Article

[JIMRPT@aol.com]

Dr. Coleman;
  Read the article with delight and  I want to say that I admire the facility
you have with words Sir !
  As in any occupation, tuners have cetain totems that we ascribe to and you
have touched on some of those in this first article.
 The "pure" yet "stretched" octave is one.  Yes it probably is possible to go
across the range of the keyboard and have (mostly) pure octaves, but I'm not
sure you would want to do it. The reason of course is that for every "pure"
note or interval you have, a compromise has to be made somewhere and as you
know that compromise is geometrically progressive.   An acceptable interval
in the mid range can become quite unacceptable in the second octave up or
down very easily. and focusing on a pure octave, or fifth, or any other combo
leads us into something other than "equal temperment"....doesn't it? (honest
question, not rhetorical).
  I vary from Horace in that I will not hesitate to turn a fifth "inside out"
if it makes melodic or musical sense in a given instance;  probably because I
don't know enough about theory to understand why it should not be done.  Of
course we are speaking in generalities and some methods will work better on
some instruments than others due to the many factors...size, type, materials,
musical score, solo,..... etc.
  I learned to tune by doing it because it sounded right and "because that's
the way it should be done, son".  So I tend to focus more on 4ths and 5ths,
than perhaps I should, checking, occasionaly, with thirds and sixths and
probably can't tell you where to find a 7th. :-)  As a consequence I depend
on my 5ths as an anchor in my tuning and I find that I prefer them on the
"pure" side and have never been able to get away from that (don't know that I
want to).  Horace's comments, and your postulations on fifths, tend to lead
me to believe that we are essentailly in agreement there.
  Jim you ask "Also, is there an ideal trade off between the width of the
4ths or 5ths and the width of the octaves?"  I think the answer is yes,
mostly; but, it changes from octave to octave and is not a static curve or
formula and this is where "stretch" comes in.  And "stretch" is what causes
the problems with pure anythings......Right ?
  Perhaps we do not use "equal temperament" for most of our tunings instead
perhaps it would better be called 'spastically ascending/descending
temparament'  :-)
  Great first part , can't wait for the next.
Jim Bryant (FL)