SOUND PATTERNS

A Structural Examination of Tonality, Vocabulary, Texture,
Sonorities, and Time Organization in Western Art Music

by PHILLIP MAGNUSON

MICROCOSMS

Chapter 45. Serialism

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Chapter 41.
Impressionism
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Chapter 42.
Primitivism
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Chapter 43.
Neo-classicism
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Chapter 44.
Expressionism
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Chapter 46.
Jazz
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Chapter 47.
Indeterminism
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Chapter 48.
Texturalism
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Chapter 49.
Minimalism
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Chapter 50.
Electronicism
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Chapter 51.
Neo-romanticism
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Chapter 52.
Eclecticism

SERIALISM: an appeal to order

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

45.1 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. Schönberg stopped composing for almost ten years while he developed a system which culminated in the creation of the twelve-tone row, or SERIES. The precept of the 12-tone series could not be simpler: each of the 12 chromatic pitches is presented in order, without repetition, until all 12 are used. Once the series is complete, another series may be used.

Schönberg 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 use of pointillism and klangfarben of Expressionism. Listen to more information about it at Arnold Schönberg's Twelve-Tone Method.

The twelve chromatic pitches can be arranged into almost half a billion combinations, and the compositional unity is achieved through the ORDER OF INTERVALS. All tone rows contain exactly the same pitches, but the intervallic structure of a given tone row is unique and unchanged in all its forms. It is important to understand the 12-tone row is a tool, an abstraction of pitch classes, and is not the music itself. The row simply provides organic unity, generally subliminal in nature, to a piece of music.

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

If you would like to experience a brilliant, thought-provoking, and really funny presentation, go to Twelve Tones on YouTube. It's a little on the long side, but is well worth the time, and you will think about music differently afterwards.

45.2 COMPOSERS ASSOCIATED WITH SERIALISM

45.3 MUSICAL ELEMENTS

At a glance:

SerialismTonalityVocabularyTextureSonorityTime
basically maintains:
generally modifies:
completely changes:xxxxx

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

  1. Development of the row

    1. The 12 different pitches of Western music are arranged into a series, or TONE ROW, creating an order of intervals. Serial music is NOT about the pitches; it is about the intervals that are formed between pitches and the order in which they occur. The first tone row in a given Serial composition is automatically called the PRIME (P) form of the row.

    2. The prime row can be transposed to 12 different pitch levels without changing the order of intervals. Note that the intervals are reduced to their smallest form: nothing larger than a tritone.

    3. The prime row can be turned upside down (the same intervals moving in the opposite direction) without disrupting the order of intervals. This is the INVERSION (I) and can also be transposed to 12 different pitch levels.

    4. The prime row can be played backwards (the same intervals in the reverse order) without disrupting the order of intervals. This is the RETROGRADE (R) and can also be transposed to 12 different pitch levels.

    5. The inverted form of the row can be played backwards (the same intervals in the opposite directions and reversed) without disrupting the order of intervals, This is the RETROGRADE INVERSION (RI) and can also be transposed to 12 different pitch levels.

    6. The final count is 48 possible row presentations:
      • 12 transposed primes
      • 12 transposed inversions
      • 12 transposed retrogrades
      • 12 transposed retrograde inversions.

    7. As Schönberg 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).

  2. Uses of the row

    1. A tone row is an abstraction: its sole purpose is to use pitch classes (rather than specific pitches) to create the order of intervals. When it is applied to a piece of music, specific pitches are used, and these 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 dichords, trichords, tetrachords, hexachords, or any combination of groups. This can then become a primary means of organizing a piece of music.

  3. Analysis techniques

    1. ORDINAL numbers are used to show the placement of each pitch within the row. They are the primary technique used when analyzing a Serial composition. They are written with a period following the number, and they are referred to as "first pitch", "second pitch", "third pitch", and so on.

      The two retrograde forms of the row use the ordinal numbers in reverse (12. 11. 10. 9. 8. 7. 6. 5. 4. 3. 2. 1.) since the intervals are presented in reverse order.

    2. CARDINAL numbers are used to show the location in half steps above the first pitch of the row, which is labelled pitch 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 in addition to letter names, and are referred to as "pitch one" (the pitch one half-step above the first pitch), "pitch two" (the pitch two half-steps above the first pitch), "pitch three" (the pitch three half-steps above the first pitch), and so on.

    3. The 48 row forms can be combined into a composite, called a MATRIX. A matrix consists of a table of 144 cells in 12 rows of 12 items. Begin making the matrix by converting the pitches of the prime form to letter names (to emphasize them as pitch classes rather than actual pitches) across the top row. Since this row form begins with pitch zero, it is called P 0 ("P" standing for "prime"). The pitches in this matrix will be spelled with natural and sharped notes (for neatness). The pitches in the piece will be spelled with accidentals that best indicate the simplest possible intervals.

      Image

    4. The next step is to write the inverted form of this row down the first column. Since this row form begins with pitch zero, it is called I 0 ("I" standing for "inversion").

