A question on 12-tone Schoenberg

[SeptimalTritone]

I looked at some test cases of 12 tone music, and, still, there is something really bothering me, especially regarding the maxim "good harmony is good counterpoint".

I don't understand how Schoenberg's counterpoint, especially of the kind where one or two instruments play one tone row while one or two other instruments play another, creates a harmony as compelling as classical or romantic harmony.

Classical harmony is primarily elaborations of the tonic and dominant, and stepwise motion around (subdominant chords, inverted chords, secondary tonicizations etc.) or between (sequences, bassline sequences, stepwise bassline) these chords. And even the dominant is a stepwise elaboration of the tonic. I know that in romantic harmony one can introduce completely unprepared chromatic dissonances, and get out of them through nontraditional enharmonic or back door "resolutions" that take one from one dissonant chord to the next. Nevertheless, it seems that these sonorities are, within enharmonic equivalence, tertian, or at least passings or neighborings between tertian entities. Even Scriabin that was mentioned above, seems to be interested primarily in passings and neighborings between tertian or quartal sonorities. Although I have only cursorily looked at Scriabin.

In Schoenberg, especially in the chorale-like passages, there are cases where one can transpose one tone row within the counterpoint and it still works! The simultaneities then become all different, but it doesn't sound wrong, and actually, the aural affect isn't too different because the shape of the linear lines is the same. Octave simultaneities stick out to the ear as a mistake and need to be avoided, unless they are quick and momentary, but other than that things work out pretty well if one sticks to the tone row. Of course, if the counterpoint involves verticalizing just one tone row, then the simulteneities are more specified, but in more linear tone row contrapuntal cases, it is different.

For example, here are two examples of Schoenberg's wind quintet movement 3 starting at measure 8. One of these is correct, and the other is modified so that the tone rows are still followed to the letter but the tone row transpositional choice may be different (and a few of the rhythmic values changed to avoid octave simultaneities).

https://musescore.com/user/4084206/scores/2687666
https://musescore.com/user/4084206/scores/2731901

Can anyone tell me which is which, without listening to the real piece or looking at the real score? Would I have put the correct version first, or would that be too obvious, and would I therefore have put the correct version second? But then would I have anticipated you guys thinking that, and therefore still put the correct version first? Or... in a final twist to outsmart everyone, put the correct version second?

I would like, not just the experts, but lay enthusiasts with an interest in serial music by Schoenberg, Boulez, or whoever to try their hand. And to explain, confidently and clearly, why one is better than the other, not just that say one "sounds" or "feels" better!

Now, don't take me for being contrarian. In this particular excerpt, two transpositions of the inverse row get played three times. Compared to the incorrect version I posted, all other transpositional choices are worse. Too many octave simultaneities that one has to get rid of, and by the time one does that it winds up being too square: too many voices changing at the same time to accomodate this problem, and too much simultaneous motion in a texture like this gives rise to squareness. In fact, there's an excerpt right after this one in the same wind quintet movement that pits the rotated prime row against the rotated inverse row, and in inverse row counterpoint is much much harder to align right without resorting to voices changing together at the same time too much.

I would also like to add that these things are not always so clear cut! For example, in the Webern symphony (this is a correct version!):

https://musescore.com/user/4084206/scores/2665606

all four voices are each their own tone row, and yet any other choice miserably fails. Why? Because of pitch fixing: each pitch class (except for E flat) is fixed to a particular octave, giving each pitch class its own identity, and any deviations sound like wrong notes, like almost as bad as cross relations in classical harmony. Obviously, cases like Webern's saxophone quartet that require (the related concept) pitch symmetry about F# fail miserably when transposing a tone row. Cases that require specific symmetry or palindromes or pitch recollection or interval recollection also fail when transposing any tone row.

(An interesting aside: Webern has a lot of simultaneous unisons in that symphony, and also in his string quartet, but very few octaves. Unisons sound like "pulses" of one note, and are less offensive than octaves.)

Still, there are other parts where I'm not convinced that changing the transpositions destroys the counterpoint. Take the Symphony again, movement 2 variation 1. One of these is correct and the other is not. Can you figure it out? Did I put the correct one first or second (no rhythmic values were changed here, only certain precise transpositions)?

https://musescore.com/user/4084206/scores/2670406
https://musescore.com/user/4084206/scores/2666081

If "good harmony is good counterpoint", and it's not obvious to me that the correct versions of these Schoenberg/Webern examples are much better than the incorrect versions, then what makes their style of counterpoint as compelling, interesting, and challenging? Granted, I picked very specific examples of linear tone row structures and very specific row transpositions to make my point (most transpositions don't work), but still, it is worrying to me.

