TWELVE TONE COMPOSITION PART 1 - PROBLEMS

TERMS AND PROBLEMS

1. Terms

row (twelve-tone row) series
set prime
inversion retrograde
retrograde inversion reference pitch
twelve-tone matrix twelve-by-twelve array
magic square atonal
tonal cell all-interval set
set type symmetrical set
derived set  

2. Self-help Problems

Problem 1: On the general use of a twelve-tone matrix.

                        1. Form of the set in the first row of the grid? _______________
                           
                        2. Form of the set in the first column of the grid? _______________
                           
                        3. What form of the set will you see if you read  
                        - from left to right? _______________
                           
                        - from right to left? _______________
                           
                        - from top to bottom? _______________
                           
                        - from bottom to top? _______________

Problem 2: Using pitch class number, what is the formula to determine the pitch class number for any square of the grid?

Each row of the grid contains a ______________ of the prime set. The reference pitch of both the prime and retrograde forms of a set is located in the _____________ _____________ of the grid. The reference pitch of both the inversion and retrograde-inversion forms of a set is located in the _____________ _____________ of the grid. A twelve-tone set is a _________________ collection of all twelve ___________ _____________. A twelve-tone aggregate is a __________________

Problem 3: Complete a twelve-tone matrix based on Schoenberg's Op. 41 set. Write the pitch class names and numbers as per the first row of the grid.

0
Csharp		 11
C		 3
E		 4
F		 8
A		 7
Gsharp		 2
E		 1
D		 5
Fsharp		 6
G		 10
B		 9
B
1
D

 

 

 

 

 

 

 

 

 

 

 
9
B

 

 

 

 

 

 

 

 

 

 

 
8
A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution 1:

(answers)

 

 

 

 

 

 

 

 

 

 

 

   1. Form of the set in the first row of the grid? Prime at 0
                           
                        2. Form of the set in the first column of the grid? Inversion at 0
                           
                        3. What form of the set will you see if you read  
                        - from left to right? Prime*
                         
                        - from right to left? Retrograde*
                           
                        - from top to bottom? Inversion*
                           
                        - from bottom to top?

Retro.-Inversion*

*at some transposition


Solution 2:

Add the PC number at the beginning of the row to the PC number at the top of the column to get the PC number in a particular cell of the grid. This is MOD12 so subtract 12 from any integer greater than 11.

transposition
first column
first row
ordered, twelve tone or pitch classes
unordered

Solution 3: (add the reference PC number to PC number in Prime–or subtract its inverse (12-PC#)

0
Csharp		 11
C		 3
E		 4
F		 8
A		 7
Gsharp		 2
E		 1
D		 5
Fsharp		 6
G		 10
B		 9
B
1
D		 0
Csharp		 4
F		 5
Fsharp		 9
B		 8
A		 3
E		 2
E		 6
G		 7
Gsharp		 11
C		 10
B
9
B		 8
A		 0
Csharp		 1
D		 5
Fsharp		 4
F		 11
C		 10
B		 2
E		 3
E		 7
Gsharp		 6
G
8
A		 7
Gsharp		 11
C		 0
Csharp		 4
F		 3
E		 10
B		 9
B		 1
D		 2
E		 6
G		 5
Fsharp
4
F		 3
E		 7
Gsharp		 8
A		 0
Csharp		 11
C		 6
G		 5
Fsharp		 9
B		 10
B 		2
E		 1
D
5
Fsharp		 4
F		 8
A		 9
B		 1
D		 0
Csharp		 7
Gsharp		 6
G		 10
B		 11
C		 3
E		 2
E
10
B		 9
B		 1
D		 2
E		 6
G		 5
Fsharp		 0
Csharp		 11
C		 3
E		 4
F		 8
A		 7
Gsharp
11
C		 10
B		 2
E		 3
E		 7
Gsharp		 6
G		 1
D		 0
Csharp		 4
F		 5
Fsharp		 9
B		 8
A
7
Gsharp		 6
G		 10
B		 11
C		 3
E		 2
E		 9
B		 8
A		 0
Csharp		 1
D		 5
Fsharp		 4
F
6
G		 5
Fsharp		 9
B		 10
B		 2
E		 1
D		 8
A		 7
Gsharp		 11
C		 0
Csharp		 4
F		 3
E
2
E		 1
D		 5
Fsharp		 6
G		 10
B		 9
B		 4
F		 3
E		 7
Gsharp		 8
A		 0
Csharp		 11
C
3
E		 2
E		 6
G		 7
Gsharp		 11
C		 10
B		 5
Fsharp		 4
F		 8
A		 9
B		 1
D		 0
Csharp

Problem 4: Canti di liberazioni No. 2 Dallapiccola

Assume that this is the R7 form of the set. Write the PØ form in the second staff. Remember, the reference pitch is the last note of all R and RI forms of a set.

Problem 5: Three Songs, Op. 25 Webern

Assume this is the PØ form of the set. Write the RI2 form of the set in the second staff. Remember, the reference pitch is the last note of all R and RI forms of a set.

 

Problem 6: Quartet 4, Op. 37 Schoenberg

Assume that this is the PØ form of the set. Write the I5 form of the set in the second staff.

Solution 4: Canti di liberazioni No. 2 Dallapiccola

Solution 5: Webern: Three Songs, Op. 25

Solution 6: Schoenberg: Quartet 4, Op. 37


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