Normalization of Historical Temperaments

[Robert Scott]

I have been wondering for quite some time whether I should normalize all 
the historical temperaments for TuneLab so that their average offset is 
zero.  This question has been touched on briefly here on pianotech, but I 
thought I might poll the users of historical temperaments to see if there 
is any consensus.

Basically, the question is how to normalize a temperament that is defined 
by 12 offsets from equal temperament.  It seems to me that a very important 
goal is to be able to switch between an historical temperament and equal 
temperament without changing the overall pitch of the piano and thus not 
incurring any pitch-raise problems.  I have seen some historical 
temperaments that are defined by offsets that are all positive.  This means 
that every note is either at the same pitch or a higher pitch when the 
piano is tuned to the historical temperament.  The average pitch change can 
be as much as 5 cents.  Given the choice between tuning a piano that is 
already at pitch and a piano that needs a 5 cent pitch raise, what would 
you choose?  On the other hand, if the 12 offsets for an historical 
temperament are all uniformly raised or lowered so that their average 
becomes zero, then this minimizes the pitch-change difficulties when 
applying the temperament.  The musical properties of the temperament would 
be unaffected by such a shift since the properties of a temperament are 
dependent on the differences between the 12 offsets and not their absolute 
value.

The other common way to normalize a temperament is to ensure that the 
offset for A is zero.  This goal ensures that if someone were to check the 
tuning of the piano using an A-440 fork, they would be satisfied.  While 
checking A-440 in ET may be valid way to check the overall pitch setting of 
a piano, I don't think it has as much meaning when tuning an HT.  But then 
if A-440 is used as a pitch reference for tuning an orchestra, perhaps the 
absolute pitch of this one note does matter, even in HT.

So my question is, which is more important to you when you tune an 
historical temperament - the average pitch of the whole piano or the 
absolute pitch of A?

-Robert Scott
  Real-Time Specialties