Len Fehskens replies to me: >>The theoretical basis of pure mathematics is of course no more (or >>less) amenable to proof than that of a musical scale. > >I just can't make any sense out of this assertion. Pure mathematics may >be synthetic, but its foundations remain grounded in objective reality >(counting). I'm confused by your confusion. Objective reality? Pure mathematics is synthetic, we agree; and what makes "counting" any more of an "objective reality" than some of my fanciful wellsprings for music (to which I'll now add the rhythm of the human heart, our old friend Crotchet=60)? Without tripping the light fantastic down paths littered with very big bear pits, can we not also agree that "counting" is conceptual, whilst the heartbeat is apprehended through the only objective reality we can truly rely on - our own senses? Now our heartbeat may indeed be a subjectively experienced sort of objective reality, as you suggest; but this still leaves music at least as rooted in real world phenomena as the towering mental constructs of pure mathematics. As to real-world modelling, just because you can't build a cantilever football stand using musical logic does not mean that it's any less utile as a real world tool. Take, for instance, the current research into the well-established and perfectly quantifiable therapeutic effects of Mozart on cows and students: a person, we might hope, is just as real as a stadium! All of which makes me worry that your "objective reality" and its "subjective" antithesis may be double-edged tools which paradoxically tend to blur at the edges the more we focus on them. Not surprising, really, as they too are just human concepts ... which feeling, to return to our onions, was probably why I took issue with you in the first place! Christopher Webber, Blackheath, London, UK. http://www.nashwan.demon.co.uk/zarzuela.htm "ZARZUELA!"