In a message dated 98-02-03 01:52:36 EST, you write:
<< Bill, List,
I'm not certain what you meant by "PTG resolution specification" >>
Dear Kieth,
Thanks for asking. What I was referring to was not the Exam standard but a
resolution passed in Council some years ago. I am not certain when that was
or what the exact language was but the intent was that PTG was endorsing A-440
as a pitch standard. It gave a tolerance of + or - 1 Hz. (or 1 cycle), not 1
cent. Essentially, this means a tolerance of + or - 4¢.
Since there has been and probably will continue to be much debate about
temperaments, I wish to draw a distinction for more than one reason between
pitch and temperament. In my view, they are completely seperate issues.
Today, there is a new post about "Universal Harmony" and a supposed pitch that
is in harmony with the cosmos. I wouldn't touch that one with a 10 foot
soundboard go bar!
I have no reason to challenge the A-440 standard and even if I did, I realize
that I would have to work with it anyway. If I tune a non-equal temperament,
I'll still want my "average pitch" to be as close to theoretical ET as
possible mainly because I'll want my tuning to be compatible with all other
instruments, fixed pitch or otherwise. By choosing the note A3 to always be
0.0, and read on octave 5, I am able to get my overall pitch much closer to
standard than if my C4 were to be a 0.0 and read on octave 5. This is
somewhat like what the RPT Exam does with the Examinee's tuning when it
"shifts" it to correct for the difference in pitch that there almost always
is between the Master Tuning and the Examinee's. Owen Jorgensen found that if
you set most any Cycle of 5ths based temperament (the kind I have been
advocating) with the A3 at 0.0, the "average pitch" will be much closer to
theoretical ET than if your C4 were a 0.0. Some of my colleagues that tune
HT's just can't swallow that. It seems illogical to have anything but the
note "C" be a 0.0.
The reason this works is that generally speaking, if your A3 is at 0.0, half
of the notes will have a deviation to the plus side, the other half will have
a deviation to the minus side, regardless of how much deviation is involved.
This line of thinking allowed me to develop a Victorian Temperament which
closely parallels theoretical ET in pitch but still retains distinct cycle of
5ths based key coloration. When no single note is even 1 Hz. deviant from
theoretical ET (less than 4¢), then the temperament is beautifully compatible
with all other instruments, fixed pitch or not.
People ask me how this could be that I could have such a seemingly
questionable arrangement for the piano as an UNEQUAL (God forbid!) temperament
and yet it plays perfectly (or so it seems) in tune with electronic keyboards,
organs, MIDI programs, tuned percussion, marimbas, another piano tuned in what
is presumed to be ET, etc.
My answer is that the deviation is so small that from note to note, it is
insignificant. At the unison level it is barely perceptible if at all. The
difference is in the harmony that the piano itself has, in it's "vibrato" as
has been detailed in earlier posts. Thus, the difference is an "internal one
to the piano", which is how I explain it briefly.
Now even though you have made a large correction towards an average pitch with
A3 at 0.0, in most cases with an HT, you are still a little on the sharp side.
If you were to set A4 first on it's fundamental, your A3 would most likely end
up reading near 1.0 (on octave 5) and your A4 around 2.0 (also on octave 5).
The exact amounts would be determined by the piano's actual inharmonicity.
So, when you set A3 on 0.0, read on octave 5, you are already about a
cent flat for that note of where you might want it if you were tuning ET.
Most piano's inharmonicity will be such that a good octave will not be created
by A4 (also read on octave 5) being set at 0.0 too. This would be a 4:2
octave yes, but most very experienced tuners will agree that a 4:2 octave is
still too narrow unless the piano has very low inharmonicity or the ultimate
goal is to have the most minimal stretch possible. Thus, A4 (read on octave
5) will probably be set at from 0.5 to 1.5, depending on the inharmonicity, to
create a good, properly stretched octave in that area of the piano. (From
what I gather, the ET by pure 5ths would have a far greater spread than this).
