# Myth of Non-Repetition in 12-Tone Music Videos



## Torkelburger

On March 16th I posted the following on this video and it appears to have been deleted. Just goes to show you the intellectual integrity of this fool isn't even half of what he pretends; alas, he has none at all.






You are dead wrong about there being a "rule" that you cannot repeat a note in the series until the other 11 have sounded when composing a piece with the row(s). That is a popular myth, but a myth nonetheless. Not repeating a note ONLY applies to CONSTUCTING THE ROW ITSELF, not when you COMPOSE THE ACTUAL MUSIC. The WIKIPEDIA page has had a paragraph about this on its entry of "TWELVE TONE TECHNIQUE" for at least a decade. It is a shame you've never even take the time to read it. Here it is under the heading "Application in composition",: "Note that rules 1-4 above apply to the construction of the row itself, and not to the interpretation of the row in the composition. (Thus, for example, postulate 2 does not mean, contrary to common belief, that no note in a twelve-tone work can be repeated until all twelve have been sounded.)"

In none of Schoenberg's writings has he ever said the "rule" you are referring to. I have his complete writings in his book "Style and Idea" which contain his two papers where he specifically explains the technique for the first time and there is no such rule. It appears nowhere in the book.
If you had taken the time to analyze his most famous twelve tone works, you would realize this as well. There are multiple examples just on the FIRST PAGES ALONE of the following famous twelve-tone compositions of Schoenberg (the scores are available on youtube posts if you don't have them, just do a youtube search):

The Piano Concerto: The very first note Eb in the right hand is repeated in bar 2 in the left hand only after 7 notes have played. The F in the left hand bar 1 is repeated in the right hand bar 2 after 4 notes have been played. The E in the left hand in bar 1 is repeated in the right hand bar 2 only after 6 notes have been played. Same for the next C, D, and F, and on and on.

Suite for Piano Op. 25: The G in right hand bar 1 is repeated in left hand bar 2 after 6 notes have played. The Cb (B) in bar 1 left hand is repeated in the right hand bar 2 after 9 notes have played. Db in bar 1 is repeated immediately two octaves lower in left hand bar 2. Eb in right hand bar 2 repeated in left hand bar 3 after 9 notes.

String Quartet No. 3: G in bar 1 is repeated in bar 2 in viola after 4 notes have played. E in bar 1 repeats in bar 2 in viola after 4 notes have played. D# in bar 1 repeats in viola in bar 2 after 4 notes have played. And on and on over and over.

Variations for Orchestra: bars 3 through 18 has hundreds of examples where a note is played and reappears before all other 11 have sounded. In very obvious context and would take pages and pages to cite each occurrence. Also note the ostinato pattern of repeated notes in the cello on Variation VIII.
Klavierstuck Op 33: D# bar 5 repeats in bar 6 after 7 notes. B in bar 8 repeats later in the measure after 7 notes. Etc.

String Quartet No. 4: Bar 8 C# in Vln II repeated 2 octaves lower in Viola same bar after 5 notes. Bb in bar 9 is repeated in bar 10 after 9 notes.

String Trio: Multiple examples on page 1 in all 3 instruments.

If you had experience in composing twelve tone music, you would understand that the mythic "rule" you are quoting doesn't make practical sense in composition. If you couldn't repeat a note until the other 11 were sounded, then you would never be able to use the other 47 transpositions/forms of the row. This is because the notes change order with each transposition/form you use. So any note will ALWAYS be earlier or later when a different transposition is selected (and if later, then another note will be earlier). It cannot be done.

Also, if you had any experience when composing this kind of music, you would understand there are two and only two methods of composing. In any given texture, you can use the notes from the same row (Method A), or use the notes from two or more rows simultaneously (Method B). So if you had a melody and chords/accompaniment together, you could use the same row for all the notes (A), or use one row for the melody and another row for the chords/accompaniment (B). Those are your only choices. In Method B, notes will repeat before the other 11 have sounded. That's the only way it can be done. This is what happens in instances such as Schoenberg's Piano Concerto. He is using a row for the right hand melody (prime), and another row for the accompaniment left hand (retrograde inversion). That's why the notes repeat in this instance. Other times, he is using a technique called "segmentation" where the row is divided up into equal parts and say the first four notes are used as an ostinato figure and so are repeated while another segment of the row is the melody. This is like the String Quartet No. 3 example.

