>>Popularity can be measured, but objective "greatness" is an impossibility.
>I am tempted to define greatness precisely in terms of what goes beyond the
>scales of measurement.
As a mathematician, I find this sentence absolutely delicious.
To "define" greatness "precisely" (very mathematical approaches)
in terms of what cannot be measured is nicely paradoxical.
So we measure greatness by how much it cannot be measured. I love it.
Or, parsing the sentence further, "what goes beyond the scales" suggests
we can measure fractional greatness, say up to a 1.0, but after that it
pegs the meter. So we can say that a composer is ".78 great", but we
are unable to say one is 1.26 great". So after a 1.0 we cannot rank
them at all --- they're just great!
I know it has been said many times in other terms, but for me, the
very idea of "linearly ordering" the set of composers (or other artists)
is not appropriate. The set is, optimistically at least, highly
multi-dimensional, but more realistically, not metrizable. Even if you
could decide on the important dimensions (say, as Steve Schwarz put forth
long ago), and supposing that these individual components themselves
could be measured (I think they cannot) how would you weight these?
E.g., how much more important is opera than ballet scores? Absurd and
maybe counter-productive (except that we like so much to try and it does
lead to some interesting analysis, I guess).
Many of the composers themselves felt pressure to live up to such a
multi-dimensionality. I think I read that Prokofiev felt compelled to
try a few genres, more or less for completeness. But I know for certain
that Brahms was driven in this way, for example with opera, to produce
at least one (in part, aty least, to compete with Wagner). And in the
case of Brahms, the symphonies also may have been mostly the result of
the pressure he put on himself (due to the onus Schumann had placed on
the Wunderkind, and in published writing, no less). Who knows what else
might have been created in place of Ein Deutsches Requiem or the symphonies
if the composer had done what came more naturally? I'm not saying,
though, that this would or would not have been preferable, even if I
have an opinion.