ROW FORMS
IN THE SERIAL WORKS OF SCHOENBERG, BERG, AND WEBERN

 

This webpage lists the prime forms of rows used in the serial works of Schoenberg, Berg, and Webern. Theory students and scholars alike may find this a useful resource in their study of these works. Complete matrixes have not been included, as they are readily generated using set-analysis software and/or resources available on the web (for useful URLs see below).

This webpage is also a reflection of a pedagogical philosophy: rather than have students comb through the score of a serial work in hopes of finding the prime form of its row (an activity whose pitfalls and limitations are well known), it is far more worthwhile to begin with both the row and an understanding of its intervallic properties, and the proceed to investigate how composers were able to exploit those properties (as well as their constraints) in making their compositional choices. It is hoped that this website helps to engender this pedagogical approach by making the prime forms of these rows readily available.

Each work is listed below in the following format:

COMPOSER: OPUS NUMBER (if applicable)--TITLE
INT: a listing of the row form in integer notation, with the first note of P0 as 0;
PO: a listing of the prime form of the row using note names (all accidentals as sharps).

Thus, by using the "find" command of your browser, you should be able to find a particular work either by name or opus number. By using the "highlight" and "copy" commands you should be able to insert a row listing into a text document or into a matrix and/or interval-calculating application.

These lists are based on a compilation prepared by Paul Metz in the early 1980s. Row forms for Webern are based on those listed by Kathryn Bailey (The Twelve-Tone Music of Anton Webern, Cambridge University Press, 1991). More recent research may have given rise to alternate views of the prime form for some of these works. As a result, this webpage should be viewed as a work in progress, and hence its row listings should not be taken as definitive in all cases. Corrections, emendations, and other suggestions are welcome; where appropriate, alternate prime forms will be added to this webpage. Please send any and all such feedback to jlondon@carleton.edu.


Some Useful Links

This webpage only lists prime forms of rows, rather than a complete matrix for each, because there are a number of other websites that contain matrix-generating software, set-type and interval-content analysis applets, and more. For these applications see:

"Java Set Theory Machine," by Jay Tomlin
http://www.webcalc.net/calc/0515.php

 


Acknowledgments

First, to Prof. Paul Metz of Colorado State University, for allowing us to use the computer-generated list of row matricies he prepared while at the University of Cincinnati (a reminder that graduate-school projects often have a long half-life). Thanks also to Prof. Mauro Botelho of Davidson college for remembering Paul's project and sending us a copy of his printout. Finally, thanks to members of the Winter 2000 20th Century Music Analysis class at Carleton College--Jonas Cartano, Kate Kingery, Bess Olsen, and Tami Santelli--for their careful reading of faded printouts and patient data entry.

Prof. Justin London, Carleton College
February 2000


SCHOENBERG: OP. 23, NO. 5--FIVE PIANO PIECES

INT: 0, 8, 10, 6, 7, 5, 9, 1, 3, 2, 11, 4

P0: C#, A, B, G, G#, F#, A#, D, E, D#, C, F

 

SCHOENBERG: OP. 24--SERENADE, MVT. 4, "SONETT"

INT: 0, 10, 11, 7, 8, 9, 4, 2, 5, 1, 3, 6

P0: E, D, D#, B, C, C#, G#, F#, A, F, G, A#

 

SCHOENBERG: OP. 24--SERENADE, MVT. 5, "TANZSCENE"

INT: 0, 1, 3, 6, 7, 9, 8, 10, 11, 2, 4, 5

P0: A, A#, C, D#, E, F#, F, G, G#, B, C#, D

 

SCHOENBERG: OP.25--SUITE FOR PIANO

INT: 0, 1, 3, 9, 2, 11, 4, 10, 7, 8, 5, 6

P0: E, F, G, C#, F#, D#, G#, D, B, C, A, A#

 

SCHOENBERG: OP. 26--WIND QUINTET

INT: 0, 4, 6, 8, 10, 9, 7, 11, 1, 3, 5, 2

P0: D#, G, A, B, C#, C, A#, D, E, F#, G#, F

 

SCHOENBERG: OP. 27--FOUR PIECES FOR MIXED CHORUS, NO. 1

INT: 0, 11, 8, 2, 1, 7, 9, 10, 4, 3, 5, 6

P0: F#, F, D, G#, G, C#, D#, E, A#, A, B, C

 

