In the previous class, we saw how to construct a 12 tone row and matrix. Today we will look at compositional methods utilizing the 12 tone row and matrix. In our discussion of these methods I will stress that one should approach the techniques of 12 tone music with creative understanding, sensativity and freedom.

"The 12 method is a means of liberation and {you} retain the right to break your own rules and make your own aesthetic choices"

Primer

Sets

1. We consider the ordering of the 12 Tones of the chromatic scale as a set or "Row"
2. The Set may have a defined purpose as a whole:

a. All-Interval Set = A row that contains all 12 possible intervals (unison +11)

b. Symmetrical Sets = A row that contains a pattern of self similarity

c. Intervallic Order = A row that contains a pattern based on intervallic purpose

In class assignment 1. Creat a 12 tone row that demonstrates an all-interval set, a symmetrical set or intervalic order

 

Derivation

1. Derivation = the construction of a row through purposeful transformations of segments.
2. Generator = that portion of the original row that is manipulated to create a new row.

In class assignment 1. Using the first trichord of your row as a generator see if you can use Derivation to construct a new 12 tone row

 

 

Subsets

1. We consider the ordering of the 12 Tones of the chromatic scale as a set or "Row"
2. When a row is divided into small sections such that any given section has a defined pupose we call the section a "subset"
3. Although the 12 tones in the row imply, infact warrant, a departure from any tonal center, smaller subsets may well imply a tonal underpinning.

4. Below we see a row used in Alban Bergs violin Concerto

5. According to the rules of 12 Tone music:

a. you must use all tones in the row
b. you can not repeat a tone until all 12 have sounded
c. a note that is immediately followed by its own pitch class is not considered a repeat
d . One statement of the tone row must be heard in full (otherwise known as aggregate completion) before another can begin.
e. Adjacent notes in the row can be sounded at the same time
f. the notes can appear in any octave
g. the order of the notes in the tone row must be maintained.
h. Durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained).

REMEMBER: "The 12 tone method is a means of liberation and {you} retain the right to break your own rules and make your own aesthetic choices"

6. Below is a melody that contains a strict interpretation of the rules as applied to Berg's Tone Row

One of the greatest miconceptions about 12 tone music is that it must be Atonal. Its greatly important to remember that Schoenberg himself described the system as a "Method of Composing with Twelve Tones Which are Related Only with One Another" and not specifically as Atonal.

7. Berg then devided the row into subsets that outline triadic formations that progress in 5ths

Alban Berg Violin Concerto:
Use of subsets of a 12 Tone row in a relatively tonal context (video @ 1:40)

REMEMBER: "The 12 tone method is a means of liberation and {you} retain the right to break your own rules and make your own aesthetic choices"

8. In Brick Impromptu we see another more tonal and liberal statement

a. Prime 0 Row divided into 3 equal subsets
b. Subsets imply Tonality: F#X7, Dø7, AX7
c. All tones in the row are used (adheres to rule)
d. Notes in undulating LH repeat before all 12 tones sound (breaks rule)
e . One statement of the tone row must be heard in full (otherwise known as aggregate completion) before another can begin.(adheres to rule)
f. Adjacent notes in the row can be sounded at the same time (modifies rule so adjacent=within the same subset)
g. the notes can appear in any octave (adheres to rule)
h. the order of the notes in the tone row must be maintained. (adheres in all subsets except C)
i. Durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained).

In class assignment 1. Using a row you have previously created, write a short piece that closely follows the rules of 12 tone composition

 

Complement

1. A complement = the remaining pitches necessary to transform a subset into a 12 tone row.

a From the derived row below we see that first 3 notes are the first three notes of P0
b. The next six notes are "derived" from R6 and T5 of P0
c. These 9 notes are a subset of a 12 tone row
d. The last 3 notes are the remaining pitches necessary to transform the subset into a 12 tone row = Complement
e. Interestingly, these last 3 complement notes are also the 4th, 5th and 6th notes of P0

2. Self-complementing Hexachords

a. A hexachord is self-complementing if the complement is the transposition or transposed inversion of the original and if it contains none of the original pitch classes.

2. Hexachordal Combinatoriality
Combinatoriality gives cohesiveness, consistency, and structure to a succession of ideas, longer span pitch modules, and to the large scale design of a composition.

A hexachord is combinatorial if

1. The complement is produced by a transposition (maps onto its complement).

2. The complement is produced by an inversion (maps onto its complement). (see above example of P. Andy's P0 Row)

3. A transposition produces the original collection of PCs (maps onto itself).

4. An inversion produces the original collection of PCs (maps onto itself).

 

 

In class assignment 1. Study your twelve tone matrix from the homework in Class 12 and identify any Hexachordal Combinatoriality that may exist. (note you may not have always have one)

 

Homework: Assignment 1&2: Due next class 1. Write a short 12 Tone passage (between single and double period) for all woodwinds That follows the rules of 12 Tone Composition closely but remember: REMEMBER: "The 12 tone method is a means of liberation and {you} retain the right to break your own rules and make your own aesthetic choices" The piece should be driving and determined and edgy . Realize your compositions with Garritan and submit your scores and mp3s hmu415@gmail.com