Sunday, January 4, 2009

The gift of plurisignificance

Yesterday's canon exercise left me pondering other issues of harmonic control in canons.  My thoughts leapt to J.S. Bach's Two-part Invention in F major -- a piece that is certainly familiar to anyone who ever got beyond a certain point in piano lessons.  Though it isn't a canon throughout the entirety of the piece, it does have some interesting canonic usage.

We do know that Bach intended these as compositional models as well as pieces to study and perform.  On the title page of the inventions, he states that one of the purposes of the inventions is to "acquire a strong foretaste of composition."

Bach begins this invention with a canon at the octave which continues to the first beat of measure 8.  I've included an annotated excerpt to show what happens harmonically.  Bach first establishes he key with five measures of arpeggios of the tonic chord and scalewise passages that simply elaborate the I chord.  If you follow the 16th notes of the right hand part of measures 4 through 6, you'll see essentially descending thirds (A-C, F-A, D-F) -- which are, of course, answered in the left hand a measure later.

Bach takes advantage of what music theorist Bernhard Ziehn (1845-1912) later called plurisignificance and herein lies the genius of the passage.

The F-A pair first serves as the root and third of an F major chord and then as the third and fifth of D minor. 

The D-F pair is first the root and third of D minor and then the fifth and seventh of G7.

By exploiting the plurisignificance of these diads, Bach is able to move the harmony along rather than have it stagnate in any one chord. See my annotations to the Bach example for clarification.

(Click on image to enlarge)


For my canon, I've also worked with the plurisignificance of thirds in a harmonic environment of descending third progressions:

F# -- F#
D   -- D   --  D
         B   --  B  --  B
                  G  --  G  --  G
                           E  --   E
I        vi       IV     ii       viiº  ---then resolution to I

This is, to be sure, a very typical tonal progression.-- a simple elaboration of tonic --subdominant -- dominant -- tonic.

Following Bach's example, I, too, begin with a few measures of elaborated tonic harmony.

With the addition of a few well-placed accidentals, my canon could also modulate and serve as part of a larger work like a two-part invention.  Perhaps another time...

Here's mine:

(click on image to enlarge)

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