PS. I know that structural considerations would prefer certain tone row transpositions. Second Viennese composers made a big structural deal of relating the pitches in two seemingly different tone row transpositions/inversions/retrogrades through rhythm, melody, and distribution of notes. So particular tone row transposition does matter structurally, and it's how one relates one section of a movement to another, or one whole movement to another whole movement. Still, I am worried about the harmony and counterpoint in itself, within the particular section.

[Mahlerian]

If you're approaching this in terms of right and wrong, you have the wrong mindset.  Given that any particular simultaneity is allowed if justified by the context, what you're asking is not so much whether one can tell the difference between a version of the passage that is destroyed because wrong, but one that is not what the composer chose.  In asking why one version is better, you're asking for the impossible.

Furthermore, you've gone out of your way to do it in the inner voice.  There have been studies that have shown that many fail to attend to the details of inner harmony, to the point where a major chord turning to a minor chord is not recognized as any kind of shift (how would they hear Mahler's Sixth, I wonder?).  Now imagine that someone redid a few bars of a Bach chorale such that all of the lines and all of the harmonies still obeyed the rules (triads, dissonances resolved conventionally, etc.), but a single inner voice was changed.  How many people would choose Bach's original, or be able to say confidently that it is, in fact, provably and demonstrably better?

You're never going to be able to resolve these kinds of issues for any music, so I don't see why they should be seen as a problem for 12-tone music specifically.

Ref: http://languagelog.ldc.upenn.edu/nll/?p=2074

(As an aside, I'm fascinated by the number of people commenting on that blog post I linked to who couldn't tell the difference between the two cadential figures.  Not just couldn't express a preference, they couldn't tell the difference at all.  The second one severely weakens the sense of (common practice) tonal resolution, and so it really sticks out to me.)

[SeptimalTritone]

I didn't transpose an inner voice: I did much more. In the Schoenberg Wind Quintet, I bumped up the entire flute part and oboe part up a whole step for the alternate version, and had to change some rhythms to avoid octave simultaneities. These voices are usually the upper two voices in that excerpt. In the Webern Symphony, I bumped up both the cello and viola up a half step for the alternate version, and did not need to change any rhythms. These voices are usually the lower two voices in that excerpt.

So, in both examples, I offset the upper two voices off of the lower two voices. That was not a change of a hidden inner voice: I offset the soprano and alto from the tenor and bass simply by direct transposition. Yes, your study shows that in isolation, people have a hard time getting a chord right, especially an inner voice. But in context, that wrong E flat note in the imperfect authentic cadence example in the article is quite noticeably wrong. One would hope that offsetting the upper two voices from the lower two voices would produce a marked effect in those 12-tone excerpts, but it doesn't seem to.

Yes, if someone changed the inner voice of a Bach chorale, and still followed the counterpoint, it would not be noticed. But there is so much more restriction in that case. In the Schoenberg/Webern, the only things that stuck out to me as sounding wrong (1) were octave simultaneities, especially long held ones, (2) not respecting pitch fixing/symmetry/palindrome when needed, (3) too many undesired rhythmic simultaneous changes when the texture didn't call for it, meaning too many notes changing together at the same time when the texture makes that inappropriate, (4) not respecting the actual tone row. One can completely transpose the upper two voices in 12-tone music with no or limited change and it still works, and that would never be the case in a chorale/contrapuntal texture in common practice music where the restrictions of tension and resolution, passings and neighborings, tertian sonorities, and so on control what vertical structures one can move between. Yes, people might have a hard time distinguishing a half-diminished seventh chord from a fully diminished seventh chord, and even rightly so (if resolved to a major chord! there would be a jarring cross-relational effect if the half-diminished seventh chord were resolved to a minor chord), but the literal transposition up of entire lines would not work.

What worries me is this: the affect of harmonic simultaneity, one by one, especially triads and seventh chords, is very powerful in common practice harmony. With 12 tone music one can offset the upper two voices from the lower two and still have it work, in certain particular textures. Which means... that the affect of particular harmonic simulteneites is much less pronounced in those textures. Which means that I don't know what is meant by "good harmony is good counterpoint" in the context of 12-tone music. Cato said earlier that Schoenberg works linearly, but with so much more freedom to produce simultaneities, the actual affect and feeling of simultaneous chords is lessened. Especially in that Webern string chorale in that symphony excerpt: what is one to hear of it beyond the linear dialogue of motivic/intervallic fragments? How is the counterpoint as interesting, when the actual simultaneity doesn't matter too much, even offsetting the soprano and alto from the tenor and bass not mattering too much? Even the notes of the all-important soprano-bass counterpoint don't matter too much...

