----- Original Message -----
From: <A440A@AOL.COM>
To: <pianotech@ptg.org>
Sent: Sunday, October 22, 2000 6:46 AM
Subject: Montal and Aristoxenes (wasHT Experience)
> Montal's instructions are an interesting point. They were in a book
> titles "How to Tune Your Own PIano". In them, one is instructed to tune
four
> contiguous minor 3rds to form the basis of the tuning. Try it!
Do you have an English translation of this?
I would like to try it. Unfortunalty I don't have an English translation of
'Art D'Accorder Soi-Meme Son Piano" if that is the book you are referring
to. The most I have gotten from what little French I can understand that is
that Montal showed that thirds and minor thirds in their pure form would not
complete the octave, that they would have to be widened (3rds) or narrowed
(m3rds) to get an octave, which demonstrated the need to temper the
intervals. It would be interesting indeed if Montal did use contiguious
3rds as part of tuning instructions, rather than as examples of the the need
to temper when tuning pianos.
>If there was a non-technical piano owner back then that could come closer
>than a Young to ET with these instructions, I would be stunned. It was
hard >for me and I am a full time tuner. I don't think his instructions
created much >exposure for ET at the time.
Is this the one (Yung) that sought to
eliminate the "wolf" by tuning half the scale in meantone 5ths and the other
half in pure fifths? Actually I tuned a "Valotti Young" or was it a "Young
Valotti" that Susan Cline sent me back in 1996. I was amazed at how easy it
was. I was also amazed that I could not hear much if any difference when I
played in that temp. But if you heard me play you might agree with a
wink.... : ()
Anyhow I think in the French version of Montal mentioned above, the
objective was ET. I was fortunate to get Kenneth Klauss of the Klauss
archives in Parkston SD to read some pages of Montal and translate as he
went. Unless a full translation proves otherwise, Montal was describing and
provided instructions for tuning ET in 1836. Also it is interesting to
note he dedicated the book to A. M. Pleyel. How much he had influence on
how the Playel pianos were tuned we don't know unless it says in the book.
The modern idea is that that ET really couldn't be defined
until the coincident partials were understood and their beat rates could be
calculated did not happen until after Helmholtz. (ca 1870).
However the idea that tuning each 5th slightly flat (Mersenne in 1638 said
"imperceptibly flat")
would eliminate the wolf or "close the circle" has existed at least in
theory since the time of Pythagoras. This is the rudementry form of ET.
Just how much "imperceptibly flat" is, has eluded
theorists until Helmholtz showed that beats of intervals occur between the
coincident partials.
>
> >>Modern orchestra
> woodwinds, reeds and brass instruments are built and tuned to ET. If you
> study the development of musical instrumenets you might wonder how they
> tuned flutes in the beginning. <<
>
> Prior to the developement of the screw machine lathe ( Maudsley,1830?)
the
> orchestral instruments were built to play in a particular key. With no
> valves, natural horns played the overtones available within them.
I wonder how recorders were bored and holed,and since there were ensambles
of recorders how they were made to sound in tune. I suppose the same is
true for brass but I wonder which had to be more precise.? If recorders are
old, I suspect lutes as fretted instruments are older. And how are the
frets spaced? ?? By an equal proportion of course. Did this "equal
proportion mean anything to the makers of wood winds of flutes? That would
be an interesting study. Try as I did in burning holes in bamboo flutes I
never got an inkling on how the holes should be spaced other than to copy a
good sounding one. It did make me appreciate the effort and knowledge
required to produce any kind of a flute "intune".
>Obviously,
> the higher in the overtone series you go, the closer the pitches are
> together, so at some point up there, a chromatic scale can be formed.
This
> takes a whole lot of lip!
Ha ha ! ! good pun....
> The lute tuning was greatly simplified by Mersenne's ratios, prior to
>that, a good lutist was expected to be able to shift string pressure to
>accomodate
This ratio (for the spacing of lute frets to give semitones) is 18/17 which
is close to 98.95 cents or 99 cents. It was reported by Mersenne as the
practice of lute makers rather than discovered by him I think. How they
discovered this ratio I would like to know. It is a superparticular ratio,
ie the
numerator is one more than the demoninator, and Mersenne alludes to the
importance of superparticular ratios from Ancient Greece on down.
> Ok, here is where we part somewhat. I don't think ET was desired. I
>think it is the entropic end to a harmonic evolution.
Of course it could be argued the other way. Look at the keyboard composers
we hear in ET, that utilized modulation through the keys without added
dissonance of an unequal temperament. Where would Chopin, the Romantics,
Saint-Saens, Debussy, or modern Jazz piano especially the accompanists of
singers be without ET? It seems to me the composers were educated enough
to know there was more than one temperament. How come they didn't specify
any other or any for that matter? If they blindly accepted ET as the
defacto status quo does that mean perhaps they didn't care that much about
temperament to begin with? Or ET was perfectly fine with them? So if they
didn't care why should we? But that is beside the point. The point is no
composer ever made any reference to any temperament including Bach even in
his WTC. While we wonder why he made no specific reference to what it was
he considered "well tempered" all kinds of research is done to support all
kinds of hypothesis as to what it might have been. And in doing such
research, tuning schemes and tuning theories for ET are encountered all the
way back to Aristoxenes a pupil of Pythagoras. However these get
"overlooked" and the various Marpurgs, Valottis, Youngs, Werckmeisters, etc
etc get mentioned as the candidates for the authentic temperments of the
period and if not one or two of them, then it must have been Meantone.
Regarding 'key color" or "color of the keys" once again which composers
talk about that? And if they do and give as examples symphonies or
instrumental music, that means there is something more to "key color" than
mere temperament. If there is such a thing as recognizing or realizing the
effects of key color it is execption rather than the norm IMHO. For those
individuals, hats off, I wouldn't be surprised if it is a gift as rare as
perfect pitch.
The crux here is that there are a growing number of musicians that
>see ET as black and white, and are attracted to the color available in the
> earlier tunings. Perhaps in a particularly Aristoxenean way, we may tune
> more musically if we listen to physical sensations rather than following
a mathematical formula. (the question is, could we sell those
tunings........)
> In light of what we know now, I am suggesting that the technician of
> today is better prepared for tomorrow if they can offer more than one way
>to tune a piano.
> Regards to all,
> Ed Foote RPT
When the performers and players or listeners, even, ask for other
temperaments, so be it, that is who we serve. When it is only the tuners
doing the suggesting, one might wonder what is the agenda? OK I know
certain situations might beg something other than ET. Like the 4
harpsichord concerto recently performed at the Shrine to Music, all were
period instruments. The conservator addressing a special tour for the
Guild said which temp was used. Of course "historical accuracy" was
abandoned in favor of a "box" (what he calls ETAs) but that was because lack
of time and staff (and talent---I should say experience) to parallel tune 4
harpsichords in an unfamiliar temperament.
---ric
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