."

Schoenberg - despite everything one may have heard - is following his soul's ear, and this is why you cannot find a clear consistency in any "cadential" section.  The method does not wag him: he wags the method.

The "melodic drive" is precisely what is important in all of Schoenberg's music, and it is what provides stability in the new universe of Zwoelftonmusik.  If you look at the score - or listen to it with the score - of  a middle-period, non-12-tone work like Erwartung, you will see that the opera is in general designed to begin with that "melodic drive," and then soon the "chromatic space" mentioned by Rosen is filled, i.e. we have the entire orchestra/ensemble playing, and when that happens, the air is then cleared, and the music begins again its build toward another filling of the chromatic space: Rosen's idea derives directly from the scores.

So yes, your own ears have led you to the correct solution in "unraveling" Schoenberg's paths in his works.  0:)

[Monsieur Croche]

Hi guys,

I have been thinking about the cadences in Schoenberg's 12 tone music. Some of Schoenberg's final resolutions are very traditional in rhythm and evocative of a clear, cadential finish chord -> chord, while others are a lot less clear to me! I.e., to take a favorite example out of many, the fourth quartet https://www.youtube.com/watch?v=L85XTLr5eBE has emphatic cadences... I think... at measure 6 beat 2*, measure 16 beat 2.5, measure 62, mm. 238 beat 4, mm. 257 beat 4, mm. 284... there are also quite a few phrase endings, pretty much whenever the upper square symbol ] is marked in the score, a few of those might be weak cadences but the majority are just phrase endings. The chordal simultaneity cadences I mentioned above are probably the stronger ones.

I was looking at the chordal set of some of those final chords, as well as where in the tone row these are, and I don't see an obvious pattern. From the standpoint of "what set" as in set theory, there seems to be variety, and form the standpoint of "which notes in the tone row", there is also variety. Yes, the final cadence is the prime tone row's hexachord h2 -> hexachord h1 with the C# held on top in the first violin, and ending on the prime hexachord seems to be standard as a big ending in Schoenberg's other pieces like op 33a, op 31, op 26's first movement, and probably many more examples than that. But the other cadences, it's not obvious, the set is different, and the tone row position is not conjunct. There's a clear melodic drive to cadence helped by the motion of the voices, but a rule for why it sounds so stable is a mystery to me. Actually, forget the tone row, because you can play these examples in isolation so that the tone row doesn't matter, and they still sound cadential!

In Charles Rosen's Schoenberg book, he says that there's a strong tendency in highly chromatic non-tertian/non-diatonic music for the 12 notes of chromatic space to want to fill it out. If one plays one hexachord simultaneously, the complementary hexachord played afterward will sound like a resolution. But if notes are held between so that the complementary hexachord doesn't get fleshed out, it won't sound as resolved.

I have little to say about this directly, but the above two paragraphs of yours should, I hope, show to anyone who knows a bit about common practice harmony that the premises of virtually all the 'old' functions of cadences, half, whole, plagal, deceptive, etc. are clearly present and working in non-tonal music.  This only affirms that Schoenberg, and "What he did," are all resoundingly traditional, and that he was far far away from having thrown out the baby with the bathwater.

Too, it shows, as Schoenberg knew and adhered to, the listener hears 'the same way,' regardless of whether it is "tonal" or "atonal" music.

No matter how 'vertical / homophonic,' I would admonish looking to understand a Schoenberg score would include, always to some degree that is often more than less, delving into his horizontal/ contrapuntal procedures (as so succinctly put above in Cato's superb post) ~ the near omnipresence of Melodic Drive. I would only add, melodic Drive In All Parts, even if the outward appearance and effect is temporarily more homophonic.  Schoenberg is but one of many composers who are examples of that dichotomy / maxim, "Good counterpoint is good harmony: Good harmony is good counterpoint."

Consider diatonic music and that it presents near exact or exact parallel problems;
The composite of individual pitches of the I, IV, V triads... with a few pitches of the seven already repeated / held in common, presents all seven pitches of that diatonic scale.  I.e. that announces all the pitch content of that scale, and of the segments of the piece in that key.  The solution in tonal as well as atonal music, is to linger in one area, which then keeps some of the pitches in reserve -- i.e. withholding some of them from that part of the piece -- and that then allows for something 'fresh for the ear,' (pitch content not previously heard) when those withheld pitches are later presented.  This has been a known premise for more than a little time :-)

"plus ça change, plus c'est la même chose"

Fine post, BTW.


Always best regards.

[Maciek]

I tried this here: https://musescore.com/user/4084206/scores/2687666 In the first example, the two hexachords are complete complements. But in the other examples, one by one, I leave a note there without moving it. In the fourth example, three notes are held. It sounds like each time I keep a note not moving, it sounds less and less satisfying.

I'm not sure if I understand what you mean, but if I do, then the first pair in your example does not contain fully complementary hexachords - both of them have G, neither has Bb/A#. As a consequence, the second and third pair are, in terms of your theory - analogous: in each of these pairs, there are two common pitches between the chords and two pitches not present in either.