[Mahlerian]

I only listened to the Wind Quartet excerpts one time, without looking at the sample scores, and then looked briefly at the sample scores as I was writing my post.  I didn't check the Webern.  I can pretty confidently say which one for Op. 26 is correct, because the other sounds VERY wrong to me.  Could I prove its wrongness to you?  No, probably not, which is why I didn't try.

I think you're going about this absolutely wrong.  You're worried not because there actually is something wrong with Schoenberg's music, but because you can't prove that it's right.  Who cares about proving it?  He didn't.  I don't either.  Stop assuming that there's something wrong with the music, and just listen.  Stop worrying about theory, and just compose.

The simultaneity does matter, as you discovered when you had to manipulate your examples extremely carefully in order to get them even half-way to where you would be about as satisfied with them as with the original, just as with the hypothetical Bach chorale.  The music may not be driven by root progressions, and maybe some of the notes in a six or seven note harmony could be altered without much change to the sonority, but you're missing the point if you think that means the sonority itself is irrelevant.  That sonority leads to others, either of the same type, or a different one; its constituent notes arrived there from one place or another and have somewhere to go from there.  To alter it would be to change the relationships between all of these things.

And also, you missed the point that many people did not only not find that E-flat in the second cadence jarring, they didn't notice that it was present at all.

[SeptimalTritone]

Yeah, I know that in the comments people couldn't notice the E flat as different from the E natural, but one would hope that Mozart would be a lot less popular among lay people if he used flatted leading tones in his imperfect authentic cadences. If we were to take their statements to heart, one might as well forget musical technique.

The sonority in 12-tone music definitely matters a ton, and thankfully, perturbations and transpositions in most cases mess things up for some of the reasons I described above in my bullet point list. In fact, the resolving power of filling out chromatic space regardless of particular chordal sets that I was talking about in my OP is proof of the importance of sonority. I am more concerned about the more linearly distributed tone row contrapuntal structures that don't make strong use of pitch fixing, pitch recall, symmetry, and so on (like in Webern's op 21 and 22, which use these elements a lot even in linear row contrapuntal structures). I want to know what makes them work, and what makes them not work.

I think it's important to check the Webern example. It is much less obvious. At what point in the Schoenberg example did it sound wrong? Was it the cumulative effect, or certain beats at certain measures? For this wind quintet excerpt, the original has the flute/oboe as the inverted row a fourth above the clarinet/horn inverted row, whereas my manipulation has it a fifth above. Other choices don't work at all, due to the nature of the tone row.

I really want to know what makes the Schoenberg example (and the Webern example) wrong.

As for proof, I think it's essential to know why certain things work. It has led me to learn things. Even though the ear is the final judge of music, we need to know why our ears react in this way or that way, and we also need to know why, or to prove why, certain musical decisions are made. Trying to prove that Schoenberg's big tetrachord or hexachord cadences are justified led me to better grasp the concept of harmonic motion through chromatic space. Trying to prove that Schoenberg's form of development is motivated by romantic classicism led me to realize the 12-tone sequential-ish structures in his music that directly mirror earlier music. Trying to prove why inversion canons are so necessary in Webern taught me how interval gets developed through chromatic space.

I remember while learning classical harmony that I couldn't prove why second inversion chords should be treated dissonantly, while first inversion chords should not be, even though from a harmonic series standpoint the first inversion bass is more remote. It led me to the conclusion that the second inversion bass is evocative of the dominant note, while the first inversion bass is evocative of the remote mediant note and therefore unevocative! The pull to the dominant is strong, while the pull to the mediant is weak, and that's why the first inversion chord doesn't beg for resolution while the second inversion chord does. So even though the first inversion chord is acoustically nastier, the gravitational pull of the second inversion chord justifies its use as a dissonance. I remember asking this question to a music student in real life, who couldn't give me the answer, when he really should have. I think it is essential to be able to explain these things: it would be stultifying to say "this dissonance treatment is what worked for common practice composers' ears" without giving further explanation.

[Mahlerian]

Yeah, I know that in the comments people couldn't notice the E flat as different from the E natural, but one would hope that Mozart would be a lot less popular among lay people if he used flatted leading tones in his imperfect authentic cadences. If we were to take their statements to heart, one might as well forget musical technique.

No, that would be the wrong thing to take away from it.  The right thing would be that people aren't always able to consciously recognize the elements of music, even when they are pointed out to them.

I think it's important to check the Webern example. It is much less obvious. At what point in the Schoenberg example did it sound wrong?