      Image

      Reading P 0 backwards reveals the retrograde form and is labelled R 0. Reading I 0 backwards reveals the retrograde inversion form and is labelled RI 0. Note that both retrograde forms are identified by their last pitch.

    5. At this point, all pitches can be labelled with cardinal numbers:
      • The first column shows the first note for all the prime forms of the row, which are read from left to right.
      • The top row shows the first note for all the inverted forms of the row, which are read from top to bottom.
      • The first column also shows the last note for all the retrograde forms of the prime row, which are read from right to left.
      • The top row also shows the last note for all the retrograde inverted forms of the row, which are read from bottom to top.

      Image

    6. The next step is to transpose these four row forms to different pitch levels. Begin with P 1, which is P 0 moved up one half-step. P 1 in this matrix is located on the fourth row.

      Image

    7. Next, transpose P 1 up one half-step to P 2, which is located on the eighth row of the matrix.

      Image

    8. The matrix is completed 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 sucessive half-steps. 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.

      Image

    9. Check the diagonal from the top left cell to the bottom right cell; it should be the same pitch class all the way. Print out a copy of this finished matrix in order to examine the serial analysis process (next section).

      Once you have completed a few matrices on your own, you can have a matrix generated automatically at musictheory.net

  4. Analysis process

    1. Now that a matrix has been generated, it can be used to identify the rows in a given piece of music. This matrix happens to be used for a song ("Des Herzens Purpurvogel fliegt durch Nacht", op. 25, no. 2) by Anton Webern. Print out a copy of this piece in order to examine the serial analysis process.

      Using the generated matrix, check to see if the first 12 pitches are P 0. Go to next page for the answer.

    2. Analysis conclusions

      1. The first step to understand why a composer selects specific row forms in a given piece of music is to make a diagram of the rows. Simply list all the rows used in the piece, showing their relative placement and duration,

        Voice: I0 -- -- P0-- --
        Piano:P0 P0RI0 I0 R0RI0P0

      2. Once the diagram is given, conclusions can be made. Things to examine include
        • Pitches in common at the beginning of each row
        • Pitches in common at the ending of each row
        • Which row forms are used
        • Pattern of row forms used
        • Pattern in the relationships of the row forms
        • Invariance
        • Combinatoriality

        In this excerpt (the song is not complete), the rows are chosen for the following reasons:

        • each row form either begins or ends with pitch "0" ("C")
        • all four row forms (P, I, R, and RI) are used
        • for each row in the voice, the piano uses three, ending with the same row as the voice
        • invariance (see below)

      3. Certain row forms are chosen because they contain pitches which remain in the same ordinal position (INVARIANCE). In the example above, notice in measure 5 that F# (ordinal "5.") is used in both the voice and piano to complete I 0 and P 0. This is also true in measure 7 with A (ordinal "9." completing I 0 in the voice and RI 0 in the piano) and measure 10 with B (ordinal "12." completing I 0 in the voice and I 0 in the piano).

        Also, in measure 12, F# (ordinal "3.") is used in both the voice and piano to complete P 0 and R 0, measure 14 with A (two different ordinals complete P 0 and RI 0), and measure 16 with F - D - C# (ordinals "10.-11.-12." completing P 0 in the voice and P 0 in the piano).

        A larger conclusion is that there are three parts to this excerpt:

        • Introduction of P 0 in piano
        • Section I presents I 0 in the voice accompanied by P 0 - RI 0 - I 0 in the piano (both parts ending with I 0)
        • Section II presents P 0 in the voice accompanied by R 0 - I 0 - P 0 in the piano (both parts ending with P 0)

        Invariance is evident only when two row forms use one note to complete each series.

      4. 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 above there are no places where combinatoriality is used, but there is the possibility for this to happen. P 0 and I 1 are complementary (see diagram below), as are I 0 and P 11. By extension, R 0 and RI 1, and RI 0 and R 11 complement each other.

        Another way to consider combinatoriality is that the first hexachord of P 0 above contains exactly the same pitches as the second hexachord of I 1, but in a different order.

    3. Other uses of the matrix

      1. Some Serial composers use sub-sets of the row rather than the complete row.

      2. Some Serial composers move the starting pitch for a row to another position, called CYCLICAL ROTATION.

      3. Some Serial composers explore diagonal and spirals within the matrix, rather than just the verticals and horizontals.

    ASSIGNMENTS:

    SUGGESTED LISTENING

    ANALYSIS

    Isolate the tone rows and locate all the musical elements that are typical, characteristic, or unique to Serialism in the following pieces in Music for Analysis:

    1. Krenek: 12 Short Pieces for Piano, op.83: Dancing Toys [#446] Listen to a performance
    2. Schönberg: Suite fur Klavier, op.25 (1923): Gavotte [#447] Listen to a performance
    3. Webern: Three Songs, op.25, no.1: Wie bin ich froh! [#449] Listen to a performance
    4. Dallapiccola: Cinque Frammenti di Saffo, no.4 (1942) [#448] Listen to a performance

    SYNTHESIS

    Write a Serial piece for two different wind or bowed instruments played by class members but which you do not play; both parts must be written at concert pitch. This must be one page or less and a complete musical thought. Consider the musicality of your work. Play back your work on the computer through MIDI (or better yet, have the two class members perform it for you) to guide you. The final result must be playable.

