Marc Goodman said the tenor section of his piano goes out of tune,
even though the tuning pins are tight.  I'll assume Marc means
intervals sound bad, rather than unisons.  I was unclear on what Marc
is calling the "tenor", but will make some more assumptions below.

If single notes sound bad by themselves, one or more of the three
strings in the unison has drifted.  This can be the result of loose
tuning pins, or an unstable tuning of a particular string (and there
are lots of reasons for unstable tuning in old pianos).  Mason and
Hamlin pianos of certain eras also have very steep string angle
changes from tuning pin to speaking length, which can be a bear to
stabilize, especially if the strings are a little rusty.

But, if individual unisons sound okay, and it is instead the
octaves and other intervals that start to sound bad, the piano belly
is moving, not individual tuning pins.

The "tenor" section is usually given as the name for the lowest
unwrapped ("plain") steel string section, just above the bass.  The
lowest strings of this section are usually of lower tension than the
rest of the piano, and are more sensitive to changes in humidity, and
the related swelling and shrinking of the wooden parts of the piano:
specifically the soundboard, bridge, and perhaps pinblock.  Tune in
December and it sounds bad in May.  Tune in August and it sounds bad
in November.  This is humidity cycle wood movement at work.

Play an octave from the lowest plain string to the wrapped bass below
to see if your piano is in or out of tune from humidity changes.  Does
the octave sound clean, or is it beating several times a second?
Wow-ow-ow-ow.

Brand new, tight pinned pianos go out of tune at this same place, in
the same way, when humidity cycles.  It has nothing to do with tuning
pin tightness.  Stabilizing the humidity swings in the piano's
environment is the key.  42 percent relative humidity is the target.
If your humidity goes to 72 in the summer and 16 in the winter, no
piano will stay in tune.  55 to 35 would be a reasonable range, but
you will still hear the low tenor drift.

Put a humidifier in the room, use air conditioning, and/or install a
Dampp-Chaser system under the piano.  Player systems don't leave much
room for Dampp-Chasers, so controlling the room environment is usually
the first line of attack.

Greg Graham, RPT