Classical Serialism

1
Classical Serialism

• Schoenbergs Method

2
The Development of the Method

• Many composers felt that a regular cycling of all
  the pitch classes was the best way to achieve
  atonality.
• Schoenberg developed the idea of arranging the
  twelve pitch classes into a row.
• The fugue theme from Thus Spake Zarathustra and
  Ives Three-Page Sonata are examples of
  twelve-note melodies that predate Schoenbergs
  method.
• These, and other examples, did not use the twelve
  pitch classes systematically throughout the
  compsosition.
• Schoenbergs method uses the row as the basic
  shape of the composition that can only be
  presented in four ways.

3
Terminology

• Tone Row (basic set, series) An ordered
  arrangement of the twelve pitch classes with each
  occurring only once.
• Prime The original set.
• Retrograde The original set in reverse order.
• Inversion The mirror inversion of the original
  set.
• Retrograde Inversion The inversion in reverse
  order.
• Order Numbers The notes position in the row.

4
The Tone Row

• Notes can be written in any octave (octave
  equivalence) and enharmonically (pitch class).
• Each form has 12 transpositions, creating 48
  versions of the row.
• Rows are identified by an abbreviation of which
  of the four basic forms is being used and a
  number from 0 to 11.

5
The Tone Row

• There are two ways that the numbers 0 - 11 (not
  to be confused with Order Number) are assigned to
  the pitches.
• The old way -- presented in the book -- assigns 0
  to the first pitch of the original set,
  regardless of what pitch class it actually is,
  and the following numbers are half-steps above
  that pitch.
• For instance, if the first four pitches of row
  are E, F, G, C-sharp, then the numbers would be
  0, 1, 3, 9.

6
The Tone Row

• The newer way -- which has become widely accepted
  and which we will use -- assigns the numbers to
  the pitch classes regardless of which is the
  first pitch of the original set (0 is C, 1 is
  C-sharp, etc.).
• This is also the system used in Allen Fortes set
  class theory.
• P-0 therefore indicates a prime form of the row
  starting on pitch class C.
• A matrix, or magic square, presents all 48
  versions of the row.
• From left to right are the prime forms, top to
  bottom the inversions, right to left the
  retrogrades, and from bottom to top the
  retrograde inversions.

7
Analyzing a Row

• Sing or play the row listening for sequences or
  familiar patterns.
• Since composers usually try to avoid any
  reference to tonality, pay particular note to any
  segments that are triads, scale segments, or
  traditional bass and melodic formulas.
• Tabulate the interval classes between adjacent
  pitches (not an interval vector).
• Some rows emphasize particular intervals, others
  do not.
• If there are two of every interval class except
  IC6 it may be an all-interval row.

8
Analyzing a Row

• A derived set uses the first 3, 4, or 6 notes as
  a pattern and then transposes, inverts, and/or
  retrogrades this cell to generate the rest of the
  row.
• Patterns of ICs may reveal patterns that are
  transposed, inverted, retrograded, and/or
  overlapped in a series.
• An invariant PC is one that is shared by any two
  pitch collections.

9
Analyzing a Row

• An invariant subset is on that appears intact in
  two forms of the row.
• The PCs must be in the same ordering to be
  invariant.
• Analyze the subsets for their PC set types.
• Analyzing the trichords and tetrachords is
  usually enough.
• The first and last hexachord will be either the
  same type or Z-related.
• The other PC sets will overlap too much to be of
  much use.

10
Compositional Uses

• The forms of the row can be presented
  consecutively or simultaneously.
• The notes can be in any octave.
• The order of a row form is usually preserved, but
  notes may be sounded simultaneously as well as
  consecutively.
• The are not rules regarding how simultaneous
  notes are arranged in the chord.

11
Compositional Uses

• Repeated notes or tremolos are not considered to
  alter the row.
• Both presenting different forms of the row
  simultaneously and distributing a single form of
  the row across different parts are common.
• It is less common to overlap segments of the row
  or to reorder it for compositional purposes.

12
Compositional Uses

• All 48 forms of the row are rarely used.
• The combining of two row forms to create an
  aggregate is called combinatoriality.
• Usually a hexachord from each set is used to
  create a secondary set.
• The combining is most often done vertically.
• Rows have to be specifically constructed to work
  -- most rows can not be used combinatorialy.
• Combinatoriality is considered by some to be an
  extension of the 12-tone technique -- it
  garuntees a more controlled recycling of the
  twelve pitches.

13
Analyzing Serial Music

• Just labeling the rows and the consideration of
  the details of their use is only part of an
  analysis.
• Form, thematic relationships, etc., are just as
  important as in tonal music.
• Use your ears!
• The use of a serialized row is only a way to
  control the pitch material -- not a system of
  composition.