For Method A, you would need to write very short pieces and use the vertical-horizontal method of assigning notes. That is too detailed to go into here, but that is what Webern did in a couple pieces. It is a very limited technique. Also, it doesn't work in solo pieces where an instrument can only play 1 note. In that case, all you would have is an isomelody if they followed your silly "rule" because it would be the same notes over and over again in the same order throughout the piece. But professional serial composers don't do that (see Krenek's solo cello pieces). Also, it gives the piece the sound of randomness (random notes playing). Being able to repeat notes as shape and cohesion to the music as well as give the music identity.

If you have intellectual integrity, you would post another video correcting this error. This kind of mis-information on the internet which appears to come from a reliable source is a huge problem and hurts the reputation of twelve tone music. These types of false rules gives the music the appearance of being rigid and academic when that is not the case at all. The row can actually be manipulated to suit various musical purposes (see Reginald Smith Brindle's text).

_______________________

I also posted this in the following videos with similar results, although not deleted (since there is so much text, I broke up the message into 6 different posts, and they are spread out for some reason in the threads):


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## Woodduck

Very impressive. He's probably still having dodecaphonic nightmares.


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## millionrainbows

> Not repeating a note ONLY applies to CONSTUCTING THE ROW ITSELF, not when you COMPOSE THE ACTUAL MUSIC.


I think you are conflating "tone rows" with "scales." Scales are unordered sets. A tone row is an _ordered set_, as I recall.

If you use "unordered" tone rows, aren't these called "tropes?" Then you are composing like Hauer, not Schoenberg.

"Constructing a row" involves placing the notes in a certain ORDER. You don't talk about "order" and its implications, do you? 
Talk about it now.


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## millionrainbows

Answer the question, please. If "order doesn't matter" as you are saying, then what does "order" do? I think you're out of your depth. You should leave 12-tone theory to the experts.


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## Torkelburger

millionrainbows said:


> Answer the question, please. If "order doesn't matter" as you are saying, then what does "order" do? I think you're out of your depth. You should leave 12-tone theory to the experts.


Sigh. This has absolutely, positively, nothing to do with what I said. I never said "order doesn't matter". Yes, a tone row is an ordered set. I agree. Yes, "constructing a row" involves placing notes in a certain order. I agree. That's what I'm conceding and talking about in my post.

There are two things I am talking about but you are combining them into one.

1) A composer constructs the row he wants to compose the piece with. That is the first thing I am talking about where pitches do not repeat in the order. There is only one pitch class per 12 notes available in a tone row.

2) THEN, the composer composes the piece with the row he has constructed. This is the second thing I am talking about where pitches CAN repeat in the music he writes. And not just A-A-A-A. You can write A-Bb-A, or A-B-C-A-B-C, etc. This is what the SCORES show, it's not just me saying it. Music Matters said you can't do this. He is wrong.

Please stop wasting my time by mis-reading what I write. You are way too much over-thinking EVERYTHING with your mental gymnastics and can't even comprehend simple English because of it. Get out of your head!

And stop flattering yourself. You are NO EXPERT.


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## millionrainbows

Torkelburger said:


> Sigh. This has absolutely, positively, nothing to do with what I said. I never said "order doesn't matter". Yes, a tone row is an ordered set. I agree. Yes, "constructing a row" involves placing notes in a certain order. I agree. That's what I'm conceding and talking about in my post.
> 
> There are two things I am talking about but you are combining them into one.
> 
> 1) A composer constructs the row he wants to compose the piece with. That is the first thing I am talking about where pitches do not repeat in the order. There is only one pitch class per 12 notes available in a tone row.
> 
> 2) THEN, the composer composes the piece with the row he has constructed. This is the second thing I am talking about where pitches CAN repeat in the music he writes. And not just A-A-A-A. You can write A-Bb-A, or A-B-C-A-B-C, etc. This is what the SCORES show, it's not just me saying it. Music Matters said you can't do this. He is wrong.
> 
> *Please stop wasting my time by mis-reading what I write. You are way too much over-thinking EVERYTHING with your mental gymnastics and can't even comprehend simple English because of it. Get out of your head!
> *
> And stop flattering yourself. You are NO EXPERT.


