When approaching twelve-tone music, it's easy to get bogged down simply identifying row forms and lose sight of the bigger picture.

A list of row forms used in a twelve-tone work is similar to a list of keys in a tonal work—useful, but not enough on its own to be called an analysis.

This chapter considers two iconic works of early twelve-tone music – Webern's Op. 21 and Op. 24 – with analysis of both the

technical details of constructing symmetrical row and composing serial canons, with

wider issues about the work to consider, such as the meaning of a "Symphony" and "Concerto" in this context.

Scores may be found on IMSLP.org (Op. 21); Op. 24))

Webern: Symphonie Op. 21 (1928)

Even the title of Anton Webern’s Symphonie Op. 21 raises questions. Why would Webern choose to call this a symphony? If we think of a symphony as having certain types of key relations, then is an atonal symphony an oxymoron? Commentators have a range of reactions to this question:

"in choosing the most resonant of classical titles Webern stressed the extent to which it could still be relevant to a work in which only certain structural principles remain valid." (Whittall 1977, 163).

"There is little or nothing in its formal procedures to compare with those of the traditional symphony." (Taruskin 2010, 728).

Keep these questions in mind as we consider the nuts and bolts of the work.

Row form

Example 1. The row of Op. 21, along with the trichordal and hexachordal divisions.

Webern frequently chooses what you might think of as "neat" row forms, and this work is no exception (see Example 1). The row breaks up neatly into two equivalent hexachords that are instances not simply of the same pitch-class set but of set 6-1 specifically: half a chromatic scale. In short, each fills the total chromatic collection of half the twelve-tone space.

Further, those hexachords are each set out with one instance of trichord (013) and one of (014). Altogether, the four trichord cells map out as (013), (014), (014), (013). These two trichords are further linked by their shared melodic shape: each involves a third (major or minor) and a semitone.

Here is the row matrix, with the symmetry of P0 and R6 highlighted by showing the first six notes of each in bold. Note that this is sometimes set out in an alternative format, with P and I the other way around. Bailey (1991, appendix II) after Webern’s sketches uses this alternative format. These kinds of decisions are often not clearly "better" one way or the other.

I0

I9

I10

I11

I7

I8

I2

I1

I5

I4

I3

I6

P0

9

6

7

8

4

5

11

10

2

1

0

3

R0

P3

0

9

10

11

7

8

2

1

5

4

3

6

R3

P2

11

8

9

10

6

7

1

0

4

3

2

5

R2

P1

10

7

8

9

5

6

0

11

3

2

1

4

R1

P5

2

11

0

1

9

10

4

3

7

6

5

8

R5

P4

1

10

11

0

8

9

3

2

6

5

4

7

R4

P10

7

4

5

6

2

3

9

8

0

11

10

1

R10

P11

8

5

6

7

3

4

10

9

1

0

11

2

R11

P7

4

1

2

3

11

0

6

5

9

8

7

10

R7

P8

5

2

3

4

0

1

7

6

10

9

8

11

R8

P9

6

3

4

5

1

2

8

7

11

10

9

0

R9

P6

3

0

1

2

10

11

5

4

8

7

6

9

R6

RI0

RI9

RI10

RI11

RI7

RI8

RI2

RI1

RI5

RI4

RI3

RI6

Example 2. Row matrix for Op. 21.

Overall, the row is retrograde equivalent, which is to say, if you play it backwards (R), you have a transposed version of the original (P). When we have equivalences of this kind, there are no longer 48 distinct row forms. Here we have pairs of equivalent rows, and so there are 24 distinct forms (48 divided by 2).

Webern brings out this symmetrical row by overlapping the ends of row forms with the beginning of the next.

Movement 1

Webern describes the first movement as a “double canon in contrary motion,” where “contrary motion” means the same thing as “inversion.” You could think of the overall form as 𝄆A𝄇𝄆BA′𝄇 as follows:

A: From m. 1 to the double bar (mm. 23-25).

B: palindromic: m. 35 as the midpoint of mm. 25–43 in the clarinet (or mm. 26–42 in the cello).

A′: "row recapitulation" from m. 43 (rows only, not motivic rhythm, etc.).

Does that remind you of something symphonic? The repeat markings and the material distribution are loosely suggestive of the Exposition and Development-Recapitulation repeats in sonata form works, or at least rounded binary.

So that might be chalked up in favor of the symphonic reading. On the other hand, the extensive symmetry of the row doesn't end there. Bailey (1991, 96) has described the middle section especially as a symmetrical "tour de force." Recapitulations and cyclic forms are one thing, but for Western classical music, serious adherence to symmetry is a peculiarly 20th-century concept. Speaking about a chordal version of this issue, the British composer Jonathan Harvey once described the symmetrical strategy of moving the bass into the middle as "our revolution" (1982, 2).

Another key consideration at odds with the notion of sonata form is the extensive canons in each section. For instance, in the opening, there's a double canon between pairs of parts (P0 and I0; I8 and P4) as follows:

Example 3. Canons in the beginning of Op. 21.

Notice the similar timbral sequences in the two pairs. For instance, in the first pair, we have a horn part, then a clarinet part, and finally a lower string instrument before returning symmetrically back the way we came. Breaking up the melodic line in this way is sometimes called Klangfarbenmelodie (sound-color melody) and is not unique to the atonalists. Mahler loved to share out melodies this way, for instance (see Orchestration). Perhaps Webern's most iconic example of this technique is his orchestration of J.S. Bach's Ricercar from the Musical Offering.

Movement 2: Variations; a double canon with retrograde

With the second movement, there's no disputing the title: "Variations" is certainly apt, and the structure is brought out in typically Webernian fashion using all the parameters. Here's a brief synopsis in note form of what's going on:

Theme (related to the coda)

M