Since then I have, as it happens, spent a fair amount of time listening to and reading the work of Frank Denyer, who in a 2009 article entitled "Some Thoughts About Linear Microtonality" makes the fascinating observation (which he has empirically tested) that musicians tune intervals – even octaves – differently if they can sound both pitches simultaneously and if they cannot. He comments that "This appeared to demonstrate two different ways of being 'in tune'. The question is: being in tune with what?"
This seems to me a crucial question. Tuning is relational. Yes, it provides a route to extrapolate from strictly musical questions to those with wider social import. But even before we get to that point it indicates that there might be a continuum between the literal and figurative uses of the term "in tune". Starting from unusual pitch relationships (that which appears out of tune is just an unfamiliar way of being in tune), we could move to the idea that pitch might not even be what one is attempting to be "in tune with" at that particular moment. Can one be "in tune" timbrally, rhythmically or dynamically? We know that the difference between what we hear as a timbral change and a pitch change can be fundamentally a matter of frequency - as, of course, is rhythm. Composers as diverse as John Zorn and James Saunders have produced work whose sounds express the extent to which an ensemble is "in tune" temperamentally. (In the sense of their personalities and behaviours, that is, not their chosen tuning systems, although perhaps this polysemy – originating in the Latin for a "correct mixture" – is not without interest.) From that point, the concentric circles can go ever wider.
Denyer observes: "While working in Kenya’s Kerio Valley I noticed that lyre players could consider two strings to have an octave relationship and be acceptably in tune even when one of them was more than a hundred cents away from the 2:1 harmonic ratio. This is probably because they employ a gamut of just five notes, somewhat casually spread out between the octave, so the identity of adjacent notes is never compromised, and the essential pitch relationships remain the same, making them indeed in tune."
Also interesting is the sense of boundaries evoked by the term: we can be "in" and "out" of tune. We can also be "in bounds" or "out of bounds" (grammatically cognate constructions), and there are "upper bounds" and "lower bounds". Hence thinking about the co-ordination of pitch and other musical parameters brings us to think about space. A number of the "paragraphs" of Cardew's composition (in particular Paragraph 4, for voices, drumming on cushions, gueros & organ, and Paragraph 7, for voices) made clear to me that the relationship between physical space and pitch space is not purely metaphorical. Different pitches really do have differently sized sound waves, and contrasts of proximity to sound source and of volume seem to help make one aware of this.
There's a lot here that I need to ponder!