How Ironic is it that our final topic of 12 Tone Music is presented in Notes 12?

In his discussion of serialism, Persechetti defers any discussion of 12 tone technique to "a treatise on counterpoint". This topic is an essential part of contemporary music theory and, as such, we will turn our attention to the following resources:

Our main text resource will be found in the 4 links below
http://jan.ucc.nau.edu/~krr2/12tone/12tone1.html © 2004 Kenneth R. Rumery Northern Arizona University		http://jan.ucc.nau.edu/~krr2/12tone/12tone1prob.html © 2004 Kenneth R. Rumery Northern Arizona University
http://jan.ucc.nau.edu/~krr2/12tone/12tone2.html © 2004 Kenneth R. Rumery Northern Arizona University		http://jan.ucc.nau.edu/~krr2/12tone/12tone2prob.html © 2004 Kenneth R. Rumery Northern Arizona University
With Supporting material found below
http://www.bandsman.co.uk/downloads/serial.pdf © 2003 Nigel Horn Accrington and Rossendale College		http://www.dancavanagh.com/music/matrix.php ©2004-2008 Daniel M. Cavanagh
http://www.math.wsu.edu/math/Lessons/Music/

 

12 Tone Technique Part I

The music of the 18th and first half of the 19th century was devised of an orderly notion of common period syntax. By the mid 19th Century (1859) Richard Wagner had completed Tristan and Isolde and the famous "Tristan Chord" had surfaced as a fundamental departure from that very order of common period syntax. The function of Tonality and its defining Consonance and Dissonance was now relative not absolute. Upon the first performance of Tristan and Isolde in 1865, Claude Debussy was 3 years old, Gustav Mahler was 5. As these and other composers continued explorations into modal and scalar systems and alternate meathods of constructing vertical sonorities the once clearly defined line of tonality quickly blurred. By the end of the 19th Century the concept of central tonality had all but vanished from discussions regarding new and unexplored techniques of music.

Perhaps the demise of tonality was leading to tonal anarchy. Perhaps there is an inherant sense in human nature to strive for order. Whatever the reason, In response to the demise of the tonal system of composing music, musicians in the early twentieth century looked for new approaches to composing that would restore a sense of coherence to music. In 1904 Arnold Schoenberg began teaching music theory and by 1910 had authored "The Theory of Harmony"

Within a few years, Schoenberg was to develop his theory of 12 tone compositional technique which in French and English was given the alternative name serialism. Schoenberg himself described the system as a "Method of Composing with Twelve Tones Which are Related Only with One Another" Twelve-tone technique (also called dodecaphony) is a means of ensuring that all 12 notes of the chromatic scale are sounded while preventing the emphasis of any single tone. All 12 notes are thus given more or less equal importance, and the music avoids a central tonality. The technique was tremendously influential on Schoenberg's students who, as composers in the mid-twentieth century, became the basis of the Second Viennese School.

Schoenberg himself described the system as a "Method of Composing with Twelve Tones Which are Related Only with One Another".[2] However, the common usage (in English) at the present time is to describe this method as a form of serialism. Later, as we will see, Serialism became a compositional technique that expanded beyond 12 Tone Technique.

1. The Tone Row
In order to ensure that every note contains equal harmonic importance, a series (or "row") of notes is devised as follows.

a. It must contain an ordering of all 12 notes of the chromatic scale
b. No single note may be repeated within the row
c. Octave transpositions of notes are considered of the same "pitch class" as their origin
d. The first note of the row is stated as the now familiar "Primary" or "Reference Pitch"
e. Enharmonics are indeterminate
e. A numerical designation of each pitch in the row is determined by that pitches position in the chromatic scale of the primary

In class assignment 1. Pick a primary note, write a chromatic scale above that note and label each notes position in the chromatic scale 2. Write a 12 tone row that begins on that primary and label it accordingly.

2. The Prime Row & Transformations
The original row of the piece is known generally as the "Prime" 0 row (or "P0") and can include 4 types of transformations. Each transformation must adhere to our principal of a set consisting of an order of 12 (base 12)

a. Transposition
To determine the transposition, we simply add the value of the note to which we apply the transposition to each member in the row. Remember that we are working with an order of 12 such that a value of 13 exceeds the base by 1 and therefore equals 1.

