> However, the tenor section (2nd last to the top) always goes out
> before the rest.

Your question seems a bit confusing to me.  You say that the tuning
pins are tight, but that the section (I term sections: bass, tenor
(below middle c to the low end of the bridge), treble, mid-range
(-treble) (which you are calling "tenor," but no matter), and high
treble), goes out of tune first.

Soundboards react differently in different pianos, and this section
often goes sharp or flat to a greater degree than the sections beside
it.  One might think that the broad central section of the soundboard
would flex the most, and it usually does, but I've found in my
experience that this "mid-range" section can go sharper and flatter
than usual.

I ascribe this phenomenon to the break in string bearing on the bridge
between the central section and this penultimate section.  I imagine
that the lack of downbearing for the width of one "ghost" unison is
enough to allow the board to flex in a non-uniform manner.  The high
treble section does not do this because it is surrounded by the
stiffening effect of the belly and bentside lands which hold it more
rigid.

My reasons for this belief are two: first, that I've experienced it
empirically; second, that the unisons (or at least the two closest
strings of the first unisons) on either side of this strut tend to be
far less stable, to not hold pitch as well as the rest of the piano,
and to go sharp or flat with the least variation in humidity.  I notice
this on Steinway grands, especially.   The previous phenomenon, the
"mid-range" changing pitch more than the other sections, I've noticed
on Baldwin grands, as well as a Mason & Hamlin "A" that I tune, among
other pianos.

Spinet pianos have thinner soundboards, and in some parts of the year
the center pitch can be way sharp or flat while the ends are just the
opposite.  Hard to guess where to set pitch to tune it, but after
experiencing it for years, I come to trust my own judgment.  Now that
I've written that, I recall that on most low vertical pianos, this
"mid-range" section is almost always noticeably more flat than the
center tenor/treble area.

Mark Ritzenhein