----------
> From: A440A@AOL.COM
> To: pianotech@ptg.org
> Subject: Re: Historical temperamentals (longer)
> Date: Monday, August 09, 1999 9:45 PM
>
> Greetings,
> Hmm, where to start? Richard Moody and I have a collection of both common
> beliefs and points of contention, I think,
Agreed!. Especially in the interpretation of History. There will be different points
of view, and each has its valid reasoning.
> Richard again:
> >From what I remember Barbour did not
> >believe even in 1934 that many tuners acheived ET.
>
> Yes, This is telling, that even after J.Cree Fischer's writings,
> (1911, which gave a workable plan to create an acceptable ET), and
> Braid-White etal, tuners were still not on the target. Were their errors
> simply random and scattered, or were there biases in there from the
> historical path? Did the deviation from ET evoke the shape of the earlier
> temperaments, or was it just a motley collection of thirds? I am open to
> suggestion on the condition of temperament practises in the early 1900's. I
> have just assumed it was all ET.
What do you call a temperament that specifies all fifths to
be tempered in such a maner that they are musically the same? If the tuner acheives
this , how does the musician know? If he "misses" it how is the error detected?
How far off does it have to be before the musican or anyone can declare, "This is
not ET". The one historical "truth" that can be expressed is that tuners have been
comming closer and closer to "true" ET or "ideal" ET through the ages that the
effort has
been made. The "improvements" have come about not so much through the "practice" of
tuning, but from knowledge gained about the acoustic properties that intervals
exhibit when near the "ideal" or "theoretical" construct. A "discovery" of these
properties based on the prediction (of beat rates) of mathematical formulas.
>
> And Richard replies:
> > ... the idea of distributing
> >this error among the 12 Fifths was obvious. Aristoxenus, a pupil of
> Aristotle....
> >is said to have advocated this." (p 548)
>
> The practical appication of this theory would be lost on an eight note
> octave species, wouldn't it?
Yes, but never the less, Pythagoras is credited with computing the Comma of
Pythagoras, or the excess of twelve fifths compared to 7 octaves. Why the excess of
6 fifths over the eight note octave was not given importance, I don not know, or
maybe it was. There is a huge volume of writing concerning scales that a
musicologist
could make a life time of study.
> In regard to our seemingly different views on Aristoxenus ,
Then the actual words of Aristoxenus, will have to be read. I don't read Greek, I
hope there is a translation. All we have been quoting are secondary sources.
>
> Richard continued, and I disagreed with:
> >I am not sure what you are disagreeing with. That ET was a goal, or that
> >no one knew how to tune it.
>
> Both, the published bearing plans don't give us the means of getting a fair
> ET before Montal, ( at least, that is what I read, but would be glad to see
> earlier bearing plans for it),
Most of the published bearing plans are again secondary sources. Later authors
quoting (we hope) the primary sources. So there are differences. For example I can
refer to the differences between Jorgensen and Barbour on Pietro Aaron's meantone
tuning
procedure. If you want to state that Aaron tuned pure thirds directly, you will need
to quote Barbour.
>I just haven't seen any evidence that it was
> doable on a pianoforte of say, 1780 with the documented procedures for
> tuning.
It is a matter of going to the sources and deciding if the procedures are calling
for ET or something else. From Mersenne on tuning spinets........
"Then it is necessary to divide the fifths into major and minor thirds so the
majors are a little small and the minors a little larger than their justness
demands."
(As a tuner you know some one made a goof, as you read Mersenne further, it becomes
apparent he or his publisher or the translator intended the opposite.) So
considering that, what tempermant do you think is being proposed? I say ET.
Meantone has pure thirds in some places and wild thirds in others. What other forms
of temp were known during Mersenne's time?
>. The fact that ET is the
> hardest to tune is also going to lend support that it was not necessarily a
> prime target of these early tuners.
Try tuning Meantone aurally. I say that is HARDER than ET. Flatening four fifths to
get a pure third is most challenging, more so I say than judging the beats of three
congruent thirds in an octave. It is a mystry to me why the early tuners didn't
realize the thirds should beat in a progressive manner, and double their rate each
octave.
>
> There sure were a lot of people that wrote specifically against the use
> of ET, (Jorgensen quotes many), obviously, there was an awareness of its
> principles and a lot of rejection.
That people object to the use of ET is fact supporting the existance of ET. I am not
stating that people have to like ET, I am proposing that ET in one form or another,
(theory or practice) has been around for longer than modern writers are leading us
to believe. And I am leading into an area that music heard in the mind's ear is in
ET by nature. Which is going to lead into a synthesizer that will play in just
intonation by computing the pitches of the keys being pressed before they sound.
Which gets back to the debate (alleged) of the Greeks of math vs nature. And you
think we are having a debate? Take 100 singers. Measure them with an ETD. Will they
sing pure thirds or will the thirds be sharp? But that's for later on.Sure,
somebody in 1880 said the organ in ET made a "hellacious row". (forgot the source,
sorry). But what is more hellacious than a wolf fifth, or the 4 wolf dim fourths in
Meantone?. (Were organs tuned in other than MT or ET? )
>
> I had used Claude Montal's book on piano care as an example of the earliest
> valid method of achieving ET,
And there will always be one surfacing that is earlier. Such as James Broadwood's
article as mentioned by Ellis of a practical method of acheiving ET on the piano.
(1811) The other assumption that needs to be examined is that Bach did NOT
advocate ET. Or that he advocated something OTHER than ET. From what I have seen
there is a paucity of what he actually did intend for WTC. So to exclude ET without
proper evidence is what they call a historical fallacy. It is possible then if ET
was used by Bach, it goes back to 1730. .
Guess who said this??
"...some people think that the temperament in which all the consonances have equal
value wiould finally carry off the prize, and in the furure...it would be
indifferent whether one would play in C or in C sharp."
From Chiapusso, _Bach's World_, "Werkmeister admits that his work only approched
the modern system of equal temperament"
And to drive history researchers nuts, quotes like the following.
"Two rather haphazard solutions for this {comma of Pythag} are suggested by
Werkmeister in _Hypomnemata Musica_. One method is to tune the fifths flightly
flat, the thirds sharp, and consequently the sixths flat." Sharp thirds and flat
sixths?? Looks like Mersenne is excused. This is from Chiapusso. One more example
of why it is vital to check the sources.
This is a facinating debate. I didn't realize there is that much history, not only
of ET but tuning in general. It is people like Ed Foote to be commended, who take a
giant step forward and put back into play something that has been forgotten or
neglected in the passage of time . Or Owen Jorgensen to reconstruct historical
temperaments in light of today's scientific advancements. And the rest of us,
peers, to make sure they got it right. ; ) Such is our gratitude.
Richard Moody
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