# Serialism, explanation thread



## ZJovicic (Feb 26, 2017)

OK, we are discussing serialism in several threads already, but it's just exchange of opinions...
I'd like to have a thread in which those who really understand it and are knowledgeable about it could explain it to others who would like to learn but don't truly understand it, hopefully in a clear and simple way.

So, I'll start with my first question. How exactly tone rows work?

Do they use just one tone row in a work, or more of them?

Example: if we represent 12 tones with symbols 1,2,3,4,5,6,7,8,9,0,A and B this would be one tone row:

7 4 0 2 5 A 3 1 B 9 6 8

Now what comes after this? Do they need to repeat this same row over and over again throughout the work or they can make a new one, as long as there's no repetition of the same tone twice in a single row.

Could there come now this, after the first row?

5 A 9 4 6 0 B 1 7 3 8 2

If it's just one tone row repeating over and over again in the whole work (even with different rhythms), is it similar to minimalism in a way? It would be kind of repetitive (in theory) though *when I listen to 12 tone works I don't notice any repetitiveness at all, quite the contrary*. I mean basing entire work on just one 12 tone row, seems rather limiting to me, and many tonal melodies are much longer.


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## Phil loves classical (Feb 8, 2017)

Check this out

http://www.carolingianrealm.info/Music.php?MusicID=29

These follow the same transformations Bach had used.


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## ZJovicic (Feb 26, 2017)

Phil loves classical said:


> Check this out
> 
> http://www.carolingianrealm.info/Music.php?MusicID=29
> 
> These follow the same transformations Bach had used.


This is very interesting, thanks!


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## Room2201974 (Jan 23, 2018)

Absolute elsewhere in the stones of your mind.


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## janxharris (May 24, 2010)

Room2201974 said:


> Absolute elsewhere in the stones of your mind.


?
..................................


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## janxharris (May 24, 2010)

Phil loves classical said:


> Check this out
> 
> http://www.carolingianrealm.info/Music.php?MusicID=29
> 
> These follow the same transformations Bach had used.


Kind of makes one realise how such music might end up sounding inhuman.


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## ZJovicic (Feb 26, 2017)

> Kind of makes one realise how such music might end up sounding inhuman.


Yes, perhaps it's a bit too algorithmic, like once you have come up with initial row, doesn't leave too much freedom to you afterwards.


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## janxharris (May 24, 2010)

ZJovicic said:


> Yes, perhaps it's a bit too algorithmic, like once you have come up with initial row, doesn't leave too much freedom to you afterwards.


Interestingly, R. Strauss employs a 12-tone row in the melody of the 'Of Science' section of Also Sprach Zarathustra:


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## calvinpv (Apr 20, 2015)

My understanding of serialism is pretty limited and I haven't analyzed any works in detail. But to answer your question using your example: there are many things I can do after introducing your tone row (which is called the prime form). 

I can reverse the order of the row, giving us 8 6 9 B 1 3 A 5 2 0 4 7 (called retrograde form). 

I can do something called inversion (which, unfortunately, I can't represent without knowing which sequence of notes corresponds to your sequence of numbers in the prime form, as inversion is based on the size of intervals between successive notes. So, for example, if my prime form tone row is the rather boring chromatic scale C C# D Eb E F F# G G# A Bb B, you can see that the interval of a minor second separates each successive note. Well, just flip each minor second in the other direction to get C B Bb A G# G F# F E Eb D C#).

I can also invert the retrograde form.

I can also transpose any of these four basic forms up and down the keyboard while preserving the interval relationships between successive notes. As you can probably see, the number of possible tones rows just exploded.

And there is nothing stopping us from introducing several of these tone rows at once or from repeating a certain tone row over and over. Nor is there anything stopping us from having multiple basic prime form rows in a piece from which we make our transformations. For example, I can have the chromatic scale above as one prime form and, say, Bb G G# C Eb F A B E D C# F# as another prime form row and do all sorts of magic with them. And both of these would, indeed, be prime in this case because no matter how much you retrograde, invert, or transpose the chromatic scale prime form, you will NOT be able to derive Bb G G# C Eb F A B E D C# F# (to use a mathematical term, this prime form and the chromatic scale prime form belong to separate "equivalence classes").

