The Fredösphere

My research into the exciting new field of nested counterpoint has made progress and today I will share my discoveries. (If you are going to need a glossary for the counterpoint terminology that's coming up, here's one.) I have decided to attempt a two-part canon at the octave. (I toyed with a tritone interval just to show off but decided not to push my luck.) I intuited that a nesting scheme based on the fibonacci sequence would be fun and might be aesthetically pleasing. It turns out, that is the minimum amount of time between entrances of the nested canons, for reasons which I will explain later if I can find a way without this post colasping under its own weight.

This crude chart shows what I mean. I will call the two voices Soprano and Bass, since Merrill and Lynch are probably under some kind of trademark protection. The brackets above the dashed line belong all to the soprano and represent the various entrances of its nested canons. Below the dashed line are those of the bass. At the bottom are beat numbers. I decided to number the beats backwards for reasons which seem compelling to me and may become obvious to you but I just don't feel like trying to articulate.

The soprano is the leader and begins at beat 34. The bass line follows at a time interval of 13 beats. This means that, when everything comes to a halt at beat "0" the base will have been in for 21 beats. These parts are the conventional, outermost canon and are represented by the A brackets.

The first nested canon begins at the B brackets. The leader-follower relationship switches back and forth; I really haven't worked out if that is switching is required, but at least I know it works. The bass' B theme is 13 beats long and the soprano will sing just the first eight beats of it.

Please realize that these inner brackets do not represent new voices entering. They simply represent new canonical relationships coming into play. Therefore, in the bass for example, the first beat of B is exactly the same music as the 9th beat of A (and must be since they are sung by only one voice.)

In a similar way, the soprano then leads with canon C which is five beats long (and the bass sings the first three beats of it) followed by the two beats of canon D, lead by the bass, with the soprano singing only one beat of it.

By the time we reach the end, we have a beat that is heavily burdened with canonical relationships. Extrapolating from the standard rules of how to write a canon systematically, I can see that I will have to start with the last beat and work backwards. This will guarantee that I will end up with a canon that follows all these rules. This working backwards will not unfortunately guarantee that the results will be beatiful. But then, counterpoint was never about beauty, was it? It's all about showing off.

My next installment should be much easier to follow because it will use a musical score instead of some goofy chart. So stay with me.

Sound of a hand briskly slapping your face several times. Odor of smelling salts.

Stay with me! Stay with me!

Labels: NestedCounterpoint