Fugue BWV 846
2015
This project on the visualization of Bach’s Fugue BWV 846 was a process of trial and error with the D3 javascript library. As I had just started to learn the basics of the tool, the final results were minimal, however the preceded sketching and research on the musical form was very helpful in developing a visual language for the task.
Here some excerpts of the initial sketchbook, as I started working on the topic:
Musical characteristics of Bach's Fugue BWV 846
Bach's Fugue BWV 846 follows the main principle found in any fugue: the use of a musical phrase, the subject, which is repeated in various sections of the work and on different voices. Subjects reappear either at the original pitch level or as answers starting on a different pitch. Despite any small interval differences that may be found in an answer (mostly due to the different starting point of the subject within the musical scale), both subject and answer refer to the same melodic and rhythmic phrase, which constitutes the core element of the fugue.
Goal of this project was to visually represent the appearance of the subject (and its answers) along Bach's Fugue BWV 846, in order to underline the structural complexity and contrapuntal quality of the musical form. Additionally, it aimed at showcasing the transitions between different tonalities (tonal centers).
Data for this work were based on the Humdrum Kern system, which is used for machine-readable music representation. A humdrum.krn file can be opened with any text editor.
Music score, m. 1-13
Melodic lines and subject appearance
Central focus of the experimentation with D3 was the generation of all melodic lines for the work's four voices: S-Soprano, A-Alto, T-Tenor, B-Bass. The following image shows the four melodic lines, emphasizing with color intensity the parts where the subject appears. The image corresponds to the measures 1-13 of the fugue:
Notice: To better understand which sections of the music carry the subject, you can have a look at http://algomus.fr/fugues/bach/wtc-i-1.html.
Subject allocation across musical measures
Subject across measures
The second visualization was inspired by the arrangement of subjects as displayed in the link above. The goal was to present in a minimalist way the first 13 measures of the music subject. The end-result can be seen in the picture.
In this example, a box is created for each measure, where the subject appears. As it was not possible to alter the length of the boxes, it was also not possible to show the exact beginning and end of each subject. Moreover, because of the thin space between consecutive measures/boxes, one could get the impression that the subject was repeated, although there was only one subject expanded across two measures (e.g. measures 1-2, Alto).
In fact, this problem could have been avoided if I used again the linear chart approach that I used in the first visualization with thicker lines. However, I wanted to try a new approach, namely the stacked bar chart algorithm. Because of that, every measure was handled independently, and this is why there were "splits" within subjects, when measures changed.
Subject allocation across voices
The third and last visualization concentrates on the connection between subject appearances across voices. The goal here is to underline the contrapuntal arrangement of a fugue, showing, for example, how the subject travels from soprano to bass, creating a weaving effect. For this purpose I used a chord diagram, which emphasized the reappearance of the same motives with its circular form and its complex structure. The following example corresponds to measures 1-13 and presents the subject as starting from its first appearance on the top in the alto voice. The viewer can read the diagram clockwise.
Subject across voices