Saturday, March 7, 2009

Hidden Canon.

I made this canon by taking the same duration row (in fact, the same canon) as February 28th and disguising it in the following manner:

In the upper part, I changed every third number in the row into a rest of the same duration. In the lower part, I articulated each unit of every third number.

Fairly simple, really but it hides the fact that it is still a mensuration canon.

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Friday, March 6, 2009

Tomorrow, Maggi and I are giving a workshop on folk hymns to the Merrimack Valley Chapter of the American Guild of Organists. We'll be presenting hymns from the shape note, Shaker, and Celtic traditions and talking about issues of style and performance practice.

I always feel compelled to try to combine my various disparate projects together in some way.

So....

Here's a canon on a old Shaker hymn that we will be doing in tomorrow's workshop.. In the spirit of the title (and first line), I've kept it simple.

It's a canon at the unison -- the pentatonic nature of the tune (and the general strength of the melody) makes even the mild dissonance of A against G sound good and traditional.

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palindrome, retrograde and paradox

In this canon, I use the same duration row as I did for Monday's. This time I used only the original (O) and inversion (I) for the upper part. In this way I could make a canon in retrograde by using RI followed by R in the lower part.

If I had kept the palindromic structure of Monday's canon, I wouldn't have been able to make a canon in retrograde...or would I?

Since a palindrome is its own retrograde, perhaps every simple canon on a palindrome is also a retrograde canon.

This puts me in mind of Messiaen's non-retrogradable rhythms. These are simply rhythms that read the same left to right as they do right to left -- in other words palindromes. They are non-retrogradable because they are their own retrograde.

A nice little paradox...

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Cage's square root form

Thinking about square root day, yesterday, I remembered John Cage's square root form.

It works like this:

The overall form is the short form (phrase level) squared. So, to use today's canon as an example. Five measure opening phrase -- 25 measure overall form.

But the real key is that the features that are present in the short form are also exemplified by the large form and each of the other parts of that form.

Again, this canon is 5 squared or 25 measures long. The overall form divides 10 + 10 + 5.

Each 5 measure section divides 2 + 2 + 1 -- This structural rhythm is also stated twice at the beginning by the dux and then, of course by each comes.

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In honor of Square Root Day

Square Root Day -- March 3, '09

A hint for the less mathematically inclined (read:" less geeky"):

3 x 3 = 9

In honor of this day, some choose (I kid you not) to eat root vegetables cut into squares. I choose to write a canon based on threes and nines.

In keeping with the current rhythmic canon set and the activities of the last few days, I again decided to work in a duration row. That row is 3, 5, 4, 2, 1.

I composed a canon in four parts in 9/8 time (of course). I used O in the upper part and then descending: I, R, and RI.

I chose the durations one through five because they total fifteen -- five beats of 3 divisions. Since 9/8 time has three beats of three divisions the pattern will cycle back to its original starting point after three repetitions.

The parts are aligned in such a way as to produce little bursts of 3 eighth motes on some of the beats.

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More work with duration rows

Also based on a duration row, this one is a rhythmic canon in six parts.

The row is 3, 4, 2, 5, 1, 6, 7 -- this time I made the row myself rather than borrowing one.

I set it in 7/8 time using the eighth note as the unit duration so that the row would take exactly 4 measures. To create the piece I followed the original with the inversion (see Saturday's entry) and then RI and R.

The whole canon theme is:

3 4 2 5 1 6 7, 5 4 6 3 7 2 1, 1 2 7 3 6 4 5, 7 6 1 5 2 4 3

Constructed this way it makes a palindrome again -- I do have a predilection for such things. I also purposely put "2 1 1 2" together in the middle to have a sort of iterative climax.

There is much independence between the parts again here and the resultant rhythm becomes more dense to the climax and then thins somewhat.

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Four-part rhythmic canon

Today's canon is based on the same rhythmic "theme" as yesterday's.

Interestingly, it works nicely as a four-part canon. What I like about is is the rhythmic independence between the parts and the way the resultant rhythm (the combined iterations of all parts together) becomes more dense around the middle (to every eighth note) and then thins again to the end.

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I'll likely use some of these as a basis for pitched canons, later.