Another canon at the fifth.

Busy day today, private lessons all morning and a performance later this afternoon...

But -- the great thing about doing this kind of thing in a public forum like a blog is that it keeps you honest. I had to write a canon today...

So here it is. Simple and to the point. A canon at the fifth for two trumpets -- again in a fairly traditional style.

For a bit of interest, I broke it up into three phrases with a successively higher climax for each.

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Canon over a Handel Bass

When Handel was living in England, he put together a series of lessons in continuo playing and fugal improvisation for Princess Anne, one of the daughters of George II. They are remarkably well-thought out and pedagogically sound. Because the Princess was unusually gifted, Handel took great care in crafting the lessons.

I wrote today’s canon over the bass that was the first of these lessons. I held strictly to the harmonies that Handel calls for -- a series of root position triads.

My choice of canon at the fourth gave me a few challenges but nothing too difficult to overcome. The harmonic progressions are varied, even in this short exercise. In the first two measure the progressions are by fourth or fifth. From the end of measure 2 through measure 4 the progressions are by descending thirds with one interspersed fifth. Starting with the last note of measure 4, the progressions are by mostly ascending seconds with one descending third. The final cadence is, of course, V - I, the reverse of the opening progression.

This simply meant that I had to choose wisely. A little trial and error (or success) and I had it done.

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I’ll likely use the Handel studies as a resource several more times in this project.

Thursday, January 29, 2009 --Canon at the 6th

[I wrote this canon on Thursday but got home too late and tired to post -- here it is:]

Yesterday's canon proved to be easy because the imitation interval of a fifth facilitated circle of fifth progressions to the point of almost making them inevitable. Today I decided to explore another interval if imitation, namely the 6th and explore its relationship to another traditional element of contrapuntal/harmonic language.

My first thought was to try a chain of 7-6 suspensions -- which, of course, could be managed in any imitation interval, if the time interval is right. The 7-6 suspension chain is a contrapuntal cliché (I mean that in a good sense.) that harmonizes a descending scale.

[For the uninitiated: A suspension is a dissonance (in this case, a 7th) that is tied from the previous measure or beat, where it is consonant, and then resolves down by step to another consonance (in this case, a 6th). When the lower voice is descending stepwise through the scale, a chain of these suspensions is possible.]

The examples show the basic, unadorned 7-6 suspension in different imitation intervals and the time interval required to make it happen (for whole notes and tied half notes). As you can see, with the imitation interval of a sixth, the time interval is one half note or half a measure of 4/4 time

Also, in the examples, you'll see the underlying structure of today's canon.

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I elaborated the suspensions with ornamental resolutions and fleshed out the rest with some simple passing tones to differentiate the voices.

As a further "control", I gradually moved from primarily quarter-note motion at the beginning to eighth-note motion at the end by carefully choosing my elaborations -- especially the ornamental resolutions of the suspensions.

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Some of the things I am discovering about harmonic control and contrapuntal clichés in canon writing are informing my technique when improvising. This is not unexpected, but I am surprised at how soon it is manifesting.

Inventio -- a canon at the fifth

I've written a two-part invention in the form of a canon at the fifth.

Since harmonic progressions in fifths are ubiquitous in the common practice era (17th-19th centuries), a very characteristic harmonic language was easy to achieve.

I begin with I - IV - viiº - I, which helps to establish the key. Then I have a middle section that moves though the circle of fifths IV - viiº - iii - vi - ii - V, extending the V for one more measure with the rests in the right hand to set up a recap of the opening section.

I tweak the canon in measure 16 to bring about a cadence.

I should really try one of these at another interval of imitation sometime -- the choice of a fifth definitely made things easier today.

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16th century style canon in augmentation

In one of my classes, today, I used, as an example, a canon in augmentation by Josquin des Prez

It is in the dorian mode on D and has two clear cadences -- a weaker one at measure 5 and a stronger one at the end. "weak" and "strong" are not used here as indicators of quality but rather, referring to relative strength. If every cadence was strong a piece would sound like it was repeatedly starting and stopping. Having different kinds of cadences makes controlling the form of a piece much easier. You usually want your strongest cadence at the end...

In Josquin's canon, both voices start at the same time but the upper voice moves at half the speed of the lower. The lower part completes the canon in measure 10 and continues more freely from there to the end.

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In my canon (also in D dorian), I chose to start the augmentation (in the lower part) one measure later. I used a typical 16th century style cadential figure and a leading tone (C#) to make the first cadence (measure 5) but by having it occur over F (making the interval of a 6th) instead of D (which would have given an octave), this cadence is weaker than the final. After the first cadence, I begin the next section with some imitation to further unify the piece,

I crossed the voices at measure 8 because I wanted to hear the leading tone-to-tonic motion on top.

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a quicky...

I worked this one out on the train this morning -- first making a note against note version and then elaborating it and adding a bass to clarify the harmonies.

Oddly, it reminds me of some of the string parts to the Beatles recordings -- probably the plagal cadence with a suspension.

Pretty simple to understand: The violin part is an inversion of the viola part.

A quick little thing for an overloaded day...

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another one on Perle's 12 tone row

Using the same 12 tone row as yesterday, I've written a very different canon.

This is a canon at the 5th in 2 parts with the upper part being a free voice. By "free" I mean non-canonic. It does seem a bit odd to refer to a melody written on a row as free. I guess it is all relative.

For the two canonic voices, I did not restrict myself in any way -- other than the canon, that is...

The structure of the piece is ABA. I tried to make the B section (measure 7 to 10) a bit more dissonant than the A section -- but not too much so. In a short piece like this, a little contrast is sufficient.

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