Temperament, A pianist responds

[Richard Moody]

----- Original Message -----
From: <A440A@AOL.COM>
To: <pianotech@ptg.org>
Sent: Sunday, December 16, 2001 4:41 PM
Subject: Re: Temperament, A pianist responds


| >    I don't think ET was a goal of many people before 1900. >>
|
| Don responds:
| <<With respect ET was known and used in the 1400's by lute players.
Please
| don't blame this on research done 500 years later, or I will have to take
a
| ride with Dr. Who!<,
|
|   Geez! the Lute Lobby! (:)}}
|     I was specifically addressing the tuning of keyboards.  Lutes'
intonation
| was set by movable frets, which can be placed in ET by linear measurment.
M.
| Mersenne, in 1690 not only gave a mathematical  way to do this, but
expressed
| doubt that ET could be tuned on strung keyboards because of the need to
use
| the ear.  This, plus the well documented disjuncture between the lutes
and
| viols versus "keyboard tuning" seems to indicate that it wasn't happening
on
| the keyboards of the time.
| Regards,
| Ed

He does suggest that organ pipes cut in the right dimensions which might
render ET but also suggests fine tuning would probably be necessary because
two identical pipes are not usually in tune.   (393,423)

A reading of the Chapman translation of Mersenne I think will reveal a
remarkable knowledge of ET based on monochord experiments, mathematical
calculations, and comparisons with theory of intonation and scales.
    "But so that we may assume all things to the advantage of those who do
not believe that this equal temperament is exact enough for harmony and for
dividing the fingerboards of instruments or cutting and construction ogan
pipes...."
"For if one moves {on the monochord} the stop of the fifth up ar away by an
eight-hundredth or even an 11/500 part of the string taken from the bridge
to the said fret, the difference of the two sounds that it will make is not
sensible or at least will not offend the ear. "  (p. 54)
    I cannot find in his book instructions for tuning in ET, but I cannot
find where  he says it cannot because the ear has to be used.   He proposes
it along with suggestions for keyboards with more than 12 note scale.  He
does not seem to advocate it though execpt for the lute.   His tuning
instructions are insteresting even though garbled in some cases and gross
editing or proofing mistakes in others.

"Now it is certain that there is no other better means of tuning the spinet
than by a good ear, which hears the exactness of tuning.  (Tune) the first
10 or 12 strings by rising in 5ths approaching more closely to the just
fifth than it will be possible for the other tunings to find.  Then it is
necessary to divide the fifths into major and minor thirds so that the
majors are a little small and the minors a little larger than their
justness
demands;"
....."But it is necessary to explain more particularly....how to tune this
instrument more quickly and exactly. This the players esteem a great secret
of the art. (158)

    And this is as far as he goes. If he meant the major 3rds were larger
thenjust , yes one could say he was suggesting ET.  But  nowhere does he
say, "I have explained ET in theoritical terms, now here is how it could be
tuned on a keyboard."
    As advanced as he was in explaination of ET in math terms apparently he
wasn't in on the "great secret of the art".   There are other tuning
instructions later in the book but they are for quarter comma meantone but
it is not called that.   Apparently he didn't have a name for
    ---ric