So long as you adhere to the basic idea that, to avoid any semblance of tonality, no note can be repeated, then the possibilities are endless. And finally, it's not like the rules of serialism are written in stone or were handed down to us from above as a set of commandments. You can break the rules however you want (listen to Schoenberg's late works, for example; you can clearly hear occasional moments of tonality). The only reason these rules exist is that they're easily the most EFFECTIVE means of avoiding tonality, if that's your intention when writing music.


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## Eschbeg (Jul 25, 2012)

ZJovicic said:


> Do they use just one tone row in a work, or more of them?
> 
> Now what comes after this? Do they need to repeat this same row over and over again throughout the work or they can make a new one, as long as there's no repetition of the same tone twice in a single row.


The answer to these questions, and to just about any other question regarding the "rules" of 12-tone music, is that it depends on the composer and piece. Sometimes a work is construcuted on a single tone row, sometimes on a single tone row plus its derivations (as explained in the link that *Phil loves classical* posted), and sometimes on more than one row.

More generally, the "rules" of 12-tone music are really nothing of the sort; they are more like guidelines. Composers "break" the rules all the time if it suits their purposes. Despite the common perception that pitches of a tone row are not to be repeated until all the remaining pitches of the row are heard, you can find countless exceptions in Schoenberg and the gang.

An interesting case is Milton Babbitt's Composition for Four Instruments: each instrument has its own tone row that is different from the rows of the other instruments (i.e. the clarinet's row is not a derivation of the violin's row, etc.). On the other hand, each of the four tone rows is a slightly complex derivation of a "master row." (I say "slightly complex" because the four instruments' rows, while they are indeed derivations of the master row, are not related to the master row via the usual methods of derivation. Babbitt found another way to derive one row from another without relying on the standard methods of transposition, retrograde, inversion, and retrograde inversions.) Thus the "master row," even though it is ultimately the source of the entire pitch content of the work, is heard only once, at the very end of the work. This technique also has the result that each instrument is contributing to two tone rows at once: its own assigned row and the master row.

On the other end of the spectrum is Berg's Violin Concerto, which does feature a tone row but also features passages that are "merely" atonal, as well as passages that are entirely tonal. Nor are these passages mutually exclusive: some of the tonal passages are also 12-tone passages. (The tone row of this work is cleverly constructed to have tonal properties.)



ZJovicic said:


> If it's just one tone row repeating over and over again in the whole work (even with different rhythms), is it similar to minimalism in a way?


Not really. Just because a composer is cycling through the same sequence of twelve pitches doesn't mean he or she has to do so the same way per cycle. Suppose, for example, that in one measure I play each note of the tone row, one after the other; then in the next measure I play two chords in succession, the first chord consisting of the first five notes of the tone row and the second chord consisting of the next seven notes. The two measures will sound nothing alike, even though they consist of the same sequence of twelve notes.



ZJovicic said:


> It would be kind of repetitive (in theory) though *when I listen to 12 tone works I don't notice any repetitiveness at all, quite the contrary*.


Exactly. A 12-tone piece will only sound as repetitive as the composer wants it to sound. If you're not aware that a work is constructed on a tone row, it may not even strike you as a 12-tone work at all, let alone a repetitive one. Even for the most seasoned listeners, telling the difference between a freely atonal work and a 12-tone one can be quite difficult; from a listening perspective, a tone row can sometimes be basically irrelevant. (As always, there are exceptions. Webern was especially adept at designing tone rows whose arcanely complex properties are somewhat audible, or at least inferable, just by listening.)


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## Phil loves classical (Feb 8, 2017)

janxharris said:


> Kind of makes one realise how such music might end up sounding inhuman.


