The Fredösphere

Follow these links for Nesting Instinct, Parts the Ith and IIth.

I kept my promise; don't keep your distance. I have completed the 2-part, quadruply nested counterpoint example. You can listen to a sound file in mp3, and you can see the score in pdf.

Remember that, in the score, there are 4 treble staffs, but they are all for the one soprano part. That's why the measures are all identical vertically. Likewise for the bass. The redundant parts simply represent new layers of canonic relationships. I drew diagonal lines to help you better see each of the four canons in their various entrances.

The result of all these nested canons is that, by measure 34, the soprano part is echoing measures spread throughout the piece: ms. 33 in the bass, which in turn echoes ms. 31 in the soprano, etc. etc. As I guessed (and proved empiracally in one frustrating evening), I had to begin at the end and work backwards. I had to start with the measure with the most canonic freight; otherwise it would need to agree contrapuntally with several contradictory measures.

But that's not quite true. I wanted the first four measures of the piece to be, well, let's just say I wanted it to have a certain distinctive sound. (Listen for yourself to find out what I mean.) It turned out I could write those ahead of time without creating an impossible puzzle.

After measure 34, a kind of shearing occurs and the various canonic relationships become contradictory. Yet that measure doesn't work as an ending. I had made sure measure 34 contained candential material, so I simply added mearsures 35 and 36 and put a tonic chord there as an abrupt close to the piece.

Okay, I solved the puzzle, but does it work musically? I see failure and success here. The canonic relationships don't really grab the ear like I hoped. My original, doubly nested example was much more successful in that regard. The problem is, since measures are reused so much, they don't sound distinctive enough at the canons' entrances. Nevertheless, the mathmatical system gives the whole peice a rigor and form which (to my ear) is detectable on a subjective level. If I may dare make this judgment, I think it's the most tasteful 36 beats of music I've ever written.

Oh, but that brings us to the First Law Of The Fredösphere: Good taste is not enough!