CCARH Publications 

Row Forms in the Serial Works of Schoenberg, Berg, and Webern
Encoded by Justin London, Paul von Hippel, David Huron, Jonas Cartano, Kate Kingery, Bess Olsen, and Tami Santelli. 
Edited, error-checked, and translated to Humdrum format by Paul von Hippel , 2000/2001.
From the README file:

encoded by Justin London, Paul von Hippel, David Huron, Jonas Cartano, Kate Kingery, Bess Olsen, and Tami Santelli
edited, error-checked, and translated to Humdrum format by Paul von Hippel

These files represent tone rows used in the serial works of Schoenberg, Berg, and Webern. Students and scholars may find these files a useful resource in their study of these works.

Data were encoded from three paper sources. Rows by Schoenberg were encoded from an unpublished compilation prepared by Paul Metz in the early 1980s. Rows by Webern were encoded from those given in Kathryn Bailey's *The Twelve-Note Music of Anton Webern* (Cambridge University Press, 1991). Rows by Berg were encoded from Dave Headlam's *The Music of Alban Berg* (New Haven, CT: Yale University Press, 1996). The inclusion of certain rows by Berg may be debated. In Wozzeck and the Chamber Concerto, it has been argued that Berg treats his rows as 12-tone "themes;" and in the Lyric Suite, as in Lulu, all the rows are related to a common source row (though the relationships can be quite indirect). Scholars wishing to ensure an independent sample of proper tone rows may wish to restrict their attention to part of the Berg database; we have left this decision to the discretion of individual researchers.

All data are encoded in the Humdrum format ( Each file begins with reference records identifying the composer, work, date, and sometimes additional information. Each file continues with two parallel spines:
 (1) a **pc spine representing the row in integer notation, with the first note of the row as 0
 (2) a **kern spine representing the prime form using note names in the octave below middle C
(Note that the **kern spine usually begins with a note other than C -- i.e., other than 0 in pc notation.  When converted using the Humdrum "pc" tool, the **kern spine will therefore differ from the **pc spine by a fixed transposition.)

In addition to the usual Humdrum reference records, several special reference records were developed for this database:

  !!!AIR: Indicates an all-interval row.
  !!!DRV: Indicates that the row can be "derived" by transformations of its first 2, 3, 4, or 6 notes.
  !!!IHC: Indicates that the row is inversionally hexachordally combinatorial.
  !!!MIR: Indicates a mirror row, and describes how it can be transformed into itself.
  !!!RKY: Reports a standardized score of the row's key or tonal implications.
               A positive score suggests that the row has strong tonal implications; a negative score suggests that the row seems to avoid tonal implications.
               (The scoring method was developed by Paul von Hippel and David Huron in an unpublished paper.)
  !!!SEM: Reports the row's number of semitone interval classes.
  !!!T33 and !!!T35: Reports the row's number of 3-3 and 3-5 trichords. (Only non-overlapping trichords are considered.)

The database has been subjected to visual inspection and a number of automatic error checks, leading to the correction of over a dozen errors. Specifically, the error checks verified that
 (1) each row represents exactly 12 distinct tones;
 (2) each row contains no invalid signifiers such as a pitch class integer (**pc value) of 19;
 (3) each file is in valid Humdrum format;
 (4) in each file, the integer representation (**pc) is consistent with the note-name representation (**kern);
 (5) the rows display symmetries and relationships remarked by scholars;
In addition, 68 of the rows (schoenberg01-42, webern03-21, berg02,04,05,09,10,17,23) were encoded twice -- once by note name, and once by pc integer. Errors were then corrected by resolving discrepancies between the two encodings. The 42 rows by Schoenberg were encoded a third time, by a different encoder using a different strategy. Comparison against this third encoding revealed no errors that had not been uncovered earlier -- suggesting that there are few if any errors error rate in the double-entered files. Errors remaining in the database are likely to be concentrated in the newest files, which were not double-entered (webern01-02, berg01,03,07,08,11-16,18-22). If you find an error or oversight, please report it to Paul von Hippel (

Scholars using this database should cite it as follows:

 London, J., von Hippel, P., Huron, D., Cartano, J., Kingery, K., Olsen, B., & Santelli, T. (2000/2001). (von Hippel, P., ed.). Row forms in the serial works of Schoenberg, Berg, and Webern. [Computer database.]  Stanford, CA: Center for Computer Assisted Research in the Humanities (

Further information and a precursor to this database are available at