Interesting analogy, though frankly it seems a bit vague to me (I never was one for applied science
). I'll zero in on the primary musical statement:
So rubato affects tempo NOT rhythm (except in the context of said tempo). If you play "rubato" on the first beat of three consecutive measures, or in a figure that is featured repetitively then what you're doing (I would argue) is not rubato, its dissruption of the rhythm.
Again, I don't think this is quite right, or at least an oversimplification. The rhythm with a uniform pattern is not really being substantively
altered because its internal pulse is consistent and the same and you can't completely
alter that when applying rubato, just change its internal consistency. It's different than playing an entirely different rhythm that indeed would result from one's negligence in keeping time. The end of the exposition of the late Haydn E-flat Major sonata is one example that popped into my head; I've heard several professional pianists incorrectly play the last two shakes as rests followed by sixteenths rather than eighths, which mathematically and unambiguously alters the duration of the measure. That, in other words, is a completely different
rhythm. You're correct in saying that the effect of rubato is one of overall tempo, but in altering that, one cannot help but make slight to moderate alterations in the rhythm of a consistent figuration, for indeed even if we mechanically follow the traditional definition of the term, the speedings up and slowings down do just that to both the tempo and the rhythm. In other words, tempo and rhythm are inextricably linked and rubato by necessity affects both (which is why your "except in the context of said tempo" doesn't really make sense to me -- because rubato always
affects both tempo and rhythm to some degree, however small). The notion of whether you find the rubato repetitive is, I think, irrelevant. Speedings up and slowings down that occur repetitively change the tempo, and internal rhythm to some degree, the same mathematical amount as speedings up and slowings down that occur with greater variation (assuming we could replicate the same amount of change in both places in the passage). You can argue that you don't find it aesthetically pleasing or that you would want to hear it applied in a different way, but "rhythmic freedom" is in fact part of the universally accepted meaning of the term.
Joe, specifically, what precisely is the musical justification in your rendition of the Op.28 no.4 for hurring
the second half of the first beat (3rd and 4th 8th-notes in cut-time) in the first
nice. But given that there is nothing of interest on those four selected time-keeping pulses (no harmonic change, no melodic change, no dynamic change) its hard to see what the purpose of
is on such "empty" pulses. In fact what happens is that you draw attention to the up-beat of beat one repeatedly. Why 1
2 & , etc. when the work is structured: