Temperament Setting Question

[Doug Hershberger]

Bill,
   This is a very good description of setting that initial octave and a
framework of thirds for the temperament. It never occured to me to also
check the 6:3 on the A3 to A4 octave. This can help speed up the process and
get on to setting the temperament. Sometimes I get confused listening to the
third-tenth test on certain pianos and it is nice to have a back-up check.
In my opinion it is easy to get that first octave too wide, which if you
start with A4 and tune down an octave your F will be too flat at about 7
bps. Another double check that I  like using is B1 as well as F2 for setting
the A440. I guess all these years I only associated the 6:3 test with the
bass. This is one of the things that keeps my interest up in this work. You
just never know it all. Thanks.
Always learning,
Doug Hershberger, RPT
----- Original Message -----
From: <Billbrpt@aol.com>
To: <pianotech@ptg.org>
Sent: Friday, December 17, 1999 7:03 AM
Subject: Re: Temperament Setting Question


> In a message dated 12/17/99 6:11:42 AM Pacific Standard Time,
> pianotoo@imap2.asu.edu (Jim Coleman, Sr.) writes:
>
> << Hey, for all practical purposes the 5/4 ratio works just
>  fine. >>
>
> Jerry,
>
> After trying all of the suggestions, especially Jim's, consider this:  It
> will be much easier to know that the relationship is not correct than when
it
> is.  It is that kind of off-balance feeling just like when you have five
> against four in music.  But when you have the A3-A4 and the F3-F4 octaves
> sounding good and your 3rds F3-A3-C#4-F4-A4 all seem to progress
> proportionately, you'll have it.  You'll also have the best framework for
> avoiding the most common error in temperament tuning today known as the
> Reverse Well error.
>
> When looking for the error, you will never change your A4.  You could have
> too wide or too narrow an octave between your A3 and A4.  The usually best
> recommended compromise is somewhere between a 4:2 and 6:3.  Using the
untuned
> (as of yet) test note, F3, the 3rd, F3-A3 should beat slightly slower than
> the 10th, F3-A4 (the test for a 2:4 octave), proving that it is wider than
a
> 4:2.
>
> Then, using the untuned (as of yet) test note C4, the minor 3rd A3-C4
should
> beat slightly faster than the 6th, C4-A4 (the test for a 6:3 octave),
proving
> that it is slightly narrow of the 6:3 octave type.  This is a very fine
> distinction.  You have to be able to discern the Rapidly Beating Intervals
> (RBI) to a very fine degree.  If both tests seem about right, the octave
is
> about right.  Sometimes there is not much difference between the 4:2 and
6:3
> at this point, particularly on a low inharmonicity piano.  You should be
able
> to hear this difference more clearly on a high inharmonicity piano such as
a
> Steinway.
>
> Once you are satisfied with your A3-A4 octave, ( it sounds more or less
> "pure" when played but the RBI tests are also satisfactory), if the A3-C#4
&
> C#4-F4 is inverted (faster-slower) [which would also be the rock solid
> foundation for a typical Reverse Well error], it means that your F3 was
too
> flat, thus causing your F4 to be too flat.  Try sharpening your F4 to see
if
> the A3-C#4-F4-A4 relationship is then satisfied.  You may still have to
> flatten the C#4 a little too but once you have the top of this correct,
see
> if you can then make an acceptable F3-F4 octave.
>
> As Jim pointed out, the low end of the tenor on a piano with plain wire on
a
> hockey stick shaped bridge will be skewed.  Your 3rds will be a little
slower
> than expected.  Your 5ths may even end up a little wide.  It is very
> important to the harmony of the music that will be made on the piano that
you
> do not have 3rds that are way out of proportion.
>
> This is where closely voiced chords are played.  It is easy to make the
piano
> sound disharmonious by concentrating on favoring 4ths, 5ths and octaves
and
> ignoring the 3rds.  Moreover, the 3rds are pretty important all the way
down
> to F2 but lose their importance after A3. After A3, you can let them
become
> faster as you stretch the octaves to get more of the "singing tones" out
of
> your 10ths.
>
> Bill Bremmer RPT
> Madison, Wisconsin
>
> P.S.  Speaking of Reverse Well, I found a particularly exaggerated example
of
> it yesterday on a nice Kawai KG-2D.  The F#3-A#3 and Ab-C4 3rds were
nearly
> pure, the F3-A3 and G3-B3 3rds very fast and sure enough, the C4-E4 3rd
was
> the very fastest 3rd in the entire temperament.  To me, all music would
sound
> like a nightmare on such a piano even though at standard pitch, I could
still
> recognize in which key the piano would be being played because of the
pitch
> alone.
>
> To me, the "color" (which I personally do not associate with the colors we
> see, i.e., blue, red, green, etc.) would be completely inappropriate even
> though the pitch is more or less standard.  It seems to me that people are
> calling two entirely different perceptions of musical tone or tonality by
the
> same use of jargon, namely the word, "color" and that is what is causing
the
> confusion about hearing "color" in ET.
>