True, but you can even arrange the row to make it sound more tonal. I actually did it in one piece. It's not that hard.


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## janxharris (May 24, 2010)

Phil loves classical said:


> True, but you can even arrange the row to make it sound more tonal. I actually did it in one piece. It's not that hard.


But if the premise is the avoidance of tonality, then shouldn't we at least be just a little sceptical? Rather, shouldn't composers avoid deliberately excluding such possibilities?


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## Room2201974 (Jan 23, 2018)

Phil loves classical said:


> True, but you can even arrange the row to make it sound more tonal. I actually did it in one piece. It's not that hard.


Yes, you can do that, you can do anything you want. Rules are made to be broken. However, if you imply tonality in a tone row, your 12 notes are no longer equal! When we wrote tone rows in 20th Century Theory and Composition, our professor always downgraded us for implied tonality in a tone row.


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## janxharris (May 24, 2010)

Room2201974 said:


> Yes, you can do that, you can do anything you want. Rules are made to be broken. However, if you imply tonality in a tone row, your 12 notes are no longer equal! When we wrote tone rows in 20th Century Theory and Composition, our professor always downgraded us for implied tonality in a tone row.


Why do you think your professor considered even a hint of tonality as something lesser than atonality?


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## Room2201974 (Jan 23, 2018)

janxharris said:


> Why do you think your professor considered even a hint of tonality as something lesser than atonality?


12 tone says that all tones are equal in the tone row. When you imply tonality you no longer have that. If I write 12 tones and my last three notes are C E G, then I've just made C the most important note in the row.


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## Phil loves classical (Feb 8, 2017)

janxharris said:


> But if the premise is the avoidance of tonality, then shouldn't we at least be just a little sceptical? Rather, shouldn't composers avoid deliberately excluding such possibilities?


You can have tonal implications without really having a clear centre, still sound floating with more tonic freedom, and greater coherence. Berg's violin concerto was like that, which not surprisingly is probably the most popular 12 tone work.

On other hand you can have a tonal work with weak tonality like Prokofiev's Sonatas 6 and 8. At some point i would imagine, they intersect


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## Torkelburger (Jan 14, 2014)

ZJovicic said:


> OK, we are discussing serialism in several threads already, but it's just exchange of opinions...
> I'd like to have a thread in which those who really understand it and are knowledgeable about it could explain it to others who would like to learn but don't truly understand it, hopefully in a clear and simple way.
> 
> So, I'll start with my first question. How exactly tone rows work?
> ...


Your question is based on a very common misunderstanding of twelve-tone technique. Some authors call it "The Myth of Non-Repetition". The rule is that when you construct the row, you do not repeat a tone, so you end up with twelve different tones. It does NOT apply to the act of composition with the tones. You may repeat a tone or group of tones when composing with the row.

Wikipedia explains it here:
https://en.wikipedia.org/wiki/Twelve-tone_technique
scroll down to "Application in Composition" where it states: "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.)"

You'll also see in the Op. 23 from the same webpage an example of the Ab repeating.

Also look throughout this entire twelve-tone piece by Schoenberg (a masterpiece in the genre), and note the repeated notes.


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## millionrainbows (Jun 23, 2012)

There is an important idea that needs to be understood.

1) A tone row is not a series of specific pitches; it is a series of intervals, creating a template of intervallic relationships. Thus, using your matrix, a tone row can be transposed in 12 different ways, but these are all based on the same series of intervals: a fourth, a third, major seventh, etc.

Thus, in listening to twelve-tone music, unlike tonality, you need to find meaning in the intervals, not in the melodic pitches. This implies an "expanded" way of listening for relationships, not single pitches. You can do this with Webern to begin with. They're short, and easier to hear because of the thin textures.



ZJovicic said:


> Example: if we represent 12 tones with symbols 1,2,3,4,5,6,7,8,9,0,A and B this would be one tone row:
> 
> 7 4 0 2 5 A 3 1 B 9 6 8
> 
> ...