Immediately.  From the very first harmony, it struck me as against Schoenberg's style.  The ending chord was important as well. (I checked my answer afterwards by listening to the original and then looking at the score, which confirmed my initial reaction.)

I really want to know what makes the Schoenberg example (and the Webern example) wrong.

Like I said, there is no way of proving it conclusively.

[SeptimalTritone]

The first chord of the Schoenberg is a 015 trichord, a very common trichord in Schoenberg, used a lot in the fourth quartet...

In fact, derived from that trichord: the first tetrachord is a major 7th chord, and the last tetrachord is also a major seventh chord.

Would the problem here be an "exposed" diatonic seventh chord as a strong/stable beat? Is an exposed 015 chord problematic, and its extension, the major 7th chord, problematic? Are they too evocative of traditional triadic tonality, and meant to be avoided? Schoenberg mentioned these chords initially as being too plain. But then again, the evocative of triadic tonality Ode to Napoleon or Berg Violin Concerto has exposed diatonic triads or seventh chords. Unless... the guideline is to use exposed diatonic seventh chords on strong/stable beats only when respecting their evocation of traditional triadic tonality?

Finally, let's say a lay hobbyist/student (sometimes, me) wanted to improve their own knowledge by writing their own second-Viennese pastiche as an exercise. A book or article would need to definitively state the problem here, or else there is a serious lack of instruction. I sometimes write little short exercises using tone rows of Schoenberg or Webern, and while I try to use concepts like linearity, imperfect sequencing, pitch symmetry, avoiding octaves, etc. I have no way to know for sure if it's right, even with using my ear. Which I suppose is the problem I had when initially trying to compose with classical harmony. Just like the guys in the comment section who didn't recognize the leading tone, even with using my ear, if I didn't know a concept was wrong I didn't recognize the sound in my mind as wrong.

Is this the only problem in my Schoenberg modification? There are quite a few traditional major 7th chords (and traditional minor 7th chords, half diminished seventh chords) within on strong beats. These tend to sound wrong-ish. Would the rule/guideline then be to avoid exposed diatonic seventh chords on strong/stable beats, except when actually utilizing their evocation of traditional triadic tonality? Then one would be able to prove (that is, prove within the standards of music theory) the modification as wrong!

[Mahlerian]

I didn't say I could tell you WHY it was wrong.  I told you, in fact, that I can't and I'm not sure anyone can (unless perhaps they have studied Op. 26 so deeply as to have fully absorbed Schoenberg's processes in that work).  It was not merely the identity of those two harmonies, but their connection with the rest of it, the rhythms, and so forth.  The differences were immediately apparent to me, and I reacted almost violently to the transposed version as opposed to the original.

There's no rule against using triads or sevenths.  The rule is that you need to justify their use by the way the music develops.  There's no rule that you must use a harmony like a Viennese trichord, and in fact you must justify the existence of that just as with the triad.  Once again, you're looking for a single "correct" solution to problems which, by their very nature, admit of multiple solutions.  In his teaching, Schoenberg would ask students to do as many versions of a single exercise as they could, in order to open them up to the possibilities of the exercise and to let them develop discernment for themselves.

Develop your ability to compose generally, and your sensitivity to details will increase.  Your ear will pick up on things that it didn't before.  Don't look for the sole correct and only true solution, because it's a fruitless search.

[SeptimalTritone]

Well, I want to know why it sounds wrong, or even violently wrong.

Turns out the the major 7th chord is the first chord of the correct version anyway and that there are also strong beat diatonic 7th chords, although the last chord is not. Sigh.

I still have no idea, beyond concerns of imitation or symmetry or octave avoidance, how 12-tone music with linear deployment of rows controls its verticals, such that certain ways sound right and certain ways quite wrong, and I am not satisfied by solely using intuition. It should be explainable, especially if one version sounds strongly incorrect. Anything that sounds incorrect, especially strongly or violently incorrect, should be explainable through some kind of music theory, otherwise one is in a dark labyrinth of confusion and hopelessness. Especially since to me, the modified version sounds very different, but not glaringly incorrect.

[Mahlerian]

Well, I want to know why it sounds wrong, or even violently wrong.

Turns out the the major 7th chord is the first chord of the correct version anyway and that there are also strong beat diatonic 7th chords, although the last chord is not. Sigh.

I still have no idea, beyond concerns of imitation or symmetry or octave avoidance, how 12-tone music with linear deployment of rows controls its verticals, such that certain ways sound right and certain ways quite wrong, and I am not satisfied by solely using intuition. It should be explainable, especially if one version sounds strongly incorrect. Anything that sounds incorrect, especially strongly or violently incorrect, should be explainable through some kind of music theory, otherwise one is in a dark labyrinth of confusion and hopelessness. Especially since to me, the modified version sounds very different, but not glaringly incorrect.

