Small temperament octave

[Richard Moody]

  I suspect that if the 2:1 octave is tuned beatless
then the double octaves will sound flat.

-Robert Scott

If you mean two contiguious octaves it depends on various parts of the piano
whether the double octaves will "sound" flat.  Piano tuninig is done first and
last by beats, not by sound or intonation.  Of course "the sound" has to be
agreeable after the tuning.
    When aurally testing double octaves, the 4th partial of the bottom note will
sound with the 1st partial of the upper note.   How sharp the 4th partial is, is
how "sharp" the 1st partial will be when "in tune".   This is what the theorists
call "stretch" but not piano tuners.  We realize theory says because of
inharmonicity a beatless octave may indeed be "stretched" from mathematical
perfect ratios.
    Stretch for tuners is how many beats sharp an octave can be before it
becomes "objectionable", or what is needed to satisfy asthetic concerns.
This of course is a judgement call and why some call tuning an art.  After all,
what is art but producing what other people will appreciate? ---ric