In the context of restoring a rusted and lead-sick comb, I have been
reviewing all the resources I could find on comb tuning stretch.

Although there is consensus (though not universal consensus) that
combs tunings were stretched, I have found nothing in print or on the
'net suggesting even an order-of-magnitude estimation of what a typical
stretch should be.  I have taken the tunings of several antique combs
and always found a great deal of stretch.

When I make my own 6-octave combs I use a stretch of 25 cents (25/100
of a halftone).  Almost half of the stretch is in the last octave.
This is in keeping with Joe Roesch's advice that rates of stretch
increase in the far treble.  It is less stretch than I have measured
in any existing box, but it still seems like much more stretch than
could be justified by the piano tuning arguments of hiding the most
disagreeable overtones in the high octaves by stretching to remove
the beats in the overtones rather than the fundamentals (if, indeed,
I understand that argument correctly).

Large treble stretches have been justified by arguments of "brightness"
but unfortunately an exponential increases in stretch in the far treble
is exactly what we would expect to see in un-stretched combs which
have undergone tip wear -- the same wear on each tip would have an
exponentially increasing sharpening effect on the teeth as the mass of
the teeth decreased exponentially up the scale.

My questions to the assembled expertise that this wonderful forums
represents are as follows:

1. Would anyone here care to make even a rough estimate of what a
typical stretch for a musical box comb should be?  I understand the
caveats that each comb is different, each tuning unique, etc., but it
would still be great to have a range of "reasonable" total stretches.

2. Were Joe Roesch and others correct in saying that the stretch is
non-linear, that the amount by which each note in a stretched chromatic
scale is greater than a halftone above its neighbor to the right
increases as you go up the scale.

3. Would you assume that the stretch, even if curved along the scale,
is a simple curve?  Is there a chance that the stretch within a given
octave falls disproportionately between two adjacent notes, or is it
spread evenly between all the intervals in the octave?  This question
collides with the question of tuning temperament, of course, as some
uneven intervals could be described as uneven stretch in an equal
temperament octave or even stretch of an unequal temperament octave.
Still, if it is the latter is the case, then we have a much more
constrained system of variable to work with in trying to recover the
original tuning.

4. Other than the exception of "Tremolo" boxes, do you think there
are ever circumstances where the same note is tuned differently on
different teeth?  Where multiple teeth are tuned to the same pitch
there is the opportunity for the teeth to "specialize".  For example,
you could select one tooth to tune to a perfect fifth with the fifth
below it and another tooth to tune to a perfect octave with the octave
below it?  Other schemes could be imagined, especially in a stretched
tuning scale.  Do you think that multiple teeth were ever treated this
way so that the arranger could select a particular tooth among its
mates at the same pitch to suit the cord, or can I safely assume that
all teeth tuned to the same pitch were originally tuned identically?
That, at least, would somewhat reduce the complexity of finding the
original intent of the tuning scale in the messy data of an out-of-tune
antique comb.

This last question makes me wonder if I am thinking entirely too hard
about the whole issue.  After all the original makers were just trying
to keep afloat in a competitive market, not spinning elaborate schemes
around harmonic analyses.  But I have complete freedom to chose the
tunings of my own combs, and I would like to do it wisely.  Equally,
when I am restoring a comb I am always worried about losing information
as I bring the comb back into tune with a scheme that relies on a
statistical averaging of the existing (noisy) tuning data.

I always provide the customer with a paper copy of the "as found"
tuning.  I think it is important that restorers always do so.  But
I would not want to erase the original intent of the maker from the
restored musical program.

Thanks to all,

Jonathan Herz - Herz Music Box Co. 
Montpelier, Vermont
http://www.herzmusicbox.com/ 

 [ At http://en.wikipedia.org/w/index.php?title=Stretched_tuning :
 [
 [ "Melodic stretch refers to tunings with fundamentals stretched
 [ relative to each other, while harmonic stretch refers to tunings
 [ with harmonics stretched relative to fundamentals which are
 [ not stretched.  For example, the piano features both stretched
 [ harmonics and, to accommodate those, stretched fundamentals."
 [
 [ -- Robbie