Acceptable levels of error

[Billbrpt@aol.com]

In a message dated 98-02-10 00:56:22 EST, you write:

<< Doesn't it matter where you start when you tune an uneven temperament.   If
the piece is to be in G minor, and once you select the temp. isn't there a
optimal starting point for G minor.  Would the starting point be different if
it were say C minor? Perhaps a knowledge of music theory would aid in that
answer. >>

   All of the HT's that have been a part of this recent discussion are created
with C as the tonal center. One chooses a key to write in because of the
character that is expected from that key.  G minor has 2 flats.  This is only
2 steps away from the top of the cycle of 5ths and so it has a moderate minor
charachter.  A minor key with many flats or sharps would be expected to have a
much darker sound.

   Your first question has been a point of contention among practitioners of
HT's.  It does not seem logical to craft an HT from anything but the note C.
However, we do have the issue of Standard Pitch at A-440 to contend with.  If
you are tuning in ET, it does not matter what note you start on, at least
theoretically.  But when you tune virtually any HT, if you use C-523.3 as a
pitch standard, your A will most certainly not be 440.  Therefore, I and many
others have learned to adapt the approach to crafting an HT from the note A
instead. This however does not mean that A is the tonal center.  It is not
"transposed"  from the tonal center but it is "transposed" in terms of which
is the starting note.   The word "Transposed" is used in yet another way in
the question you ask  below:

<<...another reason for asking is that the title of the Vallotti/Young (I am
reading)  is, "Tuning the Transposed Vallotti Well Temperament of 1781
According to Thomas Young's Rules of 1799." 
 What does "Transposed" mean?.  The scheme starts from middle C. >>

The original Vallotti temperament also has the tonal center at C but unlike
many other WT's the 5th, FC was not pure but tempered.  There was no way to
get from C to F without speculating (guessing or estimating, much as you must
do through an entire ET) and the series of pure 5ths that followed it.  Young
solved this problem by taking the pure 5th that was between B & F# and trading
it over to F & C, thus it was a "transposition" of sorts.  See the various
ways a Vallotti temperament was tuned beginning on page 176.

    When I tune a Vallotti temperament, I start on the note A but tune in a
way which is similar to that which is found on page 182.  I also figured out a
way to do an "Equal-Beating" method for Valotti from an A fork by using the
same 4 contiguous ET 3rds that you do for ET.  This gives you your C#  from
which you can get all your pure 5ths in this temperament.  Then, you tune the
remaining intervals by the EB method.  The Fs you originally tuned were only
temporary. This is also a valid historical technique, to "temporarily tune" a
note so that you can find the correct placement for another.  It is done in
the EB method quite frequently.

Regards,
Bill