SCHOENBERG: OP. 27--FOUR PIECES FOR MIXED CHORUS, NO. 2

INT: 0, 11, 4, 10, 2, 8, 3, 7, 6, 5, 9, 1

P0: C, B, E, A#, D, G#, D#, G, F#, F, A, C#

 

SCHOENBERG: OP. 27--FOUR PIECES FOR MIXED CHORUS, NO. 3

INT: 0, 11, 7, 9, 10, 8, 4, 5, 1, 3, 2, 6

P0: G, F#, D, E, F, D#, B, C, G#, A#, A, C#

 

SCHOENBERG: OP. 27--FOUR PIECES FOR MIXED CHORUS, NO. 4

INT: 0, 2, 9, 5, 7, 3, 10, 11, 1, 8, 4, 6

P0: C#, D#, A#, F#, G#, E, B, C, D, A, F, G

 

SCHOENBERG: OP. 28--THREE SATIRES FOR MIXED CHORUS, NO. 1

INT: 0, 4, 7, 1, 9, 11, 5, 3, 2, 6, 8, 10

P0: C, E, G, C#, A, B, F, D#, D, F#, G#, A#

 

SCHOENBERG: OP. 28--THREE SATIRES FOR MIXED CHORUS, NO. 3

INT: 0, 1, 11, 3, 9, 5, 2, 4, 10, 6, 8, 7

P0: F, F#, E, G#, D, A#, G, A, D#, B, C#, C

 

SCHOENBERG: OP. 29--SUITE

INT: 0, 4, 3, 7, 11, 8, 9, 6, 5, 1, 2, 10

P0: D#, G, F#, A#, D, B, C, A, G#, E, F, C#

 

SCHOENBERG: OP. 30--THIRD STRING QUARTET

INT: 0, 9, 8, 2, 5, 10, 11, 4, 3, 6, 1, 7

P0: G, E, D#, A, C, F, F#, B, A#, C#, G#, D

 

SCHOENBERG: OP. 31--VARIATIONS FOR ORCHESTRA

INT: 0, 6, 8, 5, 7, 11, 4, 3, 9, 10, 1, 2

P0: A#, E, F#, D#, F, A, D, C#, G, G#, B, C

 

SCHOENBERG: OP. 32--VON HEUTE AUF MORGEN

INT: 0, 1, 7, 11, 9, 3, 6, 5, 2, 10, 8, 4

P0: D, D#, A, C#, B, F, G#, G, E, C, A#, F#

 

SCHOENBERG: OP. 33A--TWO PIANO PIECES, NO. 1

INT: 0, 7, 2, 1, 11, 8, 3, 5, 9, 10, 4, 6

P0: A#, F, C, B, A, F#, C#, D#, G, G#, D, E

 

SCHOENBERG: OP. 33B--TWO PIANO PIECES, NO. 2

INT: 0, 2, 6, 4, 10, 9, 7, 11, 8, 5, 1, 3

P0: B, C#, F, D#, A, G#, F#, A#, G, E, C, D

 

SCHOENBERG: OP. 34--ACCOMPANIMENT TO A FILM SCENE

INT: 0, 3, 11, 1, 10, 9, 6, 8, 7, 5, 2, 4

P0: D#, F#, D, E, C#, C, A, B, A#, G#, F, G

 

SCHOENBERG: OP. 35--SIX PIECES FOR MALE CHORUS, NO. 1

INT: 0, 9, 1, 3, 2, 11, 6, 8, 7, 4, 10, 5

P0: D, B, D#, F, E, C#, G#, A#, A, F#, C, G

 

SCHOENBERG: OP. 35--SIX PIECES FOR MALE CHORUS, NO. 2

INT: 0, 3, 1, 7, 6, 8, 11, 5, 4, 9, 10, 2

P0: F#, A, G, C#, C, D, F, B, A#, D#, E, G#

 

SCHOENBERG: OP. 35--SIX PIECES FOR MALE CHORUS, NO. 3

INT: 0, 3, 4, 5, 2, 9, 6, 7, 1, 8, 11, 10

P0: D#, F#, G, G#, F, C, A, A#, E, B, D, C#

 

SCHOENBERG: OP. 35--SIX PIECES FOR MALE CHORUS, NO. 5

INT: 0, 6, 9, 1, 2, 10, 7, 3, 11, 5, 4, 8

P0: C#, C, A#, D, D#, B, G#, E, C, F#, F, A

 

