Greetings,
Richard Moody writes,
> As research continues historical evidence is mounting that ET has been
>around a lot longer than the proponents of "other than ET" have been
proposing..
>Aristoxenes of the ancient Greeks mentions the concept of it.
I would like to offer a possible alternative view of this, as applied
today.
The last 50 years of research, from Murry Barbour on, have actually pointed
out that the documented use of equal temperament on keyboards is a rather
late development. My understanding of the Aristoxeneans argument with the
Pythagoreans was that it centered not so much on temperament, ( since there
is no tempering when you string Just fifths together), but on the methodology
used to establish the notes. The Aristoxeneans held that the human ear,
listening and determining what sounded "best" was the way to properly
determine the scales.
The Pythagoreans held that the scale should come from a mathematical formula
(3/2), and they had the numerology figured out to prove that is what the
Dieties wanted! So, by 420 B.C, as the the Greek civilization went through
the last of its self destructive wars, we had two basic musical approaches
in opposition. One said the ideal tuning came from a mathematical ratio, the
other said that the ideal tuning was one that came from the human sensual
reaction.
So, a parallel today? We have tuners proposing that we tune according to
a formula and we have tuners that are proposing we listen to all alternatives
in making a choice of temperament. This is not a new debate, and I really
encourage all to remember that there are few new viewpoints here, just new
contexts in which to judge them.
>Mersenne in 1637 gives lute and monochord.
>distances accurate from .00 to .04 cents.
And mentioned, (according to Owen J.) that these would be of little
value to the strung keyboards, as they had to be tuned by ear.
>The problem it seems is that ET was a goal, but no one knew how to tune
>it.
Ah, this is were I must repectfully disagree, and would like to offer a
few points why.
The vast bulk of the documentation points to something else as a goal.
August DeMorgan was a mathematical genius, yet in the 1800's we find him
stating that he was "not against variety in the keys, but there must be some
order". This doesn't seem to indicate that ET was a goal for him, and this
is a person that was very familiar with math, the ratios would not threaten
him, yet he proposes an unequal tuning.
In addition to the "Ivory Tower" advocacy of unequal tuning , I must
mention "The "Tuner's Guide", an instruction manual of 1840 which
purportedly supports the use of "equal temperament". The TG states, in a
section on unequal tuning, that " a good tuner can accommodate the
temperament to the taste of those who play in paticular keys". (I take this
to mean that a "good" 1840's tuner was not limited to any one tuning). It
goes through a variety of temperaments as training ground for equal
temperament, and then gives instructions for a crude ET,(by our standards
today). how many tuners today are going to develope a nice even ET by
reading a book? Would the working tuner of 1850 have done so? I submit no,
but will be glad to find new info on this. Montal's booklet of 1832
certainly didn't take the world by storm, but if followed, will yield a fine
ET. How come it didn't see any widespread popularity?
To assume that the tuners of the early 1800's were working their way
through the various temperaments until they finally were tuning the most
difficult, newest, and least documented style of tuning in 1850 is, in my
opinion, a mistake. Reinforcing this is the documentation done at the
Broadwood factory in 1850, where Hipkins states the tuners weren't tuning
anything like equal temperament. I suggest that whatever was going out the
door of the factory was most closely indicative of what the general
piano-buying public favored. This is still true today, and means that when
the factorys begin shipping their pianos in well temperaments,
a landmark has been reached. ( I am not holding my breath)
The strongest evidence for temperament variety is the analysis Jorgensen
presents of Ellis's findings in 1885, 35 years after Hipkins had
"instructed" the tuners at Broadwood's to tune in ET. Scientific
measurement at the time was advanced enough for credibility, I think, and
these results clearly show a strong bias for the same style of inequality
that had been recognized for over 150 years. Is it just coincidence that the
factory tuners of 1885 were still tuning temperments that followed the intent
of Werckmiesters rules? That the harmonic form was the same, just varying by
degrees? I think not.
> How the tuners from Bach on actually practiced is being researched, but
>little direct evidence remains. All we can conclude is that anything "close
enuf"
> was probably the norm.
Bach is on record as being very particular about his tuning, allowing no
others to do it for him. I think his "close enuf" was probably pretty
exacting. Richard is right, though, is that there is little other evidence.
So, we must find a logic that poses the least amount of assumption. My
assumption is that tuners tuned in the easiest way possible.
>1830 is aprox 100 years after Bach and Werkmeister, so ET had at least
>that long to be attempted in keyboard tunings. There is very convincing
evidence cited in the Groves (14 vol edition) article "Temperament" Mark
Lindley; that organs in Northern Germany were tuned to ET at least as far
back as 1800.
Yes, and this is logical, since the Mersenne ratios could actually be put
into practise with the long extended tones of an organ. I don't see their
application to strung keyboards as being anywhere near as easy.
>Of the many temperaments proposed between Meantone and Equal Temperament,
>there is no evidence (so far) of any composition being intended for any
particular
> temperament. Even if there were, there is no evidence as to what was
actually
> heard, because of how consistant tuners were or were not in any given
>temperament.
Yes, this is true, and supports the point that a multi-temperament
approach is far more historically accurate than allegience to any one
temperament. It is this that is the crux of the temperament revival today.
We now have the ability to accurately recreate a wide range of tunings, and
discuss them amongst ourselves and our pianists. This allows the progressive
technician of today to do things that would be the envy of our predecessors.
That there is a temperament revival going on today is in response to
the programmable machines and Owen Jorgensen's research. In this revival,
there are several sides, not unlike the debates in ancient Greece. If we are
to look for historical identity, I side more with the Aristoxeneans. The
choice of tuning should be made on experience with the actual sounds, not by
a formula, regardless if that formula is the Trinity expressed in 3/2 or the
ultimate precision found in the square root of two.
Regards,
Ed Foote
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