# Chords In Twelve-Tone Music?



## Guest (Jan 28, 2014)

So, I should preface this by saying I have pretty damn limited knowledge in the music theory department (and in the musicianship department, for that matter), so it's a little insane for me to even be posting this. 

Anywho, I found myself reading about the twelve-tone technique today, and a couple hours later ended up constructing a pretty rudimentary all-interval tone row.

However, while I think I generally grasp the construction of the tone row, I didn't see any information (at least on the wikipedia article) about how chords are constructed in twelve-tone music, as the article seemed to focus mainly on the tone row and its various permutations. 

Can anyone shed some light on this subject? Maybe without even being too condescending? Would be greatly appreciated


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## Mahlerian (Nov 27, 2012)

Chords are generally taken from the notes that are not currently in use in melodic lines, so that there are no duplications. Early on, this was followed more or less strictly, but this limitation quickly relaxed because having no octave doublings invariably produces an astringent sound.

You can take your tone row and have part of it show up in a chord form while the rest appears above, and there is no necessity to run through all of the notes in the row in a single line, so long as they appear somewhere in the texture (register is irrelevant). Schoenberg breaks up his tone rows constantly, while Stravinsky usually keeps them intact.


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## Guest (Jan 28, 2014)

So, I'm going to sum up my understanding of what you just said in a very cavemanesque way. 

Are you saying that instead of playing 0-1-2-3-4-5-6-7-8-9-10-11, perhaps play 0 and 6 as a chord, 1 and 7 as a chord, and so on? Sorry if that's a confusing way to say it.

Edit: ^ as long as no pitch occurs twice, I assume.


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## Mahlerian (Nov 27, 2012)

arcaneholocaust said:


> So, I'm going to sum up my understanding of what you just said in a very cavemanesque way.
> 
> Are you saying that instead of playing 0-1-2-3-4-5-6-7-8-9-10-11, perhaps play 0 and 6 as a chord, 1 and 7 as a chord, and so on? Sorry if that's a confusing way to say it.


If the melody consists of 2-3-4-5-8, sure, that's eminently possible.

At a different point, you can use the melody 0-3-5-6-7, and accompany it with 1-2 followed by 4-8-9.

And remember that 0 can be any note, so long as the intervals following are the same as the original row.


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## Guest (Jan 28, 2014)

Sounds "fairly" doable. Thank you!


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## Mahlerian (Nov 27, 2012)

The beginning of the Largo from the Fourth Quartet (here page 63) gives a good indication of one way to use the row.

http://imslp.org/wiki/String_Quartet_No.4,_Op.37_(Schoenberg,_Arnold)

The theme is constructed, unharmonized, from this:
C-B-G-Af-Ef-Df-D-Bf-Gf-F-E-A

Next, it is broken up between all four instruments, but the intervals still appear in the correct order, viz.:
Af-Df-C-B-G-D#-E-D-A-Bf-Gf-F
which is the retrograde inversion beginning on A-flat.

The viola's repeating C-B is not in violation of the rules, even though other notes are introduced in the mean time, because it eventually comes to stop on the second of these notes.


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## Guest (Jan 29, 2014)

I have another question, if it's not too much trouble.

The tone row I initially came up with had a sort of symmetry to it that results in the retrograde and the inversion being nearly identical, thus limiting the possibilities of permutations quite a bit.

My question is: do the rules of serialism perhaps allow the composer to apply permutations to only *segments* of the tone row? Say, treating the first 6 notes and the last 6 notes as separate rows for the purpose of more diverse inversions, etc? If not, I'll make do


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## Mahlerian (Nov 27, 2012)

arcaneholocaust said:


> My question is: do the rules of serialism perhaps allow the composer to apply permutations to only *segments* of the tone row? Say, treating the first 6 notes and the last 6 notes as separate rows for the purpose of more diverse inversions, etc? If not, I'll make do


Do whatever you want, whether or not it follows the rules strictly. The purpose of an all-interval row is to have as much symmetry as possible, so possibly you'll want to create something different.

Why don't you start trying to come up with ideas for the music before constructing a row, and then create a row based on that, if you're having trouble?