I think you seriously overestimate the degree to which music theory explains the rightness or wrongness of certain sequences in common practice harmony.  These issues that you're raising are unanswerable for any music.  You will never find the true solution that will resolve all of your difficulties.  If it were as simple as that, anyone would be able to compose great music by plugging in a formula (provided that it's complex enough).

[SeptimalTritone]

I think that the answer to this question could lie in the pitch class reflection, that is, repetition or recall, of (1) vertical dyads and (2) horizontal dyads, or trichords at either strong or held beats. But I want to think about it a bit in more detail, with more examples. The original version has a lot of important pitch class reflections between the upper two and lower two voices governed by certain tone row relations, and in the modified version those are all gone, making it seem a bit more haphazard.

Important are not so much particular verticals, and the diatonic/chromatic simultaneity thing is mostly unimportant because there are diatonic seventh chords in some places in the original version and other diatonic seventh chords in other places in the modified version. More important is pitch class reflection, which thankfully is mentioned a lot in books in articles, but I didn't realize its strong importance for making Schoenberg work, even outweighing particular vertical simultaneity at each time. But I want to think for a bit.

I know all about the many parallel fifths in, say, Beethoven's pastoral symphony, and other famous rule-breaking sections or entire formal plans. Yes, as Monseiur Croche (perhaps both PetrB and Debussy) has often pointed out, there are no fixed rules that explain the greatness of music, but one has to explain why bumping up a tone row while still avoiding octaves usually makes the section much worse, regardless of expertise of the particular piece, and I think the answer is in pitch class reflection. Loosing the important strong beat/held pitch class reflections gives a haphazard sound.

[Monsieur Croche]

I really want to know what makes the Schoenberg example (and the Webern example) wrong.

When the Schoenberg quartet was first formed in L.A., the members worked closely with Schoenberg to best understand and render the music.  One member who had 'done his homework' and thoroughly knew and recognized the row in one of the quartets found what he thought was a wrong note -- a B-natural -- in his part.  He pointed it out to Schoenberg and asked, "Shouldn't that be a B-flat?"  -- whereupon Schoenberg instantly and vehemently said, "If I had wanted a B-flat there I would have written one." ~ this is an ideal lesson about serial music, theoretical methodology of any sort when taken to pedantic extremes, and a good one to take to heart.

Your transposition:  basically, dude, you chose "the wrong notes," lol, while there is nothing in theory which could possibly either prove or disprove that.  Without having listened or looked at your altered examples, I'm already convinced the 'problem' with the examples is that altered the personal choices made by the composers which were guided by both their intellect and their ears... i.e. as Mahlerian rightly said, no one can tell you why they're wrong as much as tell you what sounds 'more right.' 

I would think it far more beneficial to use the row from one of those pieces as the basis for a piece of your own, or better, devise your own row, to your liking, and then write an original piece, be it brief or otherwise -- that you consider as 'working on a piece' vs. an exercise.  That is the the surest and quickest way in to your getting truer information on what serial music (or modal, or tonal, or neotonal, etc.) can do and how it behaves.  This is exactly what happens in theory courses, assignments given to write something 'in the style of,' but using only materials freshly invented by the student.

Doing those transpositions seems to show an approach which is somehow near to totally hung up on serial music being a music-theory-composition methodology unlike all the previous methodologies of music from the eras from plainchant up through the Second Viennese School... which it is not.  Put another way, there really is no set methodology about writing any kind of music;  I think people tend to go way over the top about 'method' because that first school of serial music unfortunately became known as 'a method.'  It ain't -- any more than diatonic music is 'a method.'  In making those transpositions, you were a bit guilty of thinking of "the method" as being somehow more relatively arbitrary than the rest of music, i.e. all musical styles are innately somewhat 'arbitrary' while also heavily dependent upon 'sounds not O.K. / O.K. / Better / Best.

To mistake serial music as a method, either a rigid one of all rules or thinking it allows for such arbitrariness, would be taking to heart that egregiously mistaken explanation of serial music as given by Adrian Leverkühn in Thomas Mann's Faustus.  Mann had consulted with Theodor Adorno about serial music, and, well, between what Adorno fed Mann and what Mann then wrote (keeping in mind "If a literary man puts together two words about music, one of them will be wrong." ~ Aaron Copland) -- well, then, Damn Adorno and Damn Thomas Mann.