SCHOENBERG: OP. 36--CONCERTO FOR VIOLIN AND ORCHESTRA

INT: 0, 1, 6, 2, 7, 9, 3, 4, 10, 11, 5, 8

P0: A, A#, D#, B, E, F#, C, C#, G, G#, D, F

 

SCHOENBERG: OP. 37--FOURTH STRING QUARTET

INT: 0, 11, 7, 8, 3, 1, 2, 10, 6, 5, 4, 9

P0: D, C#, A, A#, F, D#, E, C, G#, G, F#, B

 

SCHOENBERG: FRAGMENT OF PHANTASIA FOR PIANO (FOUR HANDS)

INT: 0, 4, 2, 5, 3, 7, 11, 10, 1, 8, 9, 6

P0: C#, F, D#, F#, E, G#, C, B, D, A, A#, G

 

SCHOENBERG: FRAGMENT OF SONATA FOR ORGAN

INT: 0, 6, 10, 2, 8, 1, 7, 5, 9, 4, 11, 3

P0: C#, G, B, D#, A, D, G#, F#, A#, F, C, E

 

SCHOENBERG: FRAGMENT FOR PIANO (FOUR HANDS)

INT: 0, 3, 6, 1, 7, 8, 2, 5, 11, 4, 10, 9

P0: F#, A, C, G, C#, D, G#, B, F, A#, E, D#

 

SCHOENBERG: OP. 41--ODE TO NAPOLEON

INT: 0, 11, 3, 4, 8, 7, 2, 1, 5, 6, 10, 9

P0: C#, C, E, F, A, G#, D#, D, F#, G, B, A#

 

SCHOENBERG: OP. 42--CONCERTO FOR PIANO AND ORCHESTRA

INT: 0, 7, 11, 2, 1, 9, 3, 5, 10, 6, 8, 4

P0: D#, A#, D, F, E, C, F#, G#, C#, A, B, G

 

SCHOENBERG: DIE JAKOBSLEITER

INT: 0, 1, 4, 3, 7, 6, 11, 2, 10, 9, 5, 8

P0: C#, D, F, E, G#, G, C, D#, B, A#, F#, A

 

SCHOENBERG: OP. 44--PRELUDE TO A SUITE FROM "GENESIS"

INT: 0, 8, 4, 7, 6, 2, 1, 10, 3, 5, 11, 9

P0: A#, F#, D, F, E, C, B, G#, C#, D#, A, G

 

SCHOENBERG: OP. 45--STRING TRIO

INT: 0, 8, 1, 7, 2, 11, 9, 6, 4, 5, 3, 10

P0: D, A#, D#, A, E, C#, B, G#, F#, G, F, C

 

SCHOENBERG: OP. 46--A SURVIVOR FROM WARSAW

INT: 0, 1, 6, 2, 10, 9, 5, 4, 11, 3, 7, 8

P0: F#, G, C, G#, E, D#, B, A#, F, A, C#, D

 

SCHOENBERG: OP. 47--FANTASY FOR VIOLIN AND PIANO

INT: 0, 11, 3, 1, 7, 9, 5, 6, 2, 4, 10, 8

P0: A#, A, C#, B, F, G, D#, E, C, D, G#, F#

 

SCHOENBERG: OP. 48--THREE SONGS, NO. 1, "SOMMERMUD"

INT: 0, 1, 11, 5, 2, 4, 3, 9, 10, 6, 8, 7

P0: C#, D, C, F#, D#, F, E, A#, B, G, A, G#

 

SCHOENBERG: OP. 48--THREE SONGS, NO. 2, "TOT"

INT: 0, 1, 7, 11, 8, 2, 6, 5, 10, 9, 3, 4

P0: D, D#, A, C#, A#, B, G#, G, C, B, F, F#

 

SCHOENBERG: OP. 48--THREE SONGS, NO, 3, "MADCHENLIED"

INT: 0, 6, 8, 10, 2, 4, 9, 5, 3, 11, 7, 1

P0: C#, G, A, B, D#, F, A#, F#, B, C, G#, D

 

SCHOENBERG: ISRAEL EXISTS AGAIN

INT: 0, 3, 4, 9, 11, 5, 2, 1, 10, 8, 6, 7

P0: C, D#, E, A, B, F, D, C#, A#, G#, F#, G

 

