Tuesday, March 31, 2009

Canon at the fifth on a blues scale

This is the scale that I used for today's canon:

C Eb E F G Bb B C

Since this scale has two equal tetrachords (m3, m2, m2) it is conducive to a canon at the fifth. However, when the range of the melody exceeds the fourth that contains that tetrachord, the intervals are no longer exact.

Rather than considering that to be a liability, I've taken advantage of it to provide a bit more variety than I would have otherwise gotten.

(click on image to enlarge)

Monday, March 30, 2009

Canon at the Second on the Lydian Dominant Scale

The scale that I used in today's canon is derived from the overtone series.

C D E F# G A Bb C

"Lydian" refers to the #4 and "dominant," to the b7.

I made it a canon at the second so that most of the intervals of the opening phrase would be exactly replicated in the comes.

(click on image to enlarge)

Sunday, March 29, 2009

A Canon after Mozart

Today, while sight reading Mozart's Piano Sonata in c minor (K. 457), I noticed a little canon at the beginning of the coda to the first movement. It's only a few measures long and descends harmonically in thirds from I to VI to viiº7/V.

Here's an excerpt:
(click on image to enlarge)

I decided to pattern my entry for today after this Mozart model but to carry it on for several more measures. Mine descends in thirds fro I to VI to IV to N (the Neapolitan chord -- bII then cadences -- viiº7/V -- I 6/4 -- V7 -- I.

It is a canon at the fifteenth until measure 7 and then contracts to an octave for m. 7-8.

(click on image to enlarge)

Saturday, March 28, 2009

Canon at the third (over a bass)

Using a bass adapted from the Handel lessons for Princess Anne, I've written a canon at the third.

This type of thing is very easy --just the thing when I need a bit of a break.

(click on image to enlarge)

Friday, March 27, 2009

Another Canon on the Same Bass

I've used the same bass (from Handel) as yesterday-- but, this one is a bit unusual.

It is a canon at the third but the rhythmic distance begins at two beats and, at the end of the 3rd measure, contracts to one beat. At the fifth measure, the pitch canon ends but rhythmic imitation at two beats preserves the unity of the piece.

(click on image to enlarge)

Thursday, March 26, 2009

Another Canon over a Handel Bass.

Back on January 30th, I took a bass from the lessons that Handel gave to Princess Anne of England and set a canon over it.

I've done the same today with a different bass from the same lessons.

(Click on image to enlarge.)

Wednesday, March 25, 2009

Pushing this scale a bit farther

So, I'm still using the same scale and trying to wrestle more from it.

To recap -- it is made of two major triads a tritone apart. C and F# for example.

Today I wrote a canon at the fifth. One scale (the lower) is C and F#, the other is G and C#.

A simple canon that wears its tritone on its sleeve--starting in C major and ending in F#.

(click on image to enlarge)

Tuesday, March 24, 2009

Another Take on Inversion

This scale that I have been using has an interesting property. Its complement is also its inversion.

This feature inspired today's canon.

(click on image to enlarge)

Monday, March 23, 2009

Perpetually Descending Chorale/Canon

Using a technique that I worked with way back on January 3rd, I have written another chorale/canon. This one is on the same scale I've been using for the last few days.

The title refers to the fact that this canon can descend indefinitely -- of course, depending on the range of the instruments and the limits of good taste.

(click on image to enlarge)

Sunday, March 22, 2009

Using the same scale again, I worked with implied harmonies.

There are only two complete triads in this scale: C and F#.

I've implied G minor and C# minor using contrary motion and, in the case of the G minor, by means of the traditional resolution of a tritone.

I have included chord names below the staff to clarify my intent.

(click on image to enlarge)

Saturday, March 21, 2009

Spring (at last)

Another canon on the same scale as yesterday.

This one is at the octave.

(click on image to enlarge)

Friday, March 20, 2009

Major chords and tritone

This canon is composed on a scale that is built on two major chords a tritone apart:

E and Bb.

The tritone divides the octave exactly in half and therefore gives a great resource for symmetry.

I start by arpeggiating the chords -- one in each part, right at the beginning to kind of stake out the territory.

It's really quite straightforward.

(Click on image to enlarge)

Thursday, March 19, 2009

Mensuration Canon on the Enharmonic Pentatonic

This is a mensuration canon in which the lower part plays the first two measures worth of the upper melody in dotted quarters while the upper part moves in sixteenths.

It is in the same enharmonic pentatonic as yesterday's canon.

(click on image to enlarge)

Wednesday, March 18, 2009

Enharmonic Pentatonic

Here is a canon on an ancient Greek scale.

The enharmonic has a number of interesting forms. The one I used today is its pentatonic.

It works like this:

Two tetrachords each spanning a perfect fourth (the ratio 4:3) and connected by a whole step (9:8).

Each tetrachord contains a descending Major third and a half step.


C Ab G F Db C

(click on image to enlarge)

Tuesday, March 17, 2009

Dlí Port

Beannachtaí na Féile Pádraig agaibh!
(Blessings of the Feast of Patrick to you)

Here is a little canon/jig for St. Patrick's day.

I wrote about half of it in my head while walking to town to do some errands. I finished up when I got home.

(Click on image to enlarge)

Monday, March 16, 2009

a quicky...

Busy day, today. Business meetings and spring cleaning.

So, I took the easy way out today. I took the rhythms from an earlier rhythmic canon and filled in pitches for a canon at the unison. I took care to make the voice crossings smooth.

