Serialism

I Twelve-Tone Technique Although Arnold Schoenberg was one of the pioneers of atonal music, eventually he con­cluded that there were shortcomings in a style of composition that lacked systemization. Schoenberg was thoroughly trained in the methods and systems of tonal harmony. Despite his call for the "emancipation of the dissonance," he sought to create a systematic ap­proach to composition that would replace the conventions of tonal harmony. This search led him to develop the concept of the "tone row" and twelve-tone technique, also known as dodecaphonic technique (from the prefix dodeca-, meaning "twelve").

Schoenberg was equally influential as a composer, theorist, and teacher. Two of his students, Alban Berg and Anton Webern, studied the twelve-tone method of composi­tion with Schoenberg. Together, these three men make up what is known as the Second Viennese School of composition (the First Viennese School consists of Haydn, Mozart, and Beethoven). Schoenberg felt strongly that his system of composition was the next logi­cal step in the history of composition and that he followed in the footsteps of Beethoven and Brahms.

The goal of twelve-tone composition is to give all twelve notes of the chromatic scale equal importance-in other words, to destroy the supremacy of the dominant and tonic scale degrees that characterizes the hierarchies of tonal music. Twelve-tone music is a highly specialized technique of atonal music; it is atonal music upon which a systematic approach has been imposed. Like other types of atonal music, it is often highly dissonant.

To compose with the dodecaphonic technique, one must first make a number of choices that will become the basis of the composition. This is analogous to choosing a major or minor key before writing a tonal composition. Not only are all twelve pitches of the chromatic scale equal in twelve-tone music, but they must all be used. In this style of composition, no pitch of the twelve is omitted. The spelling of the twelve pitch classes is unimportant. When using the pitch class C#, it is just as correct to refer to it as D~.

Prior to writing a twelve-tone composition, the composer creates a specific order in which the twelve pitch classes will be used. This series of notes is known as a tone row. Placing the twelve notes of the chromatic scale into a specific order creates a "series" of pitch classes; therefore, the technique of twelve-tone music is also sometimes known as serialism.

Serialism is one of the most significant musical developments of the twentieth cen­tury. To some degree, it has influenced almost every composer of Western art music since Schoenberg. Its principles have been modified, used with greater or lesser degrees of strict­ness, and applied to every conceivable aspect of music other than pitch, but behind all the innovations lies the original twelve-tone theory developed by Arnold Schoenberg.

The Tone Row Before composing a serial piece, the composer must first construct a tone row. The tone row must use all twelve pitches classes, but they can occur in any order. Composers choose the ordering of their tone rows very carefully to create certain effects within their compositions. One of the first twelve-tone compositions was Schoenberg's Suite for Piano, op. 25. It was completed in 1923 and is based on the tone row shown in Figure 39.1.

2 3 4 5 6 7 8 9 10 11

~ be) ~0 ~0 0 II go

II 0 ~0 ~0 0

mi2 M2 A4 P4 mi3 P4 d5 M6 mi2 mi3

The pitches are numbered above the staff from 1 to 12. This is one of several types of numbering systems that will be applied to tone rows. In this case, the numbers simply convey the sequence in which the twelve pitches appear in the original row. The intervals between the tones are labeled below the staff. There are few, if any, patterns to the interval distribution within the row, apart from the fact that the row begins and ends with a minor second. There are seconds and thirds of various qualities, two tritones (an augmented fourth and a diminished fifth), and one larger leap of a major sixth. If the notes of the row are grouped together in chords, as seen in Example 39.1, dissonant structures are created.

All twelve pitch classes in the tone row above appear in this excerpt. The numbers that are placed beside the notes identify the notes of the original row. Notice that some notes of the tone row are repeated (the repetitions are not numbered). Also, the notes of the row do not necessarily appear in the exact order or the exact register in which they are presented in the original row.