All the cerebral activity in the world will not get you into really understanding music and how it works: it is through the writing, using your own invented materials, your own tone row, that you will find many an 'answer' to the questions you are asking about serial music.  I can guarantee you that once you are fairly well into such a comp, you will begin to realize that though 'nearly anything might do' (the case when composing anything), for the composer there is ultimately only one right choice and decision each point along the way; those choices are not wholly cerebral, your matrix will 'tell you nothing,' (much, anyway) lol, and you end up... like in any other style, 'just composing,' relying upon the ear if not more than the conscious intellect. -- and that boomerangs back to, "If I had wanted a __ there, I would have written one." -- As Mahlerian suggested, "Just Compose," -- and compose and compose and compose. 

Just as "music tells a story" is only analogous, so too are "Music is Math" and "Music / music theory is a science" only analogies.

A certain amount of intellectual rigor is good when it comes to music theory.  Since there is no absolute proof when analyzing any sort of music, if one takes an approach more scientific or mathematical it diverts the purpose of the understanding to be gained.  Becoming rigid and narrowed in obsessively seeking out and examining systems and looking for proofs in an area where nothing is so 97-100% percent fixed or certain is a formula for failure.  Things musical are neither that tidy -- or that facile.  It is called Music Theory for good reason, the definition accurate in not claiming it is either a science or a parallel to maths.


Best regards

P.s.

...but one has to explain why bumping up a tone row while still avoiding octaves usually makes the section much worse, regardless of expertise of the particular piece, and I think the answer is in pitch class reflection...

Stravinsky doubled pitches (octave or greater) often enough in his serial works, and they do not stand out as 'wrong.'  I could imagine some academic could write a short chapter on "How Stravinsky successfully doubled pitches in serial / pitch class music."

Ever bumped up one line of  a Bach chorale (i.e. true, sans adjustments to the key)? Hmm?  Do a true transposition of one line in any piece while leaving the remainder intact, and there is your answer... perfectly good notes in the wrong place at the wrong time, and almost every time.  Tonal or other, transpositions like this are more likely to crash and burn than not.  Regardless of the harmonic vocabulary, the maneuver will of course change the presentation of pitch content, harmony, the works.

[Karl Henning]

Just as "music tells a story" is only analogous, so too are "Music is Math" and "Music / music theory is a science" only analogies.

One of the most important insights I've read at GMG, ever, perhaps.

[jochanaan]

When the Schoenberg quartet was first formed in L.A., the members worked closely with Schoenberg to best understand and render the music.  One member who had 'done his homework' and thoroughly knew and recognized the row in one of the quartets found what he thought was a wrong note -- a B-natural -- in his part.  He pointed it out to Schoenberg and asked, "Shouldn't that be a B-flat?"  -- whereupon Schoenberg instantly and vehemently said, "If I had wanted a B-flat there I would have written one." ~ this is an ideal lesson about serial music, theoretical methodology of any sort when taken to pedantic extremes, and a good one to take to heart.

Your transposition:  basically, dude, you chose "the wrong notes," lol, while there is nothing in theory which could possibly either prove or disprove that.  Without having listened or looked at your altered examples, I'm already convinced the 'problem' with the examples is that altered the personal choices made by the composers which were guided by both their intellect and their ears... i.e. as Mahlerian rightly said, no one can tell you why they're wrong as much as tell you what sounds 'more right.' 

I would think it far more beneficial to use the row from one of those pieces as the basis for a piece of your own, or better, devise your own row, to your liking, and then write an original piece, be it brief or otherwise -- that you consider as 'working on a piece' vs. an exercise.  That is the the surest and quickest way in to your getting truer information on what serial music (or modal, or tonal, or neotonal, etc.) can do and how it behaves.  This is exactly what happens in theory courses, assignments given to write something 'in the style of,' but using only materials freshly invented by the student.

Doing those transpositions seems to show an approach which is somehow near to totally hung up on serial music being a music-theory-composition methodology unlike all the previous methodologies of music from the eras from plainchant up through the Second Viennese school... which it is not.  Put another way, there really is no set methodology about writing any kind of music;  I think people tend to go way over the top about 'method' because that first school of serial music unfortunately became known 'as a method.'  It ain't -- any more than diatonic music is 'a method.'  In making those transpositions, you were a bit guilty of thinking of "the method" as being somehow more relatively arbitrary than the rest of music, i.e. all musical styles are innately somewhat 'arbitrary' while also heavily dependent upon 'sounds not O.K. / O.K. /better / best.