You need to do some more explaining, then, if you want to present a convincing point. And this still leaves a lot unexplained. For example,
_
"There is only one pitch class per 12 notes available in a tone row" _does not explain much, because "pitch" per se is not the crucial issue in tone rows. A tone row can be transposed 12 times, so a "key" doesn't exist.

When you say _A-B-C-A-B-C, _you are using a fragment from the row, but this could just as easily be A#-B#-C#, B-C#-D#, C-D-E, C#-D#-E#, D-E-F#, Eb-F-F, E-F#-G#, F-G-A, F#-G#-A#, G-A-B, or G#-A#-B#.
Intervallic relations is the issue, not pitches.


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## Torkelburger

millionrainbows said:


> Who are you referring to?


He/she is referring to me. He/she is saying my comments were rude and mean-spirited in tone so Music Matters probably deleted them without even reading their content.


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## millionrainbows

Torkelburger said:


> He/she is referring to me. He/she is saying my comments were rude and mean-spirited in tone so Music Matters probably deleted them without even reading their content.


I thought she may have been talking about your replies to me.

When the guy in the video says "Schoenberg and the Second Viennese School were only serializing pitch," this is misleading. A tone row is not about pitch, it's about intervallic relations between pitches.


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## millionrainbows

Let's chat about tone rows.

The most "boring" tone row would be C-C#-D-D#-E-F-F#-G-G#-A-A#-B.

Why? Because of the order? No, _because of the way the order creates interval relations._ In this case, all the intervals are m2s.

What would be another "boring" tone row?

F-C-G-D-A-E-B-F#-C#-G#-D#-A#. Why? Because of the order? No, _because of the way the order creates interval relations._ In this case, all the intervals are fifths.

This is why Milton Babbitt, Elliott Carter, and George Perle were all interested in what are called "all-interval" rows (or sets).


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## Torkelburger

millionrainbows said:


> I thought she may have been talking about your replies to me.
> 
> When the guy in the video says "Schoenberg and the Second Viennese School were only serializing pitch," this is misleading. A tone row is not about pitch, it's about intervallic relations between pitches.


I agree. Yes, I think most people understand that when creating a tone row and discussing dodecaphonic music. But you can't have intervals without pitches. A fifth won't exist without the two pitches to define it. It can also be about tonal or atonal relations as well. Do these 4 notes denote a key? For example. Do these 3 notes denote a triad? But yes, you are right. In atonal music, expression is achieved through intervals, both vertically and horizontally. There are weaker intervals, stronger intervals, and neutral intervals. All on a spectrum and these must be controlled very carefully when composing atonal music.
I think what he was referring to was that it wasn't "Total Serialism" in which rhythm and dynamics and articulation were also assigned a number in a series of 12 and selected for use in the piece somewhat automatically by some kind of formula or mechanism.

"Serializing pitch" is somewhat accurate, though. To serialize something literally means to put it in an order. You are literally assigning something a number in a series (of things that are the same). That's what it means. Like the serial numbers on products we buy at the store. Yes, one considers what intervals they create when you choose your pitches, though, so you are correct.

When composing with the row, however, one must be aware of the intervals one is creating both horizontally and vertically. You can't just assign notes automatically and let the chips fall where they may.

The relations between the pitches will change from how they were originally in the row. If you have 3 planes of tone, for example and are assigning pitches, the horizontal-vertical method will change the relation of how one note sounds after the other. So will the segmentation method. Using the two rows simultaneously method may require manipulation of the order or the rhythm to get across your musical ideas.

