IMPRESSIONISM	PRIMITIVISM	NEO-CLASSICISM
	*
EXPRESSIONISM	SERIALISM	TOTAL SERIALISM
INDETERMINISM	TEXTURALISM	MINIMALISM
ELECTRONICISM	NEO-ROMANTICISM	ECLECTICISM

SERIALISM: an appeal to order

	Duchamp does more than paint a walking figure; he dissects the image into component motions, allowing us to see the order of them.
Marcel Duchamp: Nude Descending Staircase	(1912)

Background

Serialism is the language which is completely unique to the 20th century. The use of cells in Expressionism was haphazard, and it was difficult to keep all pitches equally important. Schoenberg stopped composing for almost ten years while he developed a system which culminated in the creation of the twelve-tone row, or SERIES. He made a conscious decision to avoid traditional Common Practice Period idioms which would suggest tonality, such as melodic or harmonic octaves, major and minor triads, and three or more pitches which sound like scale patterns. He would continue the pointillism and klangfarben of Expressionism.

Twelve pitches can be arranged into almost half a billion rows, but it is the ORDER OF INTERVALS which is of the greatest importance in composing with a tone row. It is important to understand the 12-tone row is a tool, or an abstraction of pitch classes, and is not the music itself. The row provides an organic unity, subliminal in nature, to a piece of music.

Serialism is a much maligned style. Read more about it by clicking here.

Composers associated with Serialism

• Arnold Schoenberg (1874-1951)
• Igor Stravinsky (1882-1971)
• Anton Webern (1883-1945)
• Alban Berg (1885-1931)
• Roger Sessions (1896-1985)
• Ernst Krenek (1900-1991)
• Luigi Dallapiccola (1904-1975)
• Bruno Maderna (1920-1973)
• Milton Babbitt (1916)

Musical elements

Serialism is a direct developement of Expressionism. From this point on, it becomes irrelevant to organize the musical elements around the five elements (tonality, vocabulary, texture, sonority, and time organization) of the Common Practice Period. The break from the past is so complete that comparisons are unproductive.

A. Development of the row

1. The 12 different pitches are arranged in a series, creating an order of intervals. Serial music is NOT about the pitches, however, but rather the intervals that are formed between pitches and the order in which they occur. The first row we hear in any given serial piece is automatically called the PRIME form.
   
2. The row can be transposed to 12 different pitch levels without disturbing the order of intervals.
   
3. The row can be turned upside down (the same intervals moving in the opposite direction) without disturbing the order of intervals (the INVERSION of the prime row), which can also be transposed to 12 different pitch levels.
   
4. The prime row can be played backwards without disturbing the order of intervals (the RETROGRADE of the prime row), which can also be transposed to 12 different pitch levels.
   
5. The inverted form of the row can be played backwards without disturbing the order of intervals (the RETROGRADE INVERSION of the prime row), which can also be transposed to 12 different pitch levels.
   
6. The final count, therefore, is 48 possible row forms: 12 primes, 12 inversions, 12 retrogrades, and 12 retrograde inversions.
7. As Schonberg originally intended, the complete series of pitches must be heard before any pitch is allowed to repeat (this does not include reiterations of the same note).

B. Uses of the row

1. A tone row is an abstraction: its sole purpose is to represent an order of pitch classes, which in turn indicates the order of intervals. When it is applied to a piece of music, specific pitches are indicated, and should always be notated to show the simplest interval relationship possible.
2. A row may be used to create melody.
3. A row may be used to create counterpoint, either by sharing one row with two or more parts, or by having two or more forms of the row sounding simultaneously.
4. A row may be used to create harmonies by having parts of the row, or multiple rows, sounding simultaneously.
5. A row may be segmented into diads, triads, tetrads, or any combination of groups. This can then become a primary means of organizing a piece of music.
   

C. Analysis techniques

1. ORDINAL numbers are supplied to show where each pitch occurs in each row form. The ordinal numbers are used to indicate the location of pitches in a row when analyzing a serial composition. They are written with a period following the number, and they are pronounced "first", "second", "third", and so on.
   
2. CARDINAL numbers are supplied to show how how many half steps each pitch is located above the first pitch that we hear in the music. Obviously, this first pitch is called zero (as in "ground zero"). The cardinal numbers are ultimately used to distinguish and label the 48 row forms, by showing the level of transposition. Ordinal numbers are simply another way to identify pitch other than letter names, and would be pronounced "pitch one", "pitch two", "pitch three", and so on.
   