To mistake serial music as a method, either a rigid one of all rules or thinking it allows for such arbitrariness would be taking to heart that egregiously mistaken explanation of serial music as given by Adrian Leverkühn in Thomas Mann's Faustus.  Mann had consulted with Theodor Adorno about serial music, and, well, between what Adorno fed Mann and what Mann then wrote (keeping in mind "If a literary man puts together two words about music, one of them will be wrong." ~ Aaron Copland) -- well, then, Damn Adorno and Damn Thomas Mann.

All the cerebral activity in the world will not get you into really understanding music and how it works: it is through the writing, using your own invented materials, your own tone row, that you will find many an 'answer' to the questions you are asking about serial music.  I can guarantee you that once you are fairly well into such a comp, you will begin to realize that though 'nearly anything might do' (the case when composing anything), for the composer, ultimately there is really only one right choice and decision each point along the way; those choices are not wholly cerebral, your matrix will 'tell you nothing,' (much, anyway) lol, and you end up... like in any other style, 'just composing, relying upon the ear if not more than the conscious intellect.' -- and that boomerangs back to "If I had wanted a __ there, I would have written one." -- As Mahlerian suggested, "Just Compose," -- and compose and compose and compose. 

Just as "music tells a story" is only analogous, so too are "Music is Math" and "Music / music theory is a science" only analogies.

A certain amount of intellectual rigor is good when it comes to music theory.  Since there is no absolute proof when analyzing any sort of music, if one takes an approach more scientific or mathematical it diverts the purpose of understanding to be gained.  Becoming rigid and narrowed in obsessively seeking out and examining systems and looking for proofs in an area where nothing is so 97-100% percent fixed or certain is a formula for failure.  Things musical are neither that tidy -- or that facile.  It is called Music Theory for good reason, the definition accurate in not claiming it is either a science or a parallel to maths.


Best regards

P.s.Stravinsky doubled pitches (octave or greater) often enough in his serial works, and they do not stand out as 'wrong.'  I could imagine some academic could write a short chapter on "How Stravinsky successfully doubled pitches in serial / pitch class music."

Ever bumped up one line of  a Bach chorale (i.e. true, sans adjustments to the key)? Hmm?  Do a true transposition of one line in any piece while leaving the remainder intact, and there is your answer... perfectly good notes in the wrong place at the wrong time, and almost every time.  Tonal or other, transpositions like this are more likely to crash and burn than not.  Regardless of the harmonic vocabulary, the maneuver will of course change the presentation of pitch content, harmony, the works.

+1!

Theory (or hypothesis, if you will) and academic rigor are good to know, because they let us know what others have found out in earlier times.  But the final choices we make when writing (or improvising, which is merely composition without pencil or paper or computer program) usually spring from instinct educated by experience.  And it's different for every musician.  For example, I doubt I could write in every detail like our estimable Karl Henning even if I tried.  What feels right to him might not feel right to me, since we are different people with different experiences and training.  "Right/wrong" just doesn't cover the innumerable choices of note, dynamic, rhythm and tone that go into making music.

[PotashPie]

The 12-tone method wasn't a comprehensive system anyway, especially the harmonic and vertical aspects. For harmonic tension and contrast, I think Schoenberg just did what he thought sounded good. I'm not even sure what this thread is about.

[PotashPie]

...Doing those transpositions seems to show an approach which is somehow near to totally hung up on serial music being a music-theory-composition methodology unlike all the previous methodologies of music from the eras from plainchant up through the Second Viennese School... which it is not.  Put another way, there really is no set methodology about writing any kind of music;  I think people tend to go way over the top about 'method' because that first school of serial music unfortunately became known as 'a method.'  It ain't -- any more than diatonic music is 'a method.'  In making those transpositions, you were a bit guilty of thinking of "the method" as being somehow more relatively arbitrary than the rest of music, i.e. all musical styles are innately somewhat 'arbitrary' while also heavily dependent upon 'sounds not O.K. / O.K. / Better / Best.

It's true that Schoenberg's 12-tone is just a 'method,' but it is not a comprehensive system the way tonality is. Tonality has a lot of principles that are inter-related in a deeper way, like a complete language. Babbitt & George Perle have tried to make serialism more comprehensive.

Just as "music tells a story" is only analogous, so too are "Music is Math" and "Music / music theory is a science" only analogies.

The Greeks considered music to be a part of the quadrivium, as a 'geometry of sound,' and to me, this is part of modernist chromatic thinking.

...A certain amount of intellectual rigor is good when it comes to music theory.  Since there is no absolute proof when analyzing any sort of music, if one takes an approach more scientific or mathematical it diverts the purpose of the understanding to be gained.  Becoming rigid and narrowed in obsessively seeking out and examining systems and looking for proofs in an area where nothing is so 97-100% percent fixed or certain is a formula for failure.  Things musical are neither that tidy -- or that facile.  It is called Music Theory for good reason, the definition accurate in not claiming it is either a science or a parallel to maths.

