Montal and Aristoxenes (wasHT Experience)

[Richard Moody]

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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.

First of all I don't know what a "Young" is. Is this the one 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 (1836) mentioned above, the
objective was ET.   Many maintain that ET couldn't be defined
until the coincident partials were understood and their beat rates could be
calculated and that could not happen until after Helmholtz. (1870)  This I
would call modern ET. However the idea that the circle of fifths in tuning
each 5th slightly flat would eliminate the wolf has existed since the time
of Pythagoras.  This is the rudementry form of ET.  Just  how much is
"exactly flat" has eluded
theorists until Helmholtz showed that beats of intervals occur between the
coincident partials.  It is my understanding that Montal described ET
somewhere between rudementry and modern. I am hoping a forthcomming
translation will prove that.

> >>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?)
> 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.

>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.  How they discovered
this I would like to know.  It is a superticular ratio, ie that the
numerator is one more than the demoninator, which it seems Mersenne was
eager to point out.

>>>>>.
>.  I don't think ET was desired.  I  think it is the entropic end to a
harmonic evolution.   The modification of  Pythagorean or Just Intonation
that occurred between 1100 and 1400,resulting  in meantone,  was an attempt
to extract the maximum usable harmony out of a  twelve lever keyboard.  This
was done by tempering the previously pure  fifths, and placing the pure
harmony in the thirds.  Polophony was increasing during this time, and the
thirds were more in control of the harmony.
>       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

I don't think I would offer, but would certainly do so if asked, or refer to
someone who was better.    ---ric