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## arpeggio (Oct 4, 2012)

Mahlerian said:


> Do whatever you want, whether or not it follows the rules strictly. The purpose of an all-interval row is to have as much symmetry as possible, so possibly you'll want to create something different.
> 
> Why don't you start trying to come up with ideas for the music before constructing a row, and then create a row based on that, if you're having trouble?


Did not Roger Sessions do this?


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## Mahlerian (Nov 27, 2012)

arpeggio said:


> Did not Roger Sessions do this?


Sorry, which part are you referring to?


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## arpeggio (Oct 4, 2012)

Mahlerian said:


> Sorry, which part are you referring to?


Creating a tone row after he came up with his themes.


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## Mahlerian (Nov 27, 2012)

arpeggio said:


> Creating a tone row after he came up with his themes.


Oh, right. Yeah, Schoenberg (usually) and Sessions both worked that way. Berg and Webern tended to create their tone rows based on what they thought they might want to get out of them.


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## millionrainbows (Jun 23, 2012)

C A F# G# B C# A# D E F G D#
E C A# B D E# C# G G# A D# A 
G E C# D# F G# E# A B  C A# D

You could use three rows, making sure they create chords vertically.

This is why Elliott Carter, Milton Babbitt, and George Perle were interested in certain kinds of rows, or sets, for their combinatoriality and other symmetry characteristics. 

An all-interval set, for example, would contain all six interval types: m2, M2, m3, M3, P4 and tritone. This set would be (0, 1, 4, 6), if I recall correctly; or (0, 1, 3, 7).


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## Guest (Jan 29, 2014)

I assumed the all-interval set had to contain every interval from: m2/M2/m3/M3/P4/D5/P5/m6/M6/m7/M7, so that's what I did.


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## Jobis (Jun 13, 2013)

arcaneholocaust said:


> I have another question, if it's not too much trouble.
> 
> The tone row I initially came up with had a sort of symmetry to it that results in the retrograde and the inversion being nearly identical, thus limiting the possibilities of permutations quite a bit.
> 
> My question is: do the rules of serialism perhaps allow the composer to apply permutations to only *segments* of the tone row? Say, treating the first 6 notes and the last 6 notes as separate rows for the purpose of more diverse inversions, etc? If not, I'll make do


Yes, Schoenberg did this himself as far as I know. I believe you split a row into two hexachords and can arrange one hexachord with another hexachord to get a new variation of the row. I love the word hexachord.


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## SuperTonic (Jun 3, 2010)

arcaneholocaust said:


> I assumed the all-interval set had to contain every interval from: m2/M2/m3/M3/P4/D5/P5/m6/M6/m7/M7, so that's what I did.


Actually, all you need for an all-interval set is m2/M2/m3/M3/P4 and the tritone. Remember, in 12 tone theory you are dealing with pitch classes, not pitches. So when you refer to PC 0 it could be a C in any octave. So an M2 can become a m7 depending on the specific pitches used. For example C up to D would be M2, but if you wrote it from C down to the next lower D it would be a m7. In set theory and 12 tone theory this concept is called an interval class where each interval is equated to its inversion and normally the smaller interval is used for reference.


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## Guest (Jan 30, 2014)

Damn. So I didn't need to achieve a tone row with all 11 of those intervals. I feel cheated


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## millionrainbows (Jun 23, 2012)

Yeah, there's really only 6 intervals. The rest are inversions. See my blogs.

You could do like Schoenberg did in his Fourth String Quartet. Use a single row for the melody, or top violin; then divide it into 4 trichords (3-note groups); label them A, B, C, and D; then make sure each section of the melody (a-b-c-d) is harmonized underneath by a different trichord.

Ex: If the melody (trichord A, 3 notes long) is in vln. 1, then put B, C, or D underneath, in vln. 2, viola, and cello. That way, you'll have 4 different notes each time.


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## PetrB (Feb 28, 2012)

arcaneholocaust said:


> Damn. So I didn't need to achieve a tone row with all 11 of those intervals. I feel cheated


Don't knock it: exercise is good for you.

With the inversions a possibility you first overlooked, there is the way to keep that row from sounding the same in the original or retrograde. There is no law you have to go in the same direction up or down from pitch to pitch as is laid out in the original row, any more than inversions are bad in tonal music.