[Cato]

... that the premises of virtually all the 'old' functions of cadences, half, whole, plagal, deceptive, etc. are clearly present and working in non-tonal music.  This only affirms that Schoenberg, and "What he did," are all resoundingly traditional, and that he was far far away from having thrown out the baby with the bathwater.

Very nice: and to prove the point even more, the phrase "Conservative Radical" has been used more than once to describe what Schoenberg did. 

See e.g.

http://nymag.com/nymetro/arts/music/classical/reviews/3164/

In fact, I believe he saw himself as more of a descendant of Brahms than of e.g. Mahler.  His article Brahms, The Progressive is instructive.  I cannot find an on-line version, but here is a nice summary and commentary:

https://friedfoo.wordpress.com/music/brahms-works-for-chamber-ensemble/arnold-schoenberg-brahms-the-progressive/

See Schoenberg's book Style and Idea for the essay.  And I simply note that Schoenberg chose Brahms and not Bruckner, Mahler, or Wagner for his essay.

[Mahlerian]

Very nice: and to prove the point even more, the phrase "Conservative Radical" has been used more than once to describe what Schoenberg did. 

See e.g.

http://nymag.com/nymetro/arts/music/classical/reviews/3164/

In fact, I believe he saw himself as more of a descendant of Brahms than of e.g. Mahler.  His article Brahms, The Progressive is instructive.  I cannot find an on-line version, but here is a nice summary and commentary:

https://friedfoo.wordpress.com/music/brahms-works-for-chamber-ensemble/arnold-schoenberg-brahms-the-progressive/

See Schoenberg's book Style and Idea for the essay.  And I simply note that Schoenberg chose Brahms and not Bruckner, Mahler, or Wagner for his essay.

In Schoenberg's mind, the conversion to Mahler came too late in his development to have much of an impact on his own personal style.  It should be remembered that his first encounter with the elder composer (the First Symphony) provoked a negative, even a hostile, reaction, while the Viennese premiere of the Third was like a "thunderbolt" and he was instantaneously and forever converted to Mahler's cause.  He even wrote an extremely effusive letter that gushes more on the level of a smitten college student than a composer of around 30.  For any who are still under the delusion that Schoenberg was not a Romantic at heart, be sure to look that letter up.

At any rate, his earlier orchestral music, which predates this conversion, is loaded with Straussian influence, both in the treatment of the ensemble and in the kind of chromaticism employed.  Both Pelleas and the Gurrelieder are mining that vein, and the Six Songs for orchestra can be put with them to some degree, but these were followed by the Chamber Symphony, which uses a lean, soloistic ensemble of the kind Mahler extracted from his large orchestras.  The work even seems to contain a reference to the second Nachtmusik of Mahler's Seventh Symphony in its scherzo, a work we know that Schoenberg loved and admired greatly.  More generally, I think the increasing independence of all of Schoenberg's lines starting from the First String Quartet can be in part attributed to the encounter with Mahler's music.

Mahler's shadow seems to hang over the Second String Quartet as well, where Ach du lieber Augustin's appearance and subsequent disintegration in the D minor scherzo is a dead ringer for all of those apparitions of popular music in Mahler's symphonies.  So too the introduction of a singer into the third and fourth movements, and while Beethoven may have introduced the chorus and soloists into a symphony (and Mendelssohn after him), Mahler not only provided a more recent model, but one that employed the solo voice alone.  Critics of the day certainly saw a connection between the two.

There is still a good bit of Strauss in the Five Orchestral Pieces and Erwartung, but by Pierrot lunaire it seems mostly excised (granted, Pierrot doesn't resemble Mahler much either).  Schoenberg did continue to admire Mahler and his music, but any influence it had after the String Quartet in F-sharp minor seems more subliminal than conscious; perhaps the Serenade could be cited as an exception.

Berg's music is much more obviously indebted to Mahler, especially in the Three Pieces for Orchestra and Wozzeck.

[San Antone]

Schoenberg was in tears as he stood on the platform and watched Mahler's train leave Vienna on his way to New York in 1908. 

[Mahlerian]

Schoenberg was in tears as he stood on the platform and watched Mahler's train leave Vienna on his way to New York in 1908.

There's also the funereal Op. 18-6 and the painting The Burial of Gustav Mahler:

[arpeggio]

I have no idea what you guys are talking about but I really enjoy the civility. 

[Cato]

In Schoenberg's mind, the conversion to Mahler came too late in his development to have much of an impact on his own personal style...  He even wrote an extremely effusive letter that gushes more on the level of a smitten college student than a composer of around 30.  For any who are still under the delusion that Schoenberg was not a Romantic at heart, be sure to look that letter up.