You're stuck on listening to specific pitches, as in tonal listening. You need to be seeking out "deeper" relationships which exist only relatively, and this is more difficult.

Do you know your intervals? Can you name them, and know them when you hear them? Do intervals mean "anything" to you, as separate entities? If not, you are facing more of the same "incomprehensibility."


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## Torkelburger (Jan 14, 2014)

> Do they use just one tone row in a work, or more of them?


Short works might just use one form of the row, most works however use the original row along with several forms of transformation (prime (the original transposed), inversion, retrograde, retrograde-inversion).



> Now what comes after this?


After a row is used, it is possible to then use any of the 48 available row forms related to the original row (prime, inversion, retrograde, retrograde-inversion). Different composers use different methods on how to select the next row to use. Myself and Stravinsky will take the very last note of the row used, and have it become the very first note of the next row used.



> Do they need to repeat this same row over and over again throughout the work or they can make a new one, as long as there's no repetition of the same tone twice in a single row.


You don't repeat the same row over and over again. You use different row forms (all related to the original), you use other primes (transposed), inversions, retrogrades, and retrograde-inversions. It's perfectly fine to have a note repeat as follows: one row ends with say, ....Bb A C and then the next row you use begins with Db A G....As long as you follow rules such as not sounding the A's together an octave or more apart, or "hidden" octaves of sounding the A immediately in one voice after it just completed sounding in another, etc.



> Could there come now this, after the first row?


For cohesion and intelligibility, it is best to not devise new rows within a composition but instead utilize the 48 row forms available.


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## ZJovicic (Feb 26, 2017)

Torkelburger said:


> Your question is based on a very common misunderstanding of twelve-tone technique. Some authors call it "The Myth of Non-Repetition". The rule is that when you construct the row, you do not repeat a tone, so you end up with twelve different tones. It does NOT apply to the act of composition with the tones. You may repeat a tone or group of tones when composing with the row.
> 
> Wikipedia explains it here:
> https://en.wikipedia.org/wiki/Twelve-tone_technique
> scroll down to "Application in Composition" where it states: "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.)"


Thanks for explaining this. I indeed believed in this Myth of Non-Repetition, but I sometimes noticed while listening that it's not really the case, and so I was confused.


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## ZJovicic (Feb 26, 2017)

> You're stuck on listening to specific pitches, as in tonal listening. You need to be seeking out "deeper" relationships which exist only relatively, and this is more difficult.
> 
> Do you know your intervals? Can you name them, and know them when you hear them? Do intervals mean "anything" to you, as separate entities? If not, you are facing more of the same "incomprehensibility."


I know what intervals are and I can feel them, but I haven't ever studied them or went through drills for their recognition.


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## ZJovicic (Feb 26, 2017)

@ Torkelburger... thanks for all explanations.


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## arpeggio (Oct 4, 2012)

These have been posted before. The Bernstein lecture is one of the best explanations of twelve tone music I have ever seen.





















Note: The _Theme and Variations, op.43_ mentioned in part three is Schoenberg's only work for concert band.

Schirmer Publishing in New York commissioned _The Theme and Variations for Full Band, Op. 43._

Schoenberg originally intended the work for high school of college bands as an educational work. Even while the piece was still being written, it soon became clear that the complexity of Schönberg's setting could possibly exceed the technical capabilities of most American wind bands. So, he make a version for symphony orchestra.

(Note: High school and college bands are so much better today. A few years ago I heard the Robinson High School Band in Fairfax County perform it.)

The orchestral Op. 43b had its world premiere in Boston with Serge Koussevitsky conducting the Boston Symphony Orchestra on October 20, 1944. The wind band version had to wait several years for its own premiere with New York-based Goldman Band on June 27, 1946 in New York.


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## Machiavel (Apr 12, 2010)

This. Simple explanation


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