Scaling

[Billbrpt]

In a message dated 98-04-01 08:18:04 EST, you write:

<< I suppose I'm looking for a scaling program that produces emotionally
satisfying screen graphics of scale colorations that will (in use) trigger
massive endorphin secretions in the brains of listeners of the music performed
thereon, no matter what the tuning scheme. >>

     Just use a normal scaling program.  This is an often asked question.  The
answer to it is that the differences in tension between one temperament and
another are so slight as to not be of consequence or consideration in this
matter.

  This is, in fact, where Helmoltz' work is of true value.  To divide the
scale into 12 equal parts for the purpposes of analysing tension and other
scaling properties is a perfectly valid approach.  There are some who will
take it to mean that since this was the approach, that the modern piano "was
designed for ET".  Well yes, in a manner of speaking.  But we all know that we
could tune the piano to a slightly non-Standard pitch without real consequence
as well, say + or - 1 Hz.  The differences in actual tension between an ET or
non-ET at Standard pitch would be on the order of such a varience.

If you really wanted to, you could however explore your idea this way:  Find
the deviations in Owen Jorgensen's book, Tuning from ET for 1/4 comma Meantone
for example.  This would probably be about the most deviant from ET that your
piano will ever be tuned.  Using the cents to Hz formula that was published on
the List recently  (by Mr. Galembo), plug those deviations into the Hz. values
for each note as they are assumed at theoretical ET.

If I am not mistaken, or behind the times, most scaling formulas work on a
theoretical ET frequency value.  Of course, when you actually tune the piano,
you will stretch the octaves to some degree or another.  Especially at the
high and low ends, you will have a difference in frequency from theoretical ET
which will be far greater than that which you would have in the midrange with
a typical HT such as a Thomas Young #1 WT.  Perhaps some newer scaling
programs take octave stretching into account, I don't really know.

In any case, after you have plugged in your 1/4 CMT values, see if they would
now significantly affect your wire size determinations.  I sincerely doubt
that they would.  But if they end up doing so, you will have asked and
answered a very important question in your case.  It is worth exploring on
theoretical grounds alone.  If you get no difference in your scaling
determination between ET and 1/4CMT, then any claims that the modern piano is
"designed exclusively for ET" will forever be disproven.  I wonder what Del
and Steven Birkett might have to say about this?

HT practitioners have often remarked that "HT's 'eat' poor scales".  By this
it is meant that a tuner can often have an abundance of mild harmony at the
top of the cycle of 5ths with a seemingly lesser and non-correspondant amount
of harsh harmony at the bottom of the cycle of 5ths as a consequence.  While
an ET tuner is frustrated at not being able to tune smooth 3rds on an
Acrosonic, for example, a WT tuner delights in being able to provide th
customer who plays the instrument with a much "sweeter" sounding piano.  While
the remote keys retain their harshness in the WT, that harshness is
significantly mitigated and may in any case be seldom used by the customer.

I hope this opinion helps you to answer the question about how to approach
your scaling project.

Sincerely,
Bill Bremmer RPT
Madison, Wisconsin