Reverse Well Data

[Billbrpt@AOL.COM]

During the heated discussion about Reverse Well Temperament (RW), one person
wanted to see some cents deviation figures that would create a RW.  As with a
true WT, it is not just one set of absolute values as you would expect ET to
be.  There can be quite a wide range from something that probably has no
negative effect on the music to the other extreme where it certainly would.

While I am totally against harming the reputation of any individual or
company, we all know that there are poor practices that go on.  Even at that,
I think it is usually much more useful to talk about the right way to do
things rather than to make fun of and scoff at substandard practices.  Since I
have observed that the RW error is being made by a very significant portion of
aural tuners, I believe the problem needs to be identified and the proper
information disseminated so that it becomes a less frequent occurrence.

I offer this one piece of documentation as an example of what I find very
frequently.  It is not the worst I've encountered, I'd say it is about
average.

I had the opportunity to tune a Yamaha C7 that is regularly tuned by a certain
individual and had been tuned "recently", so I was told.  Someone suggested
that unusual circumstances may have played a part in the errors that I found
but I have heard this person's tunings many, many times and it was entirely
consistent with his usual work.

He shall remain anonymous but he does have a very good reputation and does a
lot of concert work,  He is not a member of either PTG or MPT and shuns both
organizations.  He also condemns the use of HT's and maintains that ET and ET
only is the proper way to tune a piano.

I just happened to have the Master Tuning record for a Yamaha C7 in my exam
pages and decided to make some comparisons.  Of course, this is not a true PTG
RPT Exam circumstance and so there is perhaps some margin of error that you
might apply to it but the results are interesting nevertheless.  

Don R. asked what the definition of ET is.  You must have a series of 4ths and
5ths that are very slightly tempered, sounding nearly but not quite pure, all
exactly the same with none being purer nor more tempered than the other.  You
must also have a smooth and evenly ascending series of 3rds & 6ths that
gradually increase in speed, no two alike and contiguous 3rds must have a 4:5
ratio of beating without exception.

It's not a very easy thing to accomplish by ear but it can be done and is done
by the very best aural tuners, many of whom subscribe to this List.

To concede what I observe that was good about the tuning I am making an
example of, the octaves sounded reasonably good although they are very
inconsistent in the high treble.  The unisons were impeccably excellent.  Many
people maintain that those two things are the most important.  This person has
been in business for over 30 years so there must be something about his work
that people like.

However I might at least hypothesize that if the public and artists can and do
accept the kind of errors that you will see below, they can also accept the
kind of alterations to ET that tuning in one of the HT's would provide.  After
all, do we not expect that the HT deviations are done deliberately to make the
music sound better?  And do we not also presume that errors made at random and
especially those that create a kind of backwards version of an HT would have a
negative impact on the music?

The following figures were all pitch adjusted so that A3 would read on 0.0 for
purposes of comparison.


					Yamaha C7

        F3   F#3   G3   G#3   A3   A#3   B3   C4   C#4   D4   D#4   E4   F4

ET:   -0.9  -1.0   -0.7   -0.5  0.0   0.4    0.8 -1.3  -1.3  -1.7 -1.2   -1.2
-1.2 
EBV: 1.0  -3.0    2.7    0.5  0.0   1.0    1.0   2.0  -2.8  -1.0 -1.0  -2.5
1.5
RW:  -2.3   3.0   0.5   -1.0  0.0    1.0   -0.2  -6.7  -3.8 -1.0  -7.2  -1.6
0.0

In the RW example, F#3-C#4 5th is as wide as you would expect to find the
"wolf" 5th of a 1/7 Comma Meantone but it is in the wrong place.  The 3rd of
that "wolf" triad beats a little faster than an ET 3rd but it much slower than
the F3-A3 3rd before it.  The G3-B3 3rd is a little faster than ET but the
Ab3-C4 3rd is very slow.  The B3-D#4 3rd is also very slow and the Db4-F4 3rd
is quite a bit slower than the C4-E4 3rd.  The Ab3-Eb3 5th is as narrow as the
most extreme MT 5th, a 1/3 Syntonic Comma yet this would be the 5th that is
supposed to be very wide in such a MT.  None of the 4ths and 5ths beat
anywhere near to being similar, let alone equal. The F3-F4 octave is also very
wide, I'm afraid even wider than it should be for an ET with pure 5ths. This,
my friends, is what a typical Reverse Well temperament looks like,  yet people
can and do accept it as normal.

One of the PTG members who was going to perform for a PTG Auxillary function
at the Convention in Albuquerque was interested in the EBV tuning I did for
him on a Young Chang piano that had been set up with Yamaha Orchestra
Software.  He rightfully questioned whether a non-ET would work with the MIDI
software that was presumed to be in ET.  I assured him that it would work
perfectly well.  After he understood exactly what I did and used it to
perform, he told me, "Bill, your "unequal" is a lot more equal than a lot of
other people's equal".  This is the point I have been trying to make and the
above is but one of the far too typical examples of it.

Remember what Tim Farley RPT taught me:  If you are going to have errors in
the equality of your temperament, you should at least know how to put them in
a place that will benefit, not harm the music.

Bill Bremmer RPT
Madison, Wisconsin