The 1/2 ¢ Coupled Motion of strings effect lowers the pitch of both A3
and A4 another 1/2 ¢. This actually makes my "average pitch" fall right where
I want it! The figures of the EB Victorian Temperament are all very small and
read on octave 5 which is in the same range that the majority of coincident
partials of the Rapidly Beating Intervals (RBI) occur. Thus, it blends well
with whatever kind of harmony from other instruments it encounters. All of
the notes being within the tolerance of 1 Hz. (4¢ at A4), the EB Victorian is
close enough to a theoretical ET that it can be considered "virtually equal".
I have been told by many of my colleagues that a temperament crafted with this
kind of precision is actually closer to being truly equal than many attempts
at ET by tuners of average skill. This has been my observation as well. When
I see the kinds of errors that people who are professional piano technicians
(who make their living tuning pianos) make who take the RPT Exam and that
people accept as ET and accept as professionally done, I know that in good
conscience that it is not a requirement for me to reveal in each and every
case what the details are of what I do, as much as I would like to be able to
do so.
If I were required to tell each and every customer for example that the
tuning I am about to render on the piano will have small deviations from what
is considered Standard Equal Temperament, then virtually every other person
who tunes pianos whether they believe they are tuning in ET or not should be
required to say the very same thing.
Tom Cole likened the debate about temperaments to the debate about PTG
membership categories. I agreed with him that there are many similarities. I
think of this debate as similar to the one about whether English should be
made the "official" language of the United States. At the beginning of that
controversy, many were surprised to learn that it wasn't. Like ET has become
the accepted norm, it is our language, it is so commonly used, it has never
been necessary to stipulate it. Many people speak it imperfectly however,
native and non-native speakers alike. In some cases this is a problem but in
others it creates in individuality, a distinguishing characteristic, a certain
charm. Many people in Britain don't accept our version of English as
standard. There are differences of opinion about what is correct spelling,
grammar and punctuation. Whose English is correct, there's or ours? If both
can be considered correct is it true that everyone who speaks it does so
uniformly well? Are those who use non-Standard English wrong to do so? Now
in recent decades, there is the increasing and undeniable fact that there are
so many people living in the US that speak Spanish and other languages that
there are those who want to lay down the law about English. They always have
this phrase, "all we're saying is...". Everyone who knows better realizes
that there is a very restrictive and prejudiced agenda behind that phrase.
They want to limit and abolish what people want and will do naturally in a
free society. The idea is not likely to prevail, it's not good business.
No one really argues that learning English need not be a priority for
those living here that don't speak or read it. But with so many people
speaking Spanish, from a business angle, not a legal or civil rights point of
view, it is in the best interest of every American who only speaks English to
learn Spanish (or what ever other language or languages might be useful in
their community or business enterprise) too. The more that people know each
other's language, the less of a problem language barriers become. Europeans
are used to it. We will have to get used to it too if a global and
hemispherical economy are to work in the next Century.
Likewise, to view ET as the only standard that is important is as
musically narrow minded as it is from a business point of view. How many
recordings can you make of the same classical music played on the piano before
there is no more interest? When something isn't selling, businesses look for
a new angle to get people interested. There is no doubt in my mind that what
people scoff at as archaic, of limited interest and unworkable today will be
the very thing that people will be looking to buy in the future as fresh, new
and exciting, like Ed Foote's CD.
Bill Bremmer RPT
Madison, Wisconsin
It does not require such a mild or near ET for an HT to be compatible
with any and all other instruments and any or all other music for that matter.
This, I can say with certainty is merely a supposition. The reason is that no
other instrument, other than fixed pitch (usually keyboards) instruments play
in ET either. The very fact that good musicianship requires vibrato, which is
by definition (in most cases) pitch that varies from flat to sharp, and the
bending and sliding of pitch, means that the piano really need only be
relatively close to be considered in tune. I'm sure this fact actually saves
us in many cases whether we choose to tune ET or not. If it were an absolute
requirement that our pitch be within 1¢ of A440 and our temperament be
absolutely equal to a tolerance of 1¢, in order to sound good or even be
usable with other instruments, we would all have to be far more exacting in
our work and our tunings would become unusable far sooner than they actually
do.
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