Brindle's text is excellent in explaining this. I highly recommend it if you are interested in writing 12-tone music. In it he shows how one row yields two different expressive emotions in a two-voice texture. In one case, he had two versions of a piece that didn't change the order of the series, rather he manipulated the rhythm in each voice to create the intervals he needed to convey what you want--one tranquil, the other more vibrant. He does however, give examples of row order manipulation and note omission to achieve similar goals. By far the best book.

So my point is, in real-life application, the intervallic relations in the design of the row are rarely maintained in the composition of the piece.


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## Torkelburger

> What would be another "boring" tone row?
> 
> F-C-G-D-A-E-B-F#-C#-G#-D#-A#. Why? Because of the order? No, _because of the way the order creates interval relations._ In this case, all the intervals are fifths.


Well, I wrote a piece once doing just that. A lot of people liked it. I don't write anything remotely like this anymore, of course, I think I've matured a lot. But here is a recording for academic purposes. I still kind of like it, though. Not TOO bad for a 20 year old (I was a couple months away from turning 21 at the time). Not as bad as you make it out to be.








> This is why Milton Babbitt, Elliott Carter, and George Perle were all interested in what are called "all-interval" rows (or sets).


Yes, I love them! Especially Babbitt.


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## millionrainbows

That's a very good composition, and real good players. _Thanks_ for posting that, Mr. Torkelson. I realize it's taking a chance to post your own music, that's why I don't do it much. You have my unspoken respect from here on out, for what it's worth.


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## Phil loves classical

Yes, I've wondered about that, and have seen notes repeated. But as I understand they are usually through the overlapping use of rows or their transformations, or else it runs the risk of being more free atonal rather than dodecaphonic.


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## Torkelburger

Thanks, million!

Also, to pick your brain, what is your opinion on Berg's Violin Concerto row? It is 8 notes in thirds (though a mixture of major and minor) and then 4 notes in whole tone scale. I'm not defending it, just wondered if you thought it was boring. Berg is my least favorite of the 2nd Viennese. I do actually however, like Walton's Second Symphony third movement which uses a row almost identical. Amazing how you can get different results from similar material. Walton really exploits the tonal sound of it, though. But I love it.

Also, to pick your brain further on the intervallic relations in a tone row, I know that it is said it doesn't matter which octave you write your notes down in when designing the row. Like if you had a C and then wanted an Ab so you wrote it a major third below. But it wouldn't make any difference if you wrote the Ab an octave higher to make a minor sixth with the preceding C, would it? The relationship is still the same I believe? You would have to change pitch classes to change the interval right? Just making conversation and getting your explanation.


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## millionrainbows

Torkelburger said:


> Thanks, million!
> 
> Also, to pick your brain further on the intervallic relations in a tone row, I know that it is said it doesn't matter which octave you write your notes down in when designing the row. Like if you had a C and then wanted an Ab so you wrote it a major third below. But it wouldn't make any difference if you wrote the Ab an octave higher to make a minor sixth with the preceding C, would it? The relationship is still the same I believe? You would have to change pitch classes to change the interval right? Just making conversation and getting your explanation.


I'll reply to the second section of your post first (retrograde :lol.

As I understand it, there are really no "inversions" of intervals in serial music. There are only six intervals: the m2, M2, m3, M3, P4, and tritone. 
The rest are (tonal) inversions, C _up_ to C#(m2) = C _down_ to C#(M7), its inversion, C up to D (M2) =C down to D (m7), and so on. The C-F (P4) is invertible to a P5). The tritone is invertible onto itself, with no change. So tonal inversions don't count as being "equivalent" to each other. This "inversional equivalence" only works in tonality.

Thus, our tonal chord inversion is also different: in tonality, CEG=EGC=GCE, and all are C major triads because of inversion identity. 
In serial terms, inversions are literal quantities (intervallic distances, not identities in relation to a "1" tonic). Thus, if we invert a CEG (M3+M3) in serialism, it becomes (going counterclockwise on the chromatic circle or number line) C-Ab F. This yields an F minor (in tonal terms).

As to your example, if you write C, then _down_ (counterclockwise) to Ab, you have written a quantity: -4.

