Hi All,  First off, tuning by ear can be very painful.   ;-)

Having started with just one tuning fork light-years ago, I believe
that learning the beat rates and relationships between the various
intervals is very important to good piano tuning.  It doesn't take long
to realize that what 'works' on one piano will not work on another.
And therein lies the 'Art'.

I've heard that some of the newer electronic tuners have a memory
capability.  So once you 'get it right', you can 'save' the settings
for future reference *on the same piano*.

The older model electronic tuners have no facility for stretching the
octaves and I haven't seen any advertising which suggests that the
newer ones do have that capability.  But even if they did, it would
still be subjective since no two instruments have the same scale
design.

I'm not ashamed to admit that I utilize an electronic tuner as a visual
aid in setting the temperament and making sure that the octaves are 'on
the right side of zero'.  I don't rely on it for a number of reasons
but it is especially useful when the piano way out of tune or way below
pitch.

Using the reference tool to get you into the 'ballpark' quickly can
save quite a bit of time.  However, for fine tuning, I believe the ear
has been proven to be superior to the machine.  And let's not forget
that the machine has no function for tuning unisons.

Musically,
John A. Tuttle (john@player-care.com)