I think this is a superb topic to dwell on and explore.
As far as strict “looping music” and ways to manipulate it via tape and digital to cause information loss, most of what comes to my mind has already been talked about.
However, I thought—especially since I’ve been fascinated by the idea of “sabotaged music” for a long time now—that I’d contribute a few ideas regarding compositional techniques that might be interesting vis-à-vis disintegrating loops.
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The standard minimalist technique of “subtraction” where a repeating figure will have a note subtracted at some point in the cycle. In a motive you could strike a note with every repeat. Or you could strike a note per motive for two repeats, then add one back in, then subtract two, etc. You can also “swap missing notes”, or make notes quieter or shorter or lower in octave instead of deletion. Sky’s the limit.
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Adding dissonance over time. Either via replacing consonant notes or perhaps adding dissonant “ghost notes”. Perhaps imagine dissonance as the equivalent to noise… a form of “masking” the sound.
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Fragmenting the rhythm. Ie. Shifting notes off of downbeats, reconfiguring four 16th notes as a quintuplet with pause (ie 1 2 pause 4 5) etc for all sorts of figures, accenting strange offbeat notes in an “unmusical” ways, etc
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Stretching the motive out with pauses or held notes. Ie. A repeating motive that’s two bars long, could have a 32nd note pause inserted somewhere within the motive on every repeat, making the repeating motive ever longer and more fragmented (ie. 2 bars, 2 bars + 1/32, 2 bars + 1/16,…)
Anyhow, there are lots of other tools, but that’s just to get some ideas flowing.