There is still a good bit of Strauss in the Five Orchestral Pieces and Erwartung, but by Pierrot lunaire it seems mostly excised (granted, Pierrot doesn't resemble Mahler much either).  Schoenberg did continue to admire Mahler and his music, but any influence it had after the String Quartet in F-sharp minor seems more subliminal than conscious...

Many thanks for the comments!  Your final comment shows at least one reason perhaps why there was no essay called Mahler, The Progressive.

Concerning Richard Strauss: one might have wondered about an essay called Strauss, The Progressive, given that e.g. Erwartung could be seen as the daughter of Elektra.  On the other hand, Rosenkavalier shows Strauss making a choice not to follow at least some of the paths opened up in Elektra.  Schoenberg of course broke with Strauss after the older man commented to Alma Mahler that Arnold needed a psychiatrist * and rejected any notion that he had ever even "understood" the other composer's music.

* Strauss while conducting in Berlin had seen the score to the Five Pieces for Orchestra, and politely told Schoenberg that it was too bold for conservative Berlin.

[kishnevi]

Well, my negative opinion of Erwartung is perhaps shaped by how closely it fits Greg Mitchell's description of Elektra:* although granted there is only one lady screaming in Erwartung.  Yet I am much more positive about Elektra, despite the multiplicity of screaming ladies there.  So the differences must be more fundamental.

*Some months ago, in I forget which thread, he described it as "a bunch of women screaming at each other".

[Cato]

Well, my negative opinion of Erwartung is perhaps shaped by how closely it fits Greg Mitchell's description of Elektra:* although granted there is only one lady screaming in Erwartung.  Yet I am much more positive about Elektra, despite the multiplicity of screaming ladies there.  So the differences must be more fundamental.

*Some months ago, in I forget which thread, he described it as "a bunch of women screaming at each other".

Do you know Jessye Norman's performance of Erwartung or the Met performance of Elektra with Hildegard Behrens ?

On the other hand, Rosenkavalier shows Strauss making a choice not to follow at least some of the paths opened up in Elektra. 

I should mention that some musicologists disagree that Rosenkavalier is some sort of manifesto against "modernism" (a claim I have seen more than once), which is why I chose the phrasing above.

[kishnevi]

Do you know Jessye Norman's performance of Erwartung or the Met performance of Elektra with Hildegard Behrens ?

I should mention that some musicologists disagree that Rosenkavalier is some sort of manifesto against "modernism" (a claim I have seen more than once), which is why I chose the phrasing above.

Don't have the Norman.  Do have the Boulez and Sinopoli recordings.  The piece strikes me as ugly in both recordings.  Same with Pierrot Lunaire.  Whatever Arnold was doing in those two works, it doesn't work for me.

Elektra, on the other hand, mentally wears me out but I don't find it ugly. 

[Mahlerian]

Don't have the Norman.  Do have the Boulez and Sinopoli recordings.  The piece strikes me as ugly in both recordings.  Same with Pierrot Lunaire.  Whatever Arnold was doing in those two works, it doesn't work for me.

Elektra, on the other hand, mentally wears me out but I don't find it ugly.

My opinion is the exact opposite.  I find Pierrot and Erwartung fascinating, ethereal, and yes, quite beautiful, while I could take or leave Elektra.

[Karl Henning]

Tangentially, neither Erwartung nor Pierrot Lunaire is 12-tone.

(Just saying.)

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[Cato]

Tangentially, neither Erwartung nor Pierrot Lunaire is 12-tone.

(Just saying.)

What is fascinating is to sense the long bridge from an early work like Gurrelieder to later ones not using "the method" like Jakobsleiter those born in "the method" like  Moses und Aron.

Compare for example the song of Klaus-Narr in Gurrelieder to the song of the Revolutionary in Jakobsleiter, and then compare the opening establishment of atmosphere in Gurrelieder to the hexachordal opening in Moses und Aron.

[Karl Henning]

What is fascinating is to sense the long bridge from an early work like Gurrelieder to later ones not using "the method" like Jakobsleiter those born in "the method" like  Moses und Aron.

Compare for example the song of Klaus-Narr in Gurrelieder to the song of the Revolutionary in Jakobsleiter, and then compare the opening establishment of atmosphere in Gurrelieder to the hexachordal opening in Moses und Aron.

Indeed! The technical differences notwithstanding, there is a single voice.

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[Karl Henning]

Indeed! The technical differences notwithstanding, there is a single voice.

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Which, parenthetically, is also the truism with Stravinsky.

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[Cato]

Which, parenthetically, is also the truism with Stravinsky.

Yes, I was just thinking about the discussion under Who Actually Listens To Stravinsky !

One could change the title here to "Who Actually Listens To Late Stravinsky?"  I am old enough to recall the excitement - and the controversy - in the 1960's whenever a new Stravinsky work came out.  Requiem Canticles was particularly significant: and if one cannot hear the old Stravinsky of Le Sacre and Les Noces then one should pay closer attention!  0:)

See:

http://www.good-music-guide.com/community/index.php/topic,9671.60.html