A Canon

August 26, 2019 14:04

A ‘canon’ is a polyphonic piece of music in which a musical line, called the ‘dux’ (Latin for ‘leader’, pronounced like ‘ducks’) is repeated in other voices but offset in time. ‘Row row row your boat’ is a well-known example:

The complete piece is generated by having four singers sing this same melodic line — the same ‘dux’; the first singer starts singing the dux alone, then the second singer joins in singing the same dux but starting one bar later, the third singer starting two bars later, etc:

“Row, row, row your boat” is one of the simplest forms of canon — the dux is unchanged when the other voices sing it. In canons more generally various other transformations of the dux can happen, such as the second voice sings the dux backwards, or upside down, or twice as slow.1.

The art in writing a canon is that the final piece should be musical and graceful — not so easy.

In “Row, Row Row Your Boat” one is expected to sing the dux over and over, so its ‘score’ could be represented by a circle:

In a way, the dux functions something like DNA, which you ‘unpack’ to build the complete piece.

Here’s the score to my own new canon:

Here’s an mp3 of the unpacked piece, and a pdf. I’ve unpacked the score as follows:

  1. Introduction: A harp improvisation not based on anything, just to set a mood and get the piece started.
  2. Section A: The dux solo (the larger circle in the score), accompanied by a simple repetitive bass line in the harp (the smaller circle in the score). All the ‘A’ sections are based on the dux.
  3. Section B: A contrasting section, based on a simple mathematical Group Theory transformation — represented by the grid-like pattern in the score. (Treated in a separate blog.)
  4. Section A’: The dux in canon in two voices.
  5. Section B’: The B idea again, but with a different assignment of organ registrations to the threads.
  6. Section A”: The dux in canon in three voices.
  7. Section B’’: The B idea once more, with yet another assignment of organ registrations to the threads.

1 See the Wikipedia article on ‘Canons’()

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