Canon Notation




Crab Invention
for viola duo



NOTE: Clicking the "Canon Notation" link above will download the original crab canon notation. Please contact the composer if you need a full score realization for two violas.

This piece was composed in March, 2018 to commemorate the 333rd birthday of J. S. Bach. In order to properly pay tribute to him and his amazingly complex counterpoint, I let this piece develop in ways that require a certain amount of study to fully perceive.

I call it “Crab Invention” because, like a two-part invention, it employs the interplay (or dialogue) of two melodic lines, but is also a crab canon. It begins with two motives (or themes), one in each part that are imitated to create “double counterpoint” (themes exchange voices). Unlike most inventions, though, the two voices continue imitating each other (sometimes in inversion) throughout the piece. Also, because it is a crab canon, the entire piece is a single melodic line that, when accompanied by the retrograde of itself, creates the two-part invention described above. Before the invention proper begins, there is a slow introduction that returns (in reverse) at the end as a coda.

It will be noticed that the German musical notation of B-A-C-H appears in its original form at the beginning of the introduction. When imitated by the second viola, it then sounds as H-C-A-B. When the invention proper begins, the leaping theme presents the notes B-A-C-H while the second part’s theme accompanies it with a transposed version of that pitch motive in a more lyrical form. As the canon/invention progresses, the B-A-C-H motive is transposed further, inverted and even played in retrograde. Similar to a two-part invention, the two original themes return together near the middle of this piece. More like a fugue, however, the main theme is then also played in inverted form. After the midpoint of the piece (marked by a star on the score), all the music heard up to this point gets played backwards, with the original themes appearing in both retrograde and retrograde-inversion. Unlike a typical invention (and because it is a crab canon) the two main themes reappear at the end in retrograde form.

The number 333, or more specifically the number 3, is represented in this piece by phrase lengths and note groupings. Most obvious is that the meter is 3-4 time, but also note groups and bowing slurs often group three notes together (or three groups of 2 notes). Furthermore, the main themes are three measures long, phrase groupings in the introduction and coda are three measures long, and other 3-measure phrases can be heard throughout the piece. The two main themes present hemiola, expressed as 2:3 (or 4:6), whenever they appear together. This helps to link the four notes of B-A-C-H to the number 3 and also gives the music a playful lilt. In some places (m. 17, for example), when hemiola appears in diminution, it helps add a little energy and excitement.

Harmonically, instead of using the B-A-C-H motive in a minor-key environment (as Bach would often do with chromatic themes), I tried harmonizing it with brighter-sounding major thirds and, when possible, M7 chords. It does not follow the “rules” of Bach’s harmony because I felt that my tribute would be more heartfelt when expressed in my own language instead of trying to “improve” on his.

(Duration Ca. 2:30)