The chord in the first measure of the excerpt comprises the first four notes (or first tetrachord) of the tone row. Those numbered 5-8 in the row (the second tetrachord) appear in the tenor voice and move linearly across the staff. The final four notes of the row (its third tetrachord) appear in the bass voice and are also linear. A thorough analysis of twelve-tone music involves numbering the twelve-note groups as they appear. By adding these numbers to the staff, you can see how the composer created the texture of the composition through vertical and horizontal interaction of the twelve notes.

Mter the first presentation of a row within a composition, the row or its variations (which will be discussed in the next section) will appear again and again throughout the length of the work. In addition to numbering the individual notes that make up the sets, it is also typical to circle each complete set on the score.

12

~0

mi2

1heoretical Skills ~~~

Figure 39.1. Twelve-tone row from Schoenberg's Suite for Piano, op.25

EXAMPLE 39.1. Schoenberg, Suite for Piano, "Intermezzo," op. 25, mm. 1-3

~~ CHAPTER 39 I Serialism

PRACTICE BOX 39. 1 The following twelve-tone row is provided for Example 39.2.

2 3 4 5 6 7 8 9 10 11 12

?= 1111 0 ~0 0 gu #n 0 ~0 b·· ~0

II q,. In the example, find the twelve notes of the row and number them. Do not number repeated notes.

~ EXAMPLE 39 .2. Luigi Dallapiccola, Guaderno musicale di Annalibera, no. 1, "Simbolo," mm. 1-6

) :

:

I= ~~ ·= ~~ ·= ·= ·= ~~ ~~ ~~ # # # ·= ~~

© Sugarmusic S.p.A · Edizioni Suvini Zerboni, Milan (Italy)

I

I= ~~ I= ~~

I I ---,. - .... _ ......... //, ::o--

·= ~~ # ·= ~~ I= ~~ ·= ~~ # ·= ~~

The top staff of Example 39.3 contains the twelve-tone row. Write the row on the blank staff provided. Number the notes of the row on the top staff. Then, determine how the row is used to create the pattern on the other staves (the tone row is split between the two bottom staves). Number those notes as well. {Hint: The notes may appear out of order on the lower staves.)

EXAMPLE 39.3. Schoenberg, Wind Quintet, op. 26, 1st movement, mm. 1-7

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Ob Clar

Hom Bsn

~

II

~ I

:

~..,. jl- I

2 3 4 5

~--~, ~~ ~~

" -

~r-- -

1-'u u

"l.hJ-

~ iy ,.., ~

6 7 8 9 10 11 12

The Matrix A composition or excerpt that presents only the original version of the row, with no trans­positions or other manipulations, is analogous to writing a tonal composition that does not modulate. There are forty-eight possible versions of any tone row, and, in order to see all of them, one must create a matrix. A matrix is a table with rows and columns in which the tone row and all of its transpositions and variations are spelled out.

The original version of the row is known as the prime row. Because it has not been transposed, its transposition level is zero. Therefore, this row is given the designation P0

(prime row, no transposition). There are eleven other prime rows in the matrix, and each is a transposition of the po row. All prime rows are read across the matrix from left to right. The transpositions are not, however, the next step in the procedure.

The next step is to create the row that occupies the vertical column on the left side of the matrix. Its starting pitch is the same as P0.1his row is called the inversion row. The in­version rows are always read from top to bottom on the matrix. The leftmost column of the matrix is the non transposed version of all the inversion rows, so it is given the designation 1°.

Figure 39.2 provides an example of a matrix, showing the original version of the row (P0

) from the Schoenberg Suite (Figure 39.1) written in its proper place across the top row of the matrix. The 1° row is labeled but not filled in yet.

10

• F G D~ E~ D B c A B~

The 1° row is created using a method that inverts the direction of the original intervals in the P0 row but maintains their quality. This directional inversion is written down the left most column of the matrix. The interval between the first two notes ofP0 is a minor second up. To fill in the name of the second note of 1°, reverse the direction of the interval while maintaining its quality. A minor second down from E is D# or S. You may place either name in the first column of the second row of the matrix.