 

In class assignment 1. Write a 4th degree transposition of your Primary "P0" Row and label it accordingly.

b. Retrograde
Retrograde is simply the statement of a row in reverse order.

In class assignment 1. Write a retrograde of your Primary "P0" Row and label it accordingly.

c. Inversion
Inversion of a row is determined by finding the complement of a pitch class. In Serial Music, the complement of a given pitch class number is the number that when added to the given pitch class number will equal 12 (Pitch Class + x=12) or (x = 12-Pitch Class)

In class assignment 1. Write an inversion of your Primary "P0" Row and label it accordingly.

d. Retrograde Inversion
Retrograde Inversion of a row is determined by finding the inversion of a row and then ordering it backwards.

 

In class assignment 1. Write a retrograde inversion of your Primary "P0" Row and label it accordingly.

3. The 12 Tone Matrix or "Magic Square"
To facilitate composing or analysis of serial music, it is useful to represent all four transformations (Original, Inversion, Retrograde and Retrograde Inversion) of a row in each of the 12 chromatic transpositions (thus 48 possible forms) To do this we use the following procedure:

a. Create a 12X12 Matrix

b. In the First Row of the Matrix place the numerical representation of the Prime 0 Row of your 12 tone system
(notice that the retrograde of the row can be read right to left). We use the designation "P0" to show it is the prime row and "R0" to show the retrograde of the prime row.

"P0"	0	10	9	4	6	8	11	2	3	7	5	1	"R0"

 

c. In the First Column of the Matrix place the numerical representation of the Prime 0 Row of your 12 tone system in its P0 inversion
(notice that the retrograde inversion of the Prime 0 Row can be read in the first column bottom to top) We use the designation "I0" to show the inversion of the prime row and "RI0" to show the retrograde inversion of the prime row.

	"I0"
"P0"	0	10	9	4	6	8	11	2	3	7	5	1	"R0"
	2
	3
	8
	6
	4
	1
	10
	9
	5
	7
	11
	"RI0"

In class assignment 1. Create a 12X12 Magic Square (12 Tone Matrix) and fill in the Primary Row and 1st Column in accordance with your Primary "P0"Row

 

c. In the second row of the Matrix place the numerical representation of the transposition dictated by the reference pitch of that row.
(for example the second column of the second row = 10+2, the third column of the second row =9+2 etc)

	"I0"
"P0"	0	10	9	4	6	8	11	2	3	7	5	1	"R0"
"T2"	2	0	11	6	8	10	1	4	5	9	7	3	"R2"
	3
	8
	6
	4
	1
	10
	9
	5
	7
	11
	"RI0"

 

d. Repeat the procedure from c above for each row in the matrix until the matrix is complete

	"I0"	"I2"	"I3"	"I8"	"I6"	"I4"	"I1"	"I10"	"I9"	"I5"	"I7"	"I11"
"P0"	P0	10	9	4	6	8	11	2	3	7	5	1	"R0"
"T2"	2	0	11	6	8	10	1	4	5	9	7	3	"R2"
"T3"	3	1	0	7	9	11	2	5	6	10	8	4	"R3"
"T8"	8	6	5	0	2	4	7	10	11	3	1	9	"R8"
"T6"	6	4	3	10	0	2	5	8	9	1	11	7	"R6"
"T4"	4	2	1	8	10	0	3	6	7	11	9	5	"R4"
"T1"	1	11	10	5	7	9	0	6	4	8	6	2	"R1"
"T10"	10	8	7	2	4	6	9	0	1	5	3	11	"R10"
"T9"	9	7	6	1	3	5	8	11	0	4	2	10	"R9"
"T5"	5	3	2	9	11	1	4	7	8	0	10	6	"R5"
"T7"	7	5	4	11	1	3	6	9	10	2	0	8	"R7"
"T11"	11	9	8	3	5	7	10	1	2	6	4	0	"R11"
	"RI0"	"RI2"	"RI3"	"RI8"	"RI6"	"RI4"	"RI1"	"RI10"	"RI9"	"RI5"	"RI7"	"RI11"

In class assignment 1. Fill in Rows 2-12 with their respective transpositions

 

 

Homework: Assignment 1: Due next class 1. Create a new 12 Tone Matrix using a Primary "P0" Row you did not use in class Submit your Matrix in pdf form to hmu415@gmail.com