Symmetries suspended and the excluded middle

Two more musicianship exercises. This:
(Another rhythmic trick gathered from Morton Feldman). And this:


Rests in music can be heard (if heard is the right word) in several ways. The most basic, perhaps, is the the Cagean tacet, which is marked only by the temporal structure of a work, and stands in a curious negative relationship to the time outside of that structure, before and after the pieces as well as between movements (Cage's famous 4'33" is a work in three movements, the beginnings and ends of which are articulated by the pianist moving the lid to the keyboard). In Cage's tacet, the time envelope of the piece proper in filled by sensations usually assoicated with the time when music is not played. Then there is the "zero time" of Christian Wolff's cued pieces, which strikes me as making in the unmeasured, out-of-time, breaths and pauses and fermati of ordinary performance practice. (Luigi Nono would greatly elaborate the expressive potential of the fermata in his late works, especially the String Quartet, Fragmente - Stille, an Diotima (1980)).

But here we're dealing with a more traditional type of rest. One type has an edge of unclear or even indeterminate dimensions, into which sounds vanish or out of which they appear. Personally, I'm not much of a fade in/fade out kind of composer, and I don't use the diminuendo al niente marking that are popular among a certain circle*. Another kind of rest, and the one used in the small examples above, has a hard edge, silently articulating a pulse, a metre, the end of a tone, or the gaps between tones. The first exercise confounds a metre, by assigning rests to the points in the measure which articulate the metre most strongly, while the second reinforces the metre and metric changes by only articulating (with one exception) those points.

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* al niente, candles, masks, and stroked wine glasses... How is it that bell-bottom trousers and mood rings went away but we're still stuck with al niente?