    To prepare this writing assignment properly, use the notation guidelines appendix, located at Basic Principles of Music Notation, Semester IV.

    Submit a MIDI file via email in addition to a print-out of the project.

    1. Use 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. Use klangfarben (frequent coloristic changes) throughout
    3. Use pointillism (numerous and dramatic register changes) throughout
    4. Use highly irregular rhythms (notated with beats showing by proper beaming) throughout
    5. Use many changing meter signatures (do not use the common time or alla breve meter signatures)
    6. Indicate tempo with a metronome marking (showing the correct beat unit)
    7. Indicate mood with descriptive word(s) in English
    8. Utilize a great variety of dynamics (see #3 above), and no "mezzo" dynamics
    9. Utilize a great variety of appropriate articulations, one for each note

    The grading for this project:

    Click here to view a sample Serialism project







    THE FOLLOWING IS AN SMALL EXPLORATION OF A SPIN-OFF FROM SERIALISM

    Chapter 45a. Total Serialism

    45.4 TOTAL SERIALISM

    Classical Serialism orders the intervals (pitch events) only, but Schönberg allowed the rows to influence phrasing, and his student Anton Webern also attached register as a function of the row. In the 1940's, Olivier Messiaen began to explore ways to integrate pitch with rhythm, articulations, and register, leading the way to TOTAL SERIALISM.

    Total Serialism, also known as INTEGRAL SERIALISM, allows other events to be serialized, such as rhythm, articulations, dynamics, register, or even the row forms themselves. This basically means that the course of a piece is decided pre-compositionally. Total Serialism provides a process which imposes an organic unity to all aspects of a piece of music. If performed correctly, all performances should sound exactly alike (which in reality is highly unlikely).

    Although Total Serialism never really became popular, its extreme precision led logically into electronic music and music written by computers, and gave composers new ideas about relationships of pitch, rhythm, timbre, and dynamics. Pierre Boulez (a student of Messiaen's) and Milton Babbitt developed Total Serialism separately, and created enormously complicated mathematical systems to generate matrices for the integration of events. A simpler path will be followed as musical elements are examined; this will describe one possibility, out of many, of how music can be generated through Total Serialism.

    45.5 COMPOSERS ASSOCIATED WITH TOTAL SERIALISM

    45.6 MUSICAL ELEMENTS OF TOTAL SERIALISM

    The following musical elements describe simply one way a piece of Total Serialism may be created. Students may find it useful to study the sample project at the end of this chapter to see how all these elements might be put together to create a piece of Total Serialism.

    1. Pitch numbers

      1. Rows are constructed in the same manner as for Serialism.

      2. The cardinal numbers become the means of organizing events in addition to pitch.

        Replace the pitches with cardinal numbers only.

      3. Construct a matrix using only the cardinal numbers.

    2. Rhythm

      1. A basic rhythmic unit (a sixteenth-note in the example below) can be selected. That unit is added, one at a time, lengthening the value by a sixteenth-note. The cardinal number represents the number of basic units which have been added to the original.

      2. The resulting note lengths can then be arranged into any order to create a unique rhythm, such as this one corresponding to the numbers from P 0.

    3. Dynamics

      1. Dynamics can be assigned an absolute value. Note in the example below that only six dynamics are used, each one appearing twice.

      2. The dynamics can then be arranged into any order to create a unique pattern, such as this one corresponding to the numbers from P 0.

    4. Articulations

      1. Articulations can be assigned a cardinal number.

      2. The articulations can then be arranged into any order to create a unique pattern, such as this one corresponding to the numbers from P 0.

    5. Assigning rows

      1. Row forms can be predecided by using the matrix.

        P0:01392114107856
        Indicates:P 0P 1P 3P 9P 2P 11P 4P 10P 7P 8P 5P 6

      2. It is generally a good idea to use different row forms for different events. If P 0 were used for both pitch AND rhythm events, each presentation would be exactly the same. If, on the other hand, P 0 controls pitch and I 0 controls rhythm, a totally different effect would be created by switching I 0 for pitch and P 0 for rhythm.

    ASSIGNMENTS:

    SUGGESTED LISTENING

    ANALYSIS

    1. Karlheinz Stockhausen: Kreuzspiel (1951): I [ATM #25] Listen to a performance

    SYNTHESIS

    Write an example of Total Serialism for two melody/mallet percussion instruments, one page or less, which is a complete musical thought.

    To prepare this writing assignment properly, use the notation guidelines appendix, located at Basic Principles of Music Notation, Semester IV.

    Submit a MIDI file via email in addition to a print-out of the project. Include the following:

    1. Same row as Serial project (submit matrix)
    2. At least two P, I, R, and RI forms of row
    3. Do not use the common time or alla breve meter signatures
    4. Serialize the pitches, rhythms, articulations, dynamics, and row forms (provide a chart)

    The grading for this project:

    Click here to view a sample Total Serialism project

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