Something similar (though quite simplified?) appears in the opening mvt of all.fall.down., sans tuplets -- he gives normal durations (in 8ths, 16ths, + dots (specks? speckles?)) w/ the instruction that one transitions gradually b/t two rhythmic values (so that, for example, a string of 8ths followed by a string of 16ths followed by a string of 8ths in practice actually moves gradually from an 8th note pulse speeding up to a 16th note pulse and back again). 

But that's not at all what RB's trying to do, so I'm not at all sure why I brought it up.

Thinking about it more (excuse my slowness, I've been moving house), I ought probably not to have used the word "rubato", since this (in etymology), as well as the various tuplet-based ways of doing things, implied a reference tempo against which deviations are placed. Regardless of how such deviations might (be intended to) obscure that pulse completely, my experience as a player of non-notated music would tend to indicate that there doesn't have to be one at all, and that the division of timespans into metre, durations, tuplets and rubato is a product of the evolution of notation rather than the other way around. The question I'm trying to ask might then be rephrased as: is musical notation in principle capable of expressing duration (with more precision than time-space notation) without any kind of underlying pulse? Some, like Peter Wiegold, insist that time-space notation can be regarded as precise, but I'm inclined to doubt this. I suppose it depends on one's notion of precision, as also on one's notion of how a musical score embodies a sense of structure on the level of details.

I suppose it depends how far you want to go in banishing the underlying pulse. In a sense as long as you have quavers, crotchets and minims you have some sort of underlying ratio of fundamental durations, however many tuplets you have. In a lot of time-spacing as well you have the problem (if it's a problem) that the second (or whatever division the score has marked off on it for orientation) itself becomes the de facto underlying pulse.

I don't know whether an analogy with harmony might be worthwhile. There too there are things which various composers have sought to set aside; but on the other hand there are basic acoustic realities to deal with - the octave, for example, which various composers have managed to work around even in a system of notation which at least in part incorporates it as a given. Imagine a system of harmony based purely on vertical orientation without scale divisions - there you're in the realm of graphic notation and debatably the concept of 'harmonic precision' is foreign to such a system.

In the same way I can see how a notion of pulse being present at some level derives from a physical reality, and one even more fundamental than the octave. And there too perhaps if you're going to work around it you're stuck with the system you have. Which itself wouldn't rule out something which puts pulse aside as persuasively as some composers have the octave...

Of course: that's not a million miles away from the sort of thing Richard was talking about finding a notated equivalent for. Richard's question though was "is musical notation in principle capable of expressing duration (with more precision than time-space notation) without any kind of underlying pulse?". It seems to me that if you have precision you have some kind of measurement and and soon as you have some kind of measurement you have some kind of grid you're measuring against...

People in the heady world of physical mensuration do!

"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom."
http://physics.nist.gov/cuu/Units/second.html

Does it matter?  No, I think not, outside of where it obviously matters. Absolute speed certainly not, but rhythmic solidity when performing can be an enormous asset in a whole range of works, neh?

You are clearly wholly ignorant of the excitative effects of that particular occupation.

You actually sort of do in GR; it's just that everybody*'s is different!

(*people within different reference frames)

As for having to have some base pulse, people can also in theory say that about scales, about there being one note, one really really low note, that harmonizes will all of the others within some model.  But it doesn't really work.  I don't see any reason why one can't have a piece of music where notes side by side eachother all have rational interval ratios but that there be no overall sense of meter.  Indeed, such music has surely already been described on this thread.

I think there is actually much less of a difference between Newtonian physics and Einstein's physics than there might appear to be on this issue of absolute versus relative spatial and temporal relations. IMHO the two theories, as scientific theories, are actually both neutral on the question of whether space and time (or space-time in Einstein's case) are independent of the things which inhabit them, or whether they are second order constructions out of relations between those things and events. Newton's physics qua physics is just as relational (in that sense) as is Einstein's. The difference is that he, Newton, chose to embed it in a metaphysical doctrine of absolutism (although this was not necessary for the physics still to work). Einstein, on the other hand, was careful not to do this but his theory could be so embedded without making any difference to his physics. The important point (er, IMHO) is not that one is absolute and one is relational per se but that Einsteinian physics could not be embedded in the same absolutist framework as the one postulated by Newton.

By a strange coincidence there is an interesting chapter on this very question in an admirable B Phil thesis "Conventionality and the A Priori in the Theory of Relativity" lurking somewhere under inches of dust in the basement of the Bodleian Library. 

Not that this is much help with the notation question...