Monday, February 2, 2009

Invertible Counterpoint at the Tenth

So, I'm two days into my second month of writing a canon every day and it has yet to become a chore.

Perhaps this makes me a theory geek. (Maggi says "Tell me something I don't already know!")

Today's entry is a canon in invertible counterpoint at the tenth. "Invertible" means that either part can be the bass. "At the tenth" refers to the relationship between the two parts as they are inverted.

This has implications for the manner in which you write the parts. Inversion won't necessarily work simply because the original orientation does. If you don't take into consideration, both orientations, bad voice leading or dissonance treatment may occur. Inversion at the tenth has more strictures than the other common inversions --octave, twelfth (5th plus an 8ve), and fifteenth (two 8ves).

The fun part about this particular type of inversion is that you can convert a two-voice inversion at the tenth into a three-part texture by doubling one of the parts at the tenth.

In my canon, the original orientation is stated first. Then I double the lower part a tenth higher so that the outer parts move in parallel (measures 9-16). Finally, I invert the parts so that the original upper part is now in the bass (a tenth lower). Instead of stating the inversion in two-parts, I double the bass at the tenth above as well here which gives a satisfactory ending.

(click on image to enlarge)

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