If you write C _up _to Ab, you have written a different quantity: +8. You shouldn't confuse _note identity_ (C up or down to Ab) with _intervallic quantity.
_


Torkelburger said:


> Also, to pick your brain, what is your opinion on Berg's Violin Concerto row? It is 8 notes in thirds (though a mixture of major and minor) and then 4 notes in whole tone scale. I'm not defending it, just wondered if you thought it was boring. Berg is my least favorite of the 2nd Viennese. I do actually however, like Walton's Second Symphony third movement which uses a row almost identical. Amazing how you can get different results from similar material. Walton really exploits the tonal sound of it, though. But I love it.


I was thinking about this yesterday. From my post #11 in "What is a Diatonic Scale?" I said: The CP system is built for root movement in fifths (clockwise) and fourths (counterclockwise). This yield the complete chromatic collection.
_
There are only two intervals which, when projected (or "stacked") produce the entire chromatic scale before repeating: the fifth (and its other-direction inversion, the fourth) and the minor second.

Thus, the CP system is built on progressions of fifths/fourths, not chromatics.

Postulate 1: The interval-distance of a fifth is 7 semitones; a fourth is 5 semitones. 

Postulate 2: 12 (the chromatic collection within an octave) is divisible by 7 only when we reach 7x12=84. Similarly, 5x12=60. Both 84 and 60 lie well-outside the bounds of 12; they are the result of outward travel "outside" the octave.

Postulate 3: The minor second interval distance is 1, and 1x12=12. this interval stays "within" the octave, is recursive within an octave.

Postulate 4: Therefore, CP's "chromatic" nature is arrived at via the fifth/fourth, and is thus not "truly" chromatic as a "real" chromatic minor second is.

The "CP chromatic collection" will still use diatonic principles: one example is that it will "divide" the octave at the fifth, not the tritone. For true chromaticism, the tritone is the true dividing point of the octave (6+6=12).

_Then it occurred to me: more "modern" root movement, like the transition sections of Beethoven's Ninth, use major and minor third root movement. If you "add these up", you can still get your "chromatic 12": M3 (4 semitones) x3=12 (4x3), and m3 (3 semitones) x4= equals 12 (3x4). You've covered the entire 12-note octave with 3 or 4 root movements.

If you alternate M3s and m3s, the cycle becomes 7 (4+3), equal to a fifth (seven semitones), so you can once again cycle into 84.

Major thirds are related to whole tone scales (Liszt) (and augmented sevenths), while minor thirds are related to diminished sevenths (Wagner).

Berg's violin Concerto row is G-Bb-D-F#-A-C-E-G#-*B-C#-Eb-F*, the last four notes being from the whole tone scale. And I learned this from Beethoven's Ninth: root movement in thirds also "outlines" chords. The G-Bb-D could be root movement, or a G minor triad. Also, all the "in between" triads: G-Bb-D (G minor), Bb-D-F (Bb aug), D-F#-A (D major), F#-A-C (F# dim), A-C-E (A minor), C-E-G# (C aug), E-G#-B (E major), then the WT notes.

There are only two whole tone scales in the chromatic collection, so these can be used as "chromatic portals" (like Debussy did) into adjacent harmonic areas. Each WT scale has a tritone, so there can be a "dominant" relation created if it sounds as b7-3, or a dissonant 1-tritone sound.

BTW, I will check on the Walton.


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## millionrainbows

I think the difference between using _maximum_ variety in tone rows (as in all-interval rows) and what I called "boring" rows (as used in Torkelberger's composition) is a matter of aesthetics.

If the row is "all-interval," there will be _maximum_ variety in the intervals and the music will, as a result, sound more chromatic and less harmonic.

If the intervals of the row are all fifths, or have a predominance of thirds (as in Berg's Violin Concerto), then there will be less chromaticism and more harmonic effect.

I think this is what Pierre was complaining about when he declared that _"Schoenberg est morte." _He was complaining that the Second Viennese School did not use the 12-tone system to exploit its own inherent nature, which is chromatic, not tonal.

Notice that Milton Babbitt and Elliott Carter were both interested in these "all-interval rows" and that the resulting music is definitely "hard-core" serialism, very chromatic.


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