3. The 48 row forms can be combined into a composite, called a MATRIX. Begin making the matrix by converting the pitches on a staff to letter names (to emphasize them as pitch classes rather than actual pitches). This row form is called P 0. and is notated from left to right just as we would notate in music. Note how some pitches are notated with two enharmonic labels. The actual pitches in the piece will be spelled with the enharmonic version which best indicates the simplest possible interval.
   
4. The next step is to create the inverted form of this row, which will be call I 0 (the inverted form beginning on pitch zero) and is notated down in a column. When we read P 0 backwards, we are identifying the retrograde form. When we read I 0 backwards, we are identifying the retrograde inversion. The retrograde forms are considered to be the reverse forms of P and I and are therefore labelled with zero.
   
5. At this point, all of the pitches can be labelled with their cardinal numbers. When we read the pitches across from left to right, we will be indentifying prime forms of the row beginning on different pitch levels. When we read the pitches from top to bottom, we will be identifying inverted forms of the row beginning on different pitch levels.
   
6. We are now ready to begin transposing these four row forms to different pitch levels. It is convenient to begin with the prime form. We will begin with P 1, which means to transpose each pitch of P 0 up one half step. P 1 happens to be located on the sixth row of the matrix.
   
7. Next, we will transpose P 1 up one half step to P 2, which is located on the eighth row of the matrix.
   
8. The matrix continues by transposing each P row (P 3, P 4, P 5, P 6, P 7, P 8, P 9, P 10, and P 11) up in respective half steps. When finished, the matrix will be complete. All the prime forms will be read from left to right, all the inverted forms from top to bottom, all the retrograde forms from right to left, and all the retrograde inversions from bottom to top. Again, note that all the retrograde forms are considered to be related to specific prime and inverted forms, and are labelled by their last pitch instead of the first.
   
9. Once you have completed a few matrices on your own, you can have a matrix generated automatically at musictheory.net

D. Analysis conclusions

1. Once the rows are discovered and labeled, conclusions are drawn as to why the composer chose particular row forms. Things to examine include
   1. which row forms are used
   2. the relationship of the row forms
   3. beginning pitch of each row
   4. ending pitch of each row
2. Certain row forms are chosen because they contain segments which combine and complement each other in specific ways regarding pitch content (COMBINATORIALITY). In the example below, notice how the first hexachord of I 7 completes the first hexachord of P 0 with the six remaining pitches (and, of course, the second hexachord of both are complements as well).
   
3. Certain row forms are chosen because they contain pitches which remain in the same ordinal position (INVARIANCE). In the following example, notice that the third pitch of both row forms is G, and the sixth pitch is Eb.
   

E. Advanced uses of the matrix

1. Some serial composers use sub-sets of the row rather than the complete row.
2. Some serial composers will move the starting pitch for a row to another position, called CYCLICAL ROTATION.
   
3. Some serial composers will explore diagonal and spirals within the matrix, rather than just the verticals and horizontals.

Analysis projects

• Ernst Krenek: 12 Short Pieces for Piano, op 83: "Dancing Toys" [MA #448]
• Arnold Schoenberg: Suite fur Klavier op 25 (1923): "Gavotte" [MA #449]
• Anton Webern: Three Songs op 25 no 1: "Wie bin ich froh!" [MA #451]
• Luigi Dallapiccola: Cinque Frammenti di Saffo (1942): no 4 [MA #450]

Suggested listening

• Arnold Schoenberg: Suite fur Klavier op 25 (1923) [MA #467]
• Arnold Schoenberg: Moses und Aron (1932)
• Alban Berg: Lyric Suite (1926) [ATM #15]
• Alban Berg: Violin Concerto (1935)
• Anton Webern: String Quartet op 28 (1929) [ATM #12]
• Igor Stravinsky: Movements (1959)

Composition project

Write a Serial piece for two different wind or bowed instruments which you do not play (both parts at concert pitch), one page or less, which is a complete musical thought. Include the following:

1. At least one P, I, R, and RI form of row (label row forms directly on piece and submit complete matrix) with proper enharmonic spellings
2. Klangfarben (frequent coloristic changes)
3. Pointillism (numerous register changes)
4. Highly irregular rhythms (notated with beats showing by proper beaming)
5. Changing meters
6. Tempo-mood-dynamics-articulations (each part requires separate dynamics below each staff)

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