Thanks to fellow listmembers for many fascinating personal observations.
In particular:

Jeff Dunn:

>You can send me or others on the List the "modern" pieces you like a
>little bit, and we can give you loads of recommendations to try next.

A most generous offer!  I'll have to remember to take you up on it when
I have more time for exploratory listening.

Steve Schwartz:

>I drew the following lesson: modern or contemporary music isn't a special
>case, as far as a listener is concerned.  Most of it works like any other
>music on you, once you get at its emotional core.  ...  and Harmonically
>speaking, things are changing rapidly.  The unsettled feeling you get
>is due in large part to these quick shifts.  You don't find your feet
>all that easily.  In Modern music, the key you may be in at any moment
>is hidden by the increased level of dissonance.

I think this is the crux of it, for me.  Music "works on" me by evoking
emotion (I guess at heart I'm a sentimentalist - e.g., I love Rachmaninoff).
This doesn't necessarily mean I favor simple emotions over complex ones,
or the obvious over the subtle.  Atonal music can be exciting, threatening,
mysterious, confusing, jocular, sardonic, goofy...but seldom, for me so
far, sweet, passionate, triumphant, nostalgic - you get the idea.  I do
enjoy the former group of emotions, but it's often the latter that makes
for my favorite pieces - old friends I can depend on when I need a
recharge or an escape.  Modern music that truly moves me usually contains
at least elements of "traditional" tonality (e.g., Berg Violin Concerto).
As I interpret Bernstein's lecture about modern music, emotional impact
increases (or has historically increased) with tonal ambiguity until it
crosses a threshold (probably different for each listener) and becomes
just confusing, like (to me) Marianne Moore or Cubism (note: I don't
dislike Moore or Cubism - but I doubt I'll ever *love* them).  I do find
that with increased exposure, my threshold moves (slowly), so maybe
that's it - just keep listening.

Richard Tsuyuki