Music History
Name:__________________________
SERIALISM WORKSHEET
Tone Row Composition and the Matrix
1) Extract the 12-tone Row Pitches.
2) Translate to Numbers (C=0, C#=1, D=2, D#=3, etc.)
C
A
B G# A# D
F
E D# F# G C#
0
9 11 8 10 2
5
4
3
6
7
1
3) Transpose to 0 (If prime form is not present)
4) Write the Prime Row in the first row of the matrix
P0
I0
I9
I11
I8
I10
I2
I5
I4
I3
I6
I7
I1
0
9 11 8 10 2
5
4
3
6
7
1
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
RI
RI
RI
RI
RI
RI
RI
RI
RI
RI
RI
RI
Music History
Name:__________________________
5) To find the Left Border, Combine each of the numbers from the prime
row to equal 12 (or 0)
6) Make the 0 Diagonal.
7) Figure out the relationship between each of the numbers in the Prime
row…continue this relationship in figuring the numbers of subsequent
rows. For example, to get “9” (the second number in the prime row),
from the “0” (the first number of the prime row), we add 9. Therefore,
we add 9 to each number in our first column. We can check our work
with the zero diagonal. This continues for the entire matrix (paralleled
relationships from the prime row).
I0
I9
I2
I5
I4
I3
I6
I7
I1
P0
0
9 11 8 10 2
5
4
3
6
7
1
P3
3
0
R3
P1
1 10 0
R1
P4
4
P2
2 11
1
P10 10
7
P7
7
4
P8
8
5
P9
9
6
P6
6
3
P5
5
2
P11 11
8
I11
I8
I10
R0
R4
0
R2
0
R10
0
R7
0
R8
0
R9
0
R6
0
R5
0
0 R11
RI0 RI9 RI11 RI8 RI10 RI2 RI5 RI4 RI3 RI6 RI7 RI1
8) The left side of the outer border gives the Prime Row (P0) and its
transpositions (P3, P1, P4, etc.), the Inversion of the Prime Row (I0) and its
transpositions, the Retrograde of the Prime Row (R0) and its
transpositions and the Retrograde Inversion of the Prime Row (RI0) and
its transpositions.
Music History
Name:__________________________
PART I:
Using the provided excerpt and extracted tone row, continue filling in the matrix
below #7.
PART II:
Create your own tone row. Fill a matrix from your tone row. Compose a brief
piece of music using your prime form and 4 other forms of your original tone row.
This does not have to be completed on the computer; however, you will probably
prefer to listen to your composition.
Music History
Name:__________________________
Note to Number Conversion
C
C#, Db
D
D#, Eb
E
F
F#, Gb
G
G#, Ab
A
A#, Bb
B
=
=
=
=
=
=
=
=
=
=
=
=
0
1
2
3
4
5
6
7
8
9
10 (t)
11 (e)
Music History
I
I
Name:__________________________
I
I
I
I
I
I
I
I
I
I
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
P
R
RI RI RI RI RI RI RI RI RI RI RI RI