30 January 2015

About that Requiem... (enter the "3D fugue")

I just discovered a level of fugal polyphony that, as far as I know, not even Bach attempted. (But Mozart did, or was beginning to at least.)

This is a variation of the multiple fugue (double, triple etc.). However, instead of developing the first subject, than the second later, and so on, this is a fugue with the subjects being developed at the same time. In other words, a "three-dimensional fugue", with fugues layered on top of fugues. If the fugue is the musical equivalent of chess, than this is the music equivalent of 3D chess.

It just so happens that a two-by-two fugue has been written: the Kyrie from Mozart's Requiem. Here it is again; start at 4:46:


I'm writing a three-by-three example in the Second Symphony, fourth movement (Massachusetts), and the final reprise of the Ouverture in the First Symphony has a two-by-four-voice fugue.

(It's not quite the same as the twelve-part "group fugue" in the sixth movement of my First Symphony--that's a four-voice fugue, with each voice harmonized in three parts, but it is another example of a 3D fugue.)

Also, what I'm talking about would be an example of what could be called "hyperpolyphony". The best established example, from the Renaissance, would be Thomas Tallis' Spem in alium:


This isn't a fugue, but it's still 40-voice polyphony.

But does this mean that someday I have to write a 40-part fugue?

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