SCHOENBERG: OP. 50A--THREE TIMES A THOUSAND YEARS

INT: 0, 2, 11, 9, 10, 4, 3, 7, 5, 6, 8, 1

PO: G, A, F#, E, F, B, A#, D, C, C#, D#, G#

 

SCHOENBERG: OP. 50B--DE PROFUNDIS

INT: 0, 6, 5, 1, 11, 7, 4, 8, 9, 3, 2, 10

PO: D#, A, G#, E, D, A#, G, D, C, F#, F, C#

 

SCHOENBERG: OP. 50C--MODERN PSALMS, THE FIRST PSALM

INT: 0, 11, 8, 4, 7, 3, 1, 5, 2, 6, 9, 10

PO: E, D#, C, G#, A, G, F, A, F#, A#, C#, D

 

SCHOENBERG: MOSES AND ARON

INT: 0, 1, 7, 5, 6, 4, 10, 8, 9, 11, 2, 3

PO: A, A#, E, D, D#, C#, G, F, F#, G#, B, C

 


BERG: CHAMBER CONCERTO

INT: 0, 8, 6, 10, 3, 4, 7, 9, 1, 2, 5, 11

PO: B, G, F, A, D, D#, F#, G#, C, C#, E, A# 

 

BERG: WOZZECK, ACT I, SCENE 4 "PASSACAGLIA"

INT: 0, 8, 4, 10, 9, 3, 1, 7, 6, 2, 5, 11

PO: D#, B, G, C#, C, F#, E, A#, A, F, G#, D

 

BERG: LYRIC SUITE PRIMARY ROW

INT: 0, 11, 7, 4, 2, 9, 3, 8, 19, 5, 6

PO: F, E, C, A, G, D, G#, C#, D#, F#, A#, B

 

BERG: LYRIC SUITE, LAST MVT. PERMUTATION

INT: 0, 1, 5, 11, 8, 4, 9, 3, 2, 10, 7, 6

PO: F, F#, A#, E, C#, A, D, G#, G, D#, C, B

 

BERG: DER WEIN

INT: 0, 2, 3, 5, 7, 8, 11, 4, 6, 10, 9, 1

PO: D, E, F, G, A, A#, C#, F#, G#, C, B, D#

 

BERG: LULU: PRIMARY ROW

INT: 0, 4, 5, 2, 7, 9, 6, 8, 11, 10, 3, 1

PO: C, E, F, D, G, A, F#, G#, B, A#, D#, C# (Jarman)

 

BERG: LULU, ACT I , SCENE XX -- PERM. (EVERY 7TH NOTE OF PRIMARY ROW)

INT: 0, 8, 5, 10, 7, 1, 6, 4, 11, 2, 3, 9

PO: A#, F#, D#, G#, F, B, E, D, A, C, C#, G

 

BERG: LULU, ACT II, SCENE 1 -- PERM. (EVERY 5th NOTE OF PRIMARY ROW)

INT: 0, 9, 3, 2, 11, 4, 6, 1, 7, 10, 5, 8

PO: A#, G, C#, C, A, D, E, B, F, G#, D#, F#

 

BERG: CONCERTO FOR VIOLIN AND ORCHESTRA

INT: 0, 3, 7, 11, 2, 5, 9, 1, 4, 6, 8, 10

PO: G, A#, D, F#, A, C, E, G#, B, C#, D#, F

 


 

WEBERN: OP. NO. 17, no. 1, "ARMER SUNDER, DU"

INT: 0, 11, 6, 7, 4, 5, 8, 9, 10, 1, 2, 3

PO: B, A#, F, F#, D#, E, G, G#, A, C, C#, D

 

WEBERN: OP. 17, NO. 2, "LIEBSTE JUNGFRAU"

INT: 0, 11, 10, 6, 7, 1, 2, 5, 4, 3, 8, 9

PO: C#, C, B, G, G#, D, D#, F#, F, E, A, A#

 

WEBERN: OP. 17, NO. 3, HEILAND, UNSERE MISSETATEN . . . "

INT: 0, 9, 8, 7, 11, 10, 4, 5, 6, 3, 2, 1

PO: G#, F, E, D#, G, F#, C, C#, D, B, A#, A

 