1heoretical Skills ~~

Figure 39.2. Matrix for the tone row from Schoenberg's Suite for Piano, op. 25

~~ CHAPTER 39 I Serialism

Figure 39.3. Completed 1° row

To fill in the remaining notes of 1°, compare all the remaining notes of po with the note in the top left corner of the matrix. Comparing the distance between E and G, which is a minor third up, the next letter of 1° must be a minor third down, which is C# or D~. Continue to compare each note of po with its first note, E, reverse the direction of each interval, and complete the 1° row using the blank matrix in Figure 39.2. Compare your answers with the complete 1° row in Figure 39.3.

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• po___. E F G D~ G~ E~ AI. D B c A B~

H

c~

G

D

F

c

F~

A

G#

B

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Each prime and inversion row is named for its distance up from the starting note of P0

• The distance between E and F is one half step up; therefore, the prime row that begins with F is P\ and the inversion row that begins with F is 11.1he distance from E to G is three half steps up; therefore, the prime row that begins with G is P\ and the inversion row that begins with G is 13

• Return to the matrix in Figure 39.2 and label all of the prime and inver­sion rows.The P0 and 1° rows are labeled for you. Compare your answers with Figure 39 .3.

You can check your work in several ways. One way is to make sure that you have all twelve possible pitch classes represented in your 1° row. Another way is to check the note that forms the tritone with the first note ofpo. Since the tritone is a symmetrical interval (it splits the octave in half), it should retain the same pitch class whether it goes up or down. In this row, the tritone is formed between the first note and the last note of the row. The pitch class that forms the tritone will appear at the same position in the matrix as you count right in po and down in 1°.

To complete the rest of the matrix, transpose the P0 row using each starting note that has been placed in the 1° row. It may be easiest to do these rows out of sequence, transposing each row up a half step; in other words, you will complete the transposition of each row us­ing the naming sequence P1

, p2, p3, and so on. In this manner, you will always be transposing by half steps, which is the easiest and quickest way to fill in all the blanks in the matrix. Fill in the remaining spaces in Figure 39.3.

1heoretical Skills II Now that you have filled in the entire matrix, you will have another way to check your WEB CHAPTER 39

work. In the diagonal row formed from the upper left corner to the lower right corner of .. Alternate method for creafing a matrix the matrix, every note should be the same pitch class.

There are two more possible forms of the tone row that can be labeled once the matrix is complete. A prime row that is read in reverse, from right to left, is called a retrograde row. To name each retrograde row, use the abbreviation "R" and the same number that was used on the opposite end of the same row. In our matrix, the second row will be named P11 on the left side and R11 on the right side.

Finally, retrograde inversion rows are read from bottom to top on any column of the matrix. They are abbreviated "RI" and take the same numbers that were used at the top of each column. Finish naming all the Rand RI rows in Figure 39.3.

The completed matrix in Figure 39.4 shows the correct transposition and labeling of all forty-eight rows. Compare it with your work.

10 Jl 13 19 12 Ill 14 JlO 17 18 15 16 Figure 39.4 .

• Completed matrix

po___. E F G D~ m E~ I>J, D B c A B~ .-Ro

pll a E F# c F D G D~ B~ B I>J, A Rll

p9 c~ D E Bj, a c F B I>J, A G G R9

p3 G G~ A# E A F# B F D D~ c C# R3

plO D E~ F B E D~ G~ c A B~ G I>J, RIO

pl F F# G# D G E A D# c C# A# B Rl

p8 c D~ E~ A D B E B~ G I>J, F m Ra

p2 F~ G A D~ G~ F A# E C# D B c R2

p5 A A~ c F~ B G~ C# G E F D D~ Rs

p4 G# A B F B~ G c m a E ~ D R4

pl B c D I>J, ~ B~ E~ A G~ G E F Rl

p6 B~ B C# G c A D G# F F# D~ E R6

t RIO Rll RI3 RI9 RI2 Rill RI4 RJlO RI7 Ria Rls RI6

Before analyzing any twelve-tone composition, you must complete a matrix as you have done above. This will allow you to find and name all the versions of the original row that were used by the composer.

