Just a little 12 tone matrix

 12-tone matrix for Weber’s “Wie bin ich froh, No.1 Op. 25”

 

  Io         I11         I8           I10         I9          I6           I3          I7           I2          I5           I4           I1

F#	F	D	E	Eb	C	A	C#	G#	B	Bb	G
G	F#	Eb	F	E	C#	Bb	D	A	C	B	G#
Bb	A	F#	G#	G	E	C#	F	C	Eb	D	B
G#	G	E	F#	F	D	B	Eb	Bb	C#	C	A
A	G#	F	G	F#	Eb	C	F	B	E	Eb	Bb
C	B	G#	Bb	A	F#	Eb	G	D	F	E	C#
Eb	D	B	C#	C	A	F#	Bb	F	G#	G	E
B	Bb	G	A	G#	F	D	F#	C#	E	Eb	C
E	Eb	C	D	C#	Bb	G	B	F#	A	G#	F
C#	C	A	B	Bb	G	E	G#	Eb	F#	F	D
D	C#	Bb	C	B	G#	F	A	E	G	F#	Eb
F	E	C#	Eb	D	B	G#	C	G	Bb	A	F#

RI                       

In “Wie bin ich froh”, Webern uses 12-tone composition to add structure to his piece. The first tone row that appears in the piece is: F#,F,D,E,Eb,C,A,C#,G#,B,Bb,G; this prime form appears many times



throughout the piece but is introduced in the first two bars in the piano accompaniment. Throughout the entire piece aside from the prime form, Webern only uses three other versions of the tone row: Retrograde O, Retrograde Inversion 2, and Inversion 2. The entire piece is composed of these four variations, which is really only two rows, P0 and I2 and their inversions, switching off between each other.


While the piano accompaniment starts off by introducing the prime form, when the melody comes in at measure 3 it does so with RI2. The piano part follows it through RI2 and after reiterating P0 in the piano part and RI2 again in the vocal melody; both piano and voice introduce R0 at measure 7. The piano then moves into I2, and then back to the prime form while the vocal melody stays in RI2 throughout.


After reiterating the prime form, the piano accompaniment ends the piece with R0.


It is interesting how the vocal part only switches between the two retrograde forms (RI2 and R0) while the piano part weaves through all four variations of the twelve tones. The manner in which the piano and vocal parts seem to almost switch off, rarely overlapping adds to the disjointed dissonance, which characterizes the mood of the piece and also allows more room for playing with different structures in each respective part.