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## millionrainbows (Jun 23, 2012)

Note that the "all-interval set" (0, 1, 4, 6) has all 6 intervals. Taking "C" as zero, we get:
0-1 (C-C#): m2
0-4 (C-E): M3
0-6 (C-F#): tri-tone (inverts to itself)
1-4 (C#-E): minor 3
1-6 (C#-F#) P4
4-6 (E-F#): Major 2


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## millionrainbows (Jun 23, 2012)

SuperTonic said:


> Actually, all you need for an all-interval set is m2/M2/m3/M3/P4 and the tritone. Remember, in 12 tone theory you are dealing with pitch classes, not pitches. So when you refer to PC 0 it could be a C in any octave. So an M2 can become a m7 depending on the specific pitches used. For example C up to D would be M2, but if you wrote it from C down to the next lower D it would be a m7. In set theory and 12 tone theory this concept is called an interval class where each interval is equated to its inversion and normally the smaller interval is used for reference.


Also, I might mention that there are unordered sets, <>, and ordered sets {}. The one above is unordered...

As I recall, there are only two _ordered_ hexads which have all the intervals.


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## Eschbeg (Jul 25, 2012)

arcaneholocaust said:


> do the rules of serialism perhaps allow the composer to apply permutations to only *segments* of the tone row?


Milton Babbitt's Composition for Four Instruments might be a fruitful study for you since, as a few people here have noted, he does something similar to what you're describing. Here's what might be called the "master row" of the piece, which is divided into four trichords:

[G E Ab] [Gb F A] [Eb D C] [B C# Bb]

The tone row for each instrument is based on one of the trichords of the master row. Here's the primary row for the clarinet is:

[G E Ab] [Gb A F] [B D# C] [D Bb C#]

Notice not only that the first trichord of the clarinet row is the same as the first trichord of the master row, but also that the other trichords of the clarinet row are derivations of its first trichord: trichord 2 is the inversion of trichord 1 (transposed 11 half-steps), trichord 3 is the retrograde of trichord 1 (transposed 4 half-steps), and trichord 4 is the retrograde inversion of trichord 1 (transposed 7 half-steps). Similar to what you described above, each of the serial operations has been applied only to specific segments of the master row rather than the whole row.

Since there are four instruments in the piece, it's not hard to guess that the other three will, like the clarinet, have a tone row consisting of one of the trichords of the master row subjected to each of the serial derivations. Here's the cello's primary row:

[Eb D C] [A# B C#] [G F E] [F# G# A]

The first trichord is the same as trichord 3 of the master row. Trichords 2-4 are the I7, RI4, and R3 of trichord 1, respectively.


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## Guest (Feb 2, 2014)

So many juicy ideas posted. Thank you all for going above and beyond.


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## millionrainbows (Jun 23, 2012)

Schoenberg's usual procedure in using tone-rows was to invent a theme or melodic idea (since he was always a thematic composer), usually one that contained all 12 notes. He then subjected the line to serial procedures of inversion, retrograde, etc. Typically, he divided the row into smaller segements such as hexachords, tetrachords, and trichords. He used these smaller units to create accompaniment figures, chords, and motives. In doing this, he used various note durations, registers, created contours, and textures, so this is where a lot of the real craft comes in.

When using chords from the row, this is where finding an "unordered" content would be applicable, to find the sonorities in the vertical stack. This would be like an unordered scale or chord, where every note is related to _every _other note, not just its adjacent notes in the row. Vertical stacking "frees" us from the order of the row, at least momentarily, and sonority can be considered, just as in tonality.


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## millionrainbows (Jun 23, 2012)

Here is an "all-interval row" that the opening poster mentioned. This one was used by Berg in his song* Schliesse mir die Augen beide (1925), *and later used in his* Lyric Suite.*

F-E-C-A-G-D-Ab-Db-Eb-Gb-Bb-B

The intervals between the notes are:

m2/m6/m3/m7/P4/tritone/P5/M2/M6/M3/M7.

Note also the symmetry of the intervals: the central tritone is symmetrically surrounded by intervals and their inversions: P5/P4, M2/m7, etc.


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