I think that there are appropriate uses for seeing things mathematically, or geometrically, especially when music has become chromatic, and the principles these 12 notes embody are no longer simply based on sensual phenomena or harmonic considerations like tonality was.

[jochanaan]

It's true that Schoenberg's 12-tone is just a 'method,' but it is not a comprehensive system the way tonality is. Tonality has a lot of principles that are inter-related in a deeper way, like a complete language. Babbitt & George Perle have tried to make serialism more comprehensive.

The Greeks considered music to be a part of the quadrivium, as a 'geometry of sound,' and to me, this is part of modernist chromatic thinking.

I think that there are appropriate uses for seeing things mathematically, or geometrically, especially when music has become chromatic, and the principles these 12 notes embody are no longer simply based on sensual phenomena or harmonic considerations like tonality was.

By that reasoning, we should never have developed equal temperament; we should have stayed with the Pythagorean ratios, which haven't been used in pure form for about 400 years!

[PotashPie]

By that reasoning, we should never have developed equal temperament; we should have stayed with the Pythagorean ratios, which haven't been used in pure form for about 400 years!

I don't know what made you jump to that conclusion!

I said that it's gone the opposite direction, into non-harmonically based ways of thinking ("geometric," I called it).

CP tonality and its scale system are still ostensibly based on harmonic principles, but these are mere vestiges...

The "12-ness" of our ET octave is what drives more modern, post tonal thinking. Symmetry, divisions of 3 & 4, freer modal thinking, etc.

Speaking of "Pythagoran," it is the Pythagoran notion of stacking fifths (yes, I know they were originally 3:2s) that gave us our 12-division octave.

Our present-day ET system's fifths are ONLY 2 cents sharp. Our 12-division octave is definitely biased towards fifths, not thirds, which is where all the tempered tunings came from.

[PotashPie]

I looked at some test cases of 12 tone music, and, still, there is something really bothering me, especially regarding the maxim "good harmony is good counterpoint".

I don't understand how Schoenberg's counterpoint, especially of the kind where one or two instruments play one tone row while one or two other instruments play another, creates a harmony as compelling as classical or romantic harmony.

In Schoenberg, especially in the chorale-like passages, there are cases where one can transpose one tone row within the counterpoint and it still works! The simultaneities then become all different, but it doesn't sound wrong, and actually, the aural affect isn't too different because the shape of the linear lines is the same. Octave simultaneities stick out to the ear as a mistake and need to be avoided, unless they are quick and momentary, but other than that things work out pretty well if one sticks to the tone row. Of course, if the counterpoint involves verticalizing just one tone row, then the simulteneities are more specified, but in more linear tone row contrapuntal cases, it is different.

...If "good harmony is good counterpoint", and it's not obvious to me that the correct versions of these Schoenberg/Webern examples are much better than the incorrect versions, then what makes their style of counterpoint as compelling, interesting, and challenging? Granted, I picked very specific examples of linear tone row structures and very specific row transpositions to make my point (most transpositions don't work), but still, it is worrying to me.

...Still, I am worried about the harmony and counterpoint in itself, within the particular section.

You're talking as if the rows were self-contained lines, and they might not be. In using a row, a composer might do 3 chords, with row notes 1,2,& 3 as the top note of each chord, notes 3,4,& 5 as the second note down, and so on. Or 4 chords, using row notes (bottom up)1-2-3, 4-5-6, 7-8-9, 10-11-12 as the 4 chords. The possibilities are many.

"Harmony" in this early 12-tone music is entirely subject to the whim of the composer, since the 12-tone method was not "codified" as far as harmony.

It sounds to me, the way you've been moving these rows around, that you have some sort of computer music program going, where you can just move things around. You might be moving things around as a "line" that were not put together that way, as I explained above.

[Parsifal]

I don't understand how Schoenberg's counterpoint, especially of the kind where one or two instruments play one tone row while one or two other instruments play another, creates a harmony as compelling as classical or romantic harmony.

Schoenberg's 12-tone method is not guaranteed to create a compelling harmony. Classical harmony is more-or-less guaranteed to create something that doesn't sound ugly, but it doesn't guarantee a compelling harmony either. It is up to the composer to find something compelling within the constraints of whichever system. Clearly the 12-tone system puts a greater burden on the composer to find something beautiful within the constraints of the system.

For me, the proof of Schoenberg's system is not found in a logical or musical argument, but in the music he created using it.