HTs using cents offset from ET

[Billbrpt@aol.com]

In a message dated 7/14/98 4:23:21 PM Central Daylight Time, rscott@wwnet.net
writes:

<< What is involved in creating a "cents offset from ET" program for
 tuning an historical temperament?  This is what people want to know
 if they are going to tune an historical temperament by means of a
 visual tuning aid.  But it may not always be possible to come up
 with such a program. >> etc. (snip)

My hat is off to you on this post, colleague.  You are the very first person
who seems to understand what I've been saying for a long while.  While I know
very well that many HT tuners use the FAC/Cents Deviation Program (FAC/CDP)
and have good artistic results, I have never trusted nor even tried (because
of my mistrust) it.  To use it, you have to assume that both sets of
calculations are correct, without error (or reasonably so) and that the amount
of octave stretching is appropriate for the situation.

I believe that you are correct when you assume that Jorgensen's figures are
for zero inharmonicity.  He was more or less required to calculate them that
way.  (You have to start somewhere.)  If however, you create an FAC (or RCT)
program that deviates theoretical ET into an artistically good and musical
interpretation of ET as would be appropriate for the modern piano, then
deviate each of its pitches by the theoretical values that Jorgensen has
computed, you will get a reasonable approximation of the desired temperament.
Just as with ET, you can get a certain range of interpretations of the same
idea and still consider that they all qualify as one single kind of
temperament.

The idea I have at present to come up with the deviations for the EB Vic is to
take a good program such as the one I did for the Walter Grand and "back the
FAC program out" of them.  That is to say, subtract each FAC value from the
actual value.  The remainder would be the Cents Deviation Program (CDP).  This
might be done with several different tunings of different pianos and a
comparison be made to see how much consistency there is.  If one could get
reasonably consistent results when comparing a Steinway, a Yamaha then a
Kawai, for example, you might conclude that a single set of deviations would
apply to any appropriate FAC program.  If you get different results each time,
you might conclude (as I have), that you need to think in terms of the piano
being a *High*, *Medium* or *Low* inharmonicity piano and produce an
appropriate CDP for each.

>From what I have heard, both Reyburn and Sanderson have incorporated increased
octave stretching into their program capabilities.  I assume however, that the
stretching would always follow a smooth curve, which would indeed be
appropriate for ET.  The kind of *tempered octaves* that I came to discover
and use, however, vary in size from note to note.  I do not think either the
RCT nor the SAT can do this.  I must add however, that the difference between
what I do with the *Equal Beating* method, where the beats are not quantified,
merely *reproduced exactly*, and the scientific, mathematically calculated
method of Sanderson and Reyburn, may be aurally insignificant.  The more these
ideas are explored, the more questions will be raised.

I hope this thread will continue and that we can really accomplish something
here.  The questions you raised were the very reason that I developed an Equal
Beating (EB) method for a Victorian Temperament (VT).  None of the VT's in the
book, Tuning, are of the EB method.  They all have irrational, theoretical
beat specifications.  The best one can do is to use the FAC/CDP.  Skip Becker
RPT, the host of the Temperament Festival at the Convention does the Usual
Broadwood Temperament this way as a normal part of his practice.  Although I
have not heard one of his pianos tuned this way, I have no reason to doubt
that it produces a very fine and distinct kind of character for his pianos.
Our colleague on the List, Paul Bailey RPT does all of his temperaments this
way, including the Meantone type which he generated on computer.  His tunings
are no less than superb.

There is only really one thing we can all agree upon.  When we manipulate the
temperament and the octaves, we alter the way the music sounds when performed
on the piano.  We can be very precise about what we do or we can choose to
accept a broad tolerance.  We can choose to practice what is considered
standard or we can choose to take the riskier route of innovation.  It will
still always be a practice of art:  good, sometimes bad, but hopefully not too
often mediocre.

Bill Bremmer RPT
Madison, Wisconsin