Analyzing Twelve-Tone Music Mter determining the tone row and completing a matrix, you can analyze a twelve-tone composition. This process involves finding the presentations of the tone row, highlighting them in some manner, usually with a circle, and labeling the versions of the row that have

~~ CHAPTER 39 I Serialism

WEB CHAPTER 39 ~ More obout twelve-tone onolysis

been used. You may need to use colored pencils to make the versions of the row more clear. You may also need to number the various pitches within each twelve-tone grouping. 1his process can help show how the tone row and its variations are distributed within the actual composition.

The conclusions that are drawn from this process will point to a variety of charac­teristics of the compositions and the composers who wrote them. You will discover that some composers consistently use certain versions of the row, for example, 16 or R0

• Other composers will use certain patterns to distribute the twelve notes. For example, in a piano composition, one presentation of the row may appear exclusively in the right hand, present­ing the notes in exact order, 1-12. Simultaneously, another row might be presented in the left hand, perhaps in retrograde. Other composers prefer to construct chords from their tone rows. The chords may present the sequence of pitches from bottom to top, top to bot­tom, or randomly.

When searching for versions of the row within a composition, it can be very helpful to note the beginning and ending intervals of the row. For both the prime and inversion forms of the row, the beginning interval will always be the same (of course the direction will be different), no matter which transposition is used. The retrograde and retrograde inversion forms will likewise both have the same starting interval. Knowing these intervals will help narrow down the possible starting (and ending) notes for all forms of the row.

PRACTICE BOX 39.2 The following matrix presents the P0 row for Example 39.4 on page 555. Complete the matrix and label all forty-eight versions of the row.

AI B D D~ F G c A E

1heoretical Skills ~~

PRACTICE BOX 39.2 continued

Analyze the following composition. Circle each presentation of a tone row. Label the version of the row and number the individual notes within the row. Pay close attention to the clef on each staff. All tone row presentations include notes on both staves. Once you have identified all of the rows, can you find any pattern in the way that they are used?

~ EXAMPLE 39 .4. Dallapiccola, Quaderno musicale di Annalibera, no. 1, "Simbolo," mm. 1-17

© Sugormusic S.p.A- Edizioni Suvini Zerboni, Milan (Italy)

~~ CHAPTER 39 I Serialism

EXAMPLE 39.5. Schoenberg, Suite for Piano, "Gigue," op. 25, mm. 1-8

7 ~~~~-1\ 1- b.

.., 3

. . I

Music for Analysis Analyze the following excerpt using the matrix provided in Figure 39.4. The first appear­ances of the row are fairly easy to find. If you have trouble finding the next row, remember that this tone row contains a tritone between its third and fourth notes. Look for a tritone and let that guide you in finding the beginning of the row. By the time you reach the final row in this excerpt, you should be able to discern a pattern and predict the name of the final row used.

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qt~ -,J' J 'I

L ~~ qe: ~~ ~~ 3

"'~ r ~:t !111 -,J

I Melody The following four- and five-note melodies are atonal. Sing them using fixed-do solfege.

1. ~ .. ., ~0 II .. #n II II .. ~0 0 #e-

2. ~0 fo 110 ~0 110 , .. II 0 0 0

3. II 0 # .. 0 0 0

4. f): fo II ~0 ., lin fo

5. ~0 ftn b·· llo II

#o 0

?= 0 0 l»«l fo 11° -0 6. 0 II

7. ~ .. II ~0 0 II

~0 0 u

f): lzu gu lllzu 0 ~II 8. ftn ~0 0

fo

l)«l

~0

~0

Aural Skills ~~

WEB CHAPTER 39 ~ Dictntion Exercises

0 0 II

0 II 0

u fo II

II

~0 II

II

II

II II

0

II

~~ CHAPTER 39 I Serialism

Two-Part Rhythms for Practice Practice these two-part rhythms, which include many of the rhythmic techniques that you have studied in the last three chapters.

3 3 3

3 3 3

I Use the following staff to compose a twelve-tone row.

Use your tone row to write a composition. You may use only the P0 form of the row. Or, if you want to create a matrix for your row, you may use other forms of the row. Be prepared to perform your composition.

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Keyboard Applications IJ

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