That's about it.

(click on image to enlarge)

Sunday, March 15, 2009

Rendering unto Caesar ...

Since today is the Ides of March, I render unto Caesar -- a lament.

It is based on the letters of his name

C, A, E, Eb ("es" or "s" in German note names), A, and for "R" -- a rest.

Not much else to say about it.

Interesting... you can't spell Marcus Brutus using notes...

(click on image to enlarge)

Saturday, March 14, 2009

Fanfare Canon for Pi Day 3.14

In celebration of Pi Day, here is a fanfare-canon.

The rhythms and pitches are represented by the following numbers (of course):
3 1 4 1 5 9 6 5 and then 8 to enable an ending on the tonic.

(click on image to enlarge)

Friday, March 13, 2009

I was thinking about the Balinese Kecak (also called the Monkey Chant) today and I remembered that it has canonic features as well. These are quite difficult to hear because of the complexity of the resulting texture and the number of parts.

Here is one of a number of versions on you tube:


It is a bit easier to see on my transcription (of another version -- there are many).

The canons are as follows (all based on a sixteenth note unit):

--the first three parts are based on 3, 3, 2

--parts 5 & 6 are based on 3, 3, 3, 3, 2, 2
part 4 is very closely related to these two with 3, 3, 3, 3, 4

(click on image to enlarge)

My canon for today is a cak in 9/8 time which results in a kind of Irish Slip Jig-Cak.

There are two canons in the cak parts:

--the first 3 parts are based on an eighth note unit -- 2, 1, 5, 1

--parts four through six are based on sixteenth notes -- 3, 7, 6

I've also included a vocal ostinato canon in four voices to create a dorian mode harmonic accompaniment. This is a canon with two voices in unison and another with two a fifth above the first. Both of these imitate at one measure distance.

(click on image to enlarge)

Friday, March 13, 2009

Thursday, March 12, 2009

A technique from Elliot Carter that he called tempo modulation but is commonly called metric modulation.

His term makes more sense. Through a series of meter changes the tempo of a piece is made to change (either faster or slower) in a controlled manner.

In this canon, I have written a tempo modulation that speeds up. First I establish the dotted quarter note beat in 6/8 and then speed up the pulse by moving to a quarter note beat in 2/4. Then I maintain that beat rate but change the beat back to a dotted quarter.

(click on image to enlarge)

Wednesday, March 11, 2009

A different kind of retrograde.

A second canon on the row from Webern's Symphony Op. 21.

For this one, I made an unusual kind of retrograde canon.

I made the upper part from O and I and the lower from RI and R. All this seems to create the the retrograde in the lower part. However, the retrograde in time points ends up being quite a different thing. Here the retrograde is 4 measures lone, for instance. (I repeated the first for bars of the upper part...)

So, even though I used the exact numerical retrograde, I have an entirely different type of musical retrograde.

(click on image to enlarge)

Tuesday, March 10, 2009

Canon after Webern

Using time points again, I made this rhythmic canon in three parts from the row that Webern used in his Symphony op.21.

0, 3, 2, 1, 5, 4, 10, 11, 7, 8, 9, 6

Of course, Webern used the row as pitch classes, not time points but he was fond of canon...

(click on image to enlarge)

Monday, March 9, 2009

Canon on two different rhythmic techniques

I'm trying to find less common ways to make canons. In this one I've used another rhythmic technique from the arsenal of Milton Babbitt. This one is the time-point system.

Essentially, the system sets up a series of time points upon which the rhythm of a piece is built. A series of numbers is again used for the rhythmic materials but this series refers to points on a time continuum. I've chosen six points (0 to 5) in each measure of 6/8 time.

The numbers are then used as they occur in the series. Babbitt has used this technique with 12 time points as a parallel to the twelve pitches of the chromatic scale. It enables him to perform the same operations on rhythm as he does on pitch.

Again, I'm not trying to imitate Babbit's sound or technique here -- just borrowing an interesting idea to use in my own way...

I've decided to make my canon from both the time-point system and duration rows (introduced a few days back).

I've chosen a rhythmic row 1, 5, 3, 4, 2 and turned it into a palindrome by using O. I, RI, R:

15342, 51324, 42315, 24351

I treated this series a duration row in the upper part and in time-points for the lower part.

So, the same numbers form both parts but they are quite different. I have a feeling that this type of idea may be fertile ground for me when I reintroduce pitch to my canons in a few days.

(click on image to enlarge)

Sunday, March 8, 2009

Another "hidden" canon

This one uses the canon from February 26 and hides it in a manner similar to yesterday's entry.

I altered the same notes in both parts but I altered them in different ways. Ithe measure one I added grace notes before the second half note but in the lower part (meas. 2), I replaced that note with a rest.

In places that I altered notes by dividing them in one part, i divided the other with different note values.

I find this to be an interesting way of working and may explore it further.

(click on image to enlarge)

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.

(click on image to enlarge)

Saturday, March 7, 2009

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.


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.

(click on image to enlarge)

Thursday, March 5, 2009

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...

(click on image to enlarge)

Wednesday, March 4, 2009

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.

(click on image to enlarge)

Tuesday, March 3, 2009

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.

(click on image to enlarge)

Monday, March 2, 2009

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.

(click on image to enlarge)

Sunday, March 1, 2009

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.

(click on image to enlarge)

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