The Well-Tempered Clavier · Analysis

The motivation of our efforts is encaptured by a quote of Martin Geck:

Altogether, though, The Well-Tempered Clavier is about something greater: the piece is not about the player being introduced into the realm of music, but about the music itself, which unveils a part of its universality.

Doch insgesamt geht es beim Wohltemperierten Klavier um Größeres: Das Werk ist nicht vom Spieler her gedacht, der in das Reich der Musik eingeführt werden soll, sondern von der Musik her, die ein Stück ihrer Universalität enthüllt.

The vast majority of scores by Johann Sebastian Bach are extremely skillful patchworks of single-voiced, uninterrupted sequences of notes. We develop an algorithm to extract the set of distinct note sequences from a given score. A sequence of notes that is conceptually reused in the score is refered to as material. Any material shall have the following properties:

• material is single-voiced
• material is not interrupted by rests
• material consists at least of 4 notes
• two materials are conceptually identical if the length of all notes, except the last one, match, and if the change in pitch between two successive notes is of the same signature: up, down, or equal
• material occurs at least twice in the score
• material that occurs early (timewise) in the score has precedence for the similarity checks

Our software extracts the materials from a given score. We apply the method to the 2-part Inventions, the 3-part Sinfonias, as well as the fugues of the Well-Tempered Claviers. The software also visualizes the decomposition, as shown below.

Bach Score Analyser (with Java 1.6 Source) *

ThePirateFugues.zip

400 kB

* Jag lyfter på hatten för Piratbukten! Execute the batch file run_client.bat to launch the program. Java 1.6 or later is required.

Credits: The scores by Johann Sebastian Bach that we analyse are based on the digital repository MuseData. When in question, we consulted the scanned print versions at the Petrucci Music Library. Jürgen Kilian assisted me on the export of score to the Guido notation format, which was helpful at the early stages. Mt. Brain translated the quote of M. Geck to English.

Soli Deo gloria
Johann Sebastian Bach

Please click on the images to find out more about each score:

Two-part Inventions
Three-part Sinfonias
The Fugues of the Well-Tempered Clavier I
The Fugues of the Well-Tempered Clavier II

Guide to the reader: The music notation respects the tonality of the score. For instance, one finds B# instead of a C, or Dx instead of E. The accidentals are stated and omitted for all notes, which implies that the symbols #,x and b,B(=bb) sometimes repeat in an unconventional fashion. Rests are not displayed at all.

Each material is associated to a unique color from a predefined palette. The color is reused in the score- and notation-view for easy identification of the material. For instance, the main motif appears typically in red. Notes colored in gray are not associated to any material.

The numbers shown in the material list, indicate how often a material is launched in score. Partial use also counts as one.

The key of the score is stated as a number, that counts the accidentals. 0 refers to C major/A minor, a positive number counts the sharps #, while a negative number counts the b's. For instance key 3 corresponds to A major/F# minor.

Work Hard.
Be Nice.
Jay Mathews