WEBERN: OP. 18, NO. 1, "SCHATZERL KLEIN"

INT: 0, 11, 5, 8, 10, 9, 3, 4, 1, 7, 2, 6

PO: C, B, F, G#, A#, A, D#, E, C#, G, D, F#

 

WEBERN: OP. 18, NO. 2, "ERLOSUNG"

INT: 0, 3, 11, 2, 10, 1, 9, 5, 8, 4, 7, 6

PO: F#, A, F, G#, E, G, D#, B, D, A#, C#, C

 

WEBERN: OP. 18, NO. 3, "AVE, REGINA C0ELORUM"

INT: 0, 11, 3, 2, 1, 7, 6, 10, 9, 8, 5, 4

PO: E, D#, G, F#, F, B, A#, D, C#, C, A, G#

 

WEBERN, OP. 19, NO. 1, "WEISS WIE LILIEN"

INT: 0, 3, 11, 10, 8, 2, 1, 6, 7, 4, 9, 5

PO: G, A#, F#, F, D#, A, G#, C#, D, B, E, C

 

WEBERN, OP. 19, NO. 2, "ZIEHN DIE SCHAFE"

INT: 0, 8, 1, 10 ,11, 4, 3, 9, 7, 6, 2, 5

PO: G#, E, A, F#, G, C, B, F, D#, D, A, C#

 

WEBERN: OP. 20--STRING TRIO

INT: 0, 11, 6, 5, 10, 9, 1, 2, 7, 8, 4, 3

PO: G#, G, D, C#, F#, F, A, A#, D#, E, C, B

 

WEBERN: OP. 21--CHAMBER SYMPHONY

INT: 0, 3, 2, 1, 5, 4, 10, 11, 7, 8, 9, 6

PO: F, G#, G, F#, A#, A, D#, E, C, C#, D, B

 

WEBERN: OP. 22--QT. FOR VIOLIN, CLARINET, TENOR SAX, AND PIANO

INT: 0, 9, 8, 11, 10, 2, 3, 4, 5, 7, 1, 6

PO: F#, D#, D, F, E, G#, A, A#, B, C#, G, C

 

WEBERN: OP. 23--THREE SONGS

INT: 0, 7, 11, 8, 2, 10, 6, 9, 5, 4, 1, 3

PO: G#, D#, G, E, A#, F#, D, F, C#, C, A, B,

 

WEBERN: OP. 24--CONCERTO FOR NINE INSTRUMENTS

INT: 0, 11, 3, 4, 8, 7, 9, 5, 6, 1, 2, 10

PO: B, A#, D, D#, G, F#, G#, E, F, C, C#, A

 

WEBERN: OP. 25--THREE SONGS

INT: 0, 9, 8, 11, 6, 10, 7, 4, 3, 5, 2, 1

PO: G, E, D#, F#, C#, F, D, B, A#, C, A, G#

 

WEBERN: OP. 26--DAS AUGENLICHT

INT: 0, 2, 1, 4, 3, 7, 8, 5, 9, 6, 10, 11,

PO: G#, A#, A, C, B, D#, E, C#, F, D, F#, G

 

WEBERN: OP. 27--VARIATIONS FOR PIANO

INT: 0, 8, 7, 11, 10, 9, 3, 1, 4, 2, 6, 5

PO: D#, B, A#, D, C#, C, F#, E, G, F, A, G#

 

WEBERN: OP. 28--STRING QUARTET

INT: 0, 11, 2, 1, 5, 6, 3, 4, 8, 7, 10, 9

PO: C#, C, D#, D, F#, G, E, F, A, G#, B, A#

 

WEBERN: OP. 29--CANTATA I

INT: 0, 8, 11, 10, 2, 1, 4, 3, 7, 6, 9, 5

PO: D#, B, D, C#, F, E, G, F#, A#, A, C, G#

 

WEBERN: OP. 30--VARIATIONS FOR ORCHESTRA

INT: 0, 1, 4, 3, 2, 5, 6, 9, 8, 7, 10, 11

PO: A, A#, C#, C, B, D, D#, F#, F, E, G, G#

 

WEBERN: OP. 31--CANTATA II

INT: 0, 3, 11, 10, 2, 9, 1, 5, 4, 8, 7, 6

PO: F#, A, F, E, G#, D#, G, B, A#, D, C#, C