SAT- learning aural tuning

[Jim]

Dear Associates and other interested:

In the previous 2 series, I discussed how to practice a small portion of the
Baldassin-Sanderson Temperament on each tuning job you do, using the SAT.

In this article we will consider how to absolutely nail the middle note,
namely B3.

In the last article I neglected to mention tuning the C#3 as an octave below
C#4 and also as contiguous 3rds between A2 and F3.  It's rather simple, just
do it.  Make the A2 M3rd balance with the C#3 M3rd

Now we have the following notes all within .3 cents of where the SAT says
they should be:

                A2      C#3     F3      A3      C#4     F4      A4

If we can accurately locate B3 and then tune down a 3rd and up a 3rd,
we will have a whole tone scale of 3rds that can be perfectly even.
                                            |
                                            |        D#4
                                                 /
                                            B3
                                         /
                                    G3

The standard method of locating the B3 is to tune two contiguous 4ths up
from F3 and two contiguous 4ths down from F4.  If these are carefully done
so that each beats exactly at 1 bps, then one can balance the B3 between
the G3 and D#4 so that they, as contiguous 3rds will be in a 4 to 5 ratio,
just as the F3 and A3 3rds are in a 4 to 5 ratio.  The speeds may not be the
same in relation to the previously tuned 3rds, but in respect to each other
they must be in a 4 to 5 ratio.  For beginners, this may be a little diffi-
cult.  And besides, it will be necessary to redo each of the 4 4ths.

A simpler method is to do as Michael Kimbel and Fred Tremper have suggested
to me.  Tune 2 perfect 5ths, one down from C#4 to F#3 and the other up from
A3 to E4, then tune B3 as balanced between F#3 and E4.  One of the object-
ions to this has been that the 2nd and 3rd partials of notes in this area
are often a little irregular and may give unpredictable results because
these are the partials which are used in 5ths.  Never-the-less, it is
possible to tune these intervals with more precision and you have half as
many possibilities to go wrong as with tuning 4 4ths, and then trying to
estimate the 4 to 5 ratio with decimal point accuracy.

So, Tune F#3 from C#4 and check with the m3rd-M3rd test: F#3-A3 = A3-C#4.
You may also use the other test: A2-F#3 = A2-C#4.  Do the same for the A3-
E4 fifth.  A3-C4 = C4-E4 or C3-A3 = C3-E4.  Both F#3 and E4 will need to be
adjusted to tempered 5th later.

Now tune B3 as a 4th above F#3 and as a 4th below D4, such that the two 4ths
are equal.  If anything let the upper 4th be only slightly faster than the
lower 4th.  This will positively nail down the B3 location.  Check with
the SAT to see that you are within .3 cents accuracy. Repeat this
portion on each piano you tune for the next few days until you can come out
within .3 cents of what the SAT calls for.

After you tune G3 to B3 to balance equally between the F3 3rd and the A3 3rd
and you tune the D#4 to balance the B3 3rd between the A3 3rd and the C#4
3rd, the A#3 can be balanced between the F3 and the D#4 as contiguous 4ths.
The C4 can be balanced between the G3 and the F4 as contiguous 4ths.  Now it
is possible to retune the F#3 as a tempered 5th to C#4, as a tempered 4th to
B3 and as a M3rd balanced between the F3 3rd and the G3 3rd.  Next, we can
retune the E4 as a tempered 5th to A3, as a tempered 4th to A4, as a M3rd to
C4 to fit between the B3 3rd and the C#4 3rd.  From here on to the finish of
the temperament, it is just impossible to make a misteak (Oops).

My suggestion is to use your SAT to tune everything up to the two trial
5ths, then practice tuning the trial 5ths and balancing the
two 4ths contiguous to B3 until you can always come within .3 cents.

>From thereon, you will have no problems.  Guaranteed.  But still, use the
SAT to check on the remaining notes: G3, D#4, A#3, C4, F#3, and D4 to
complete this series.  When you can do all of these within .3 cents, you
will have gained great confidence in your aural tuning abilities.

BTW, I used this temperament in my preparation work for the Tuneoff in
Chicago, but in the final tuning, I just used the machines SAT and RCT.
For those of you who have the Reyburn CyberTuner, you can program in this
USER TEMPERAMENT so that the machine will follow this order.

Tune in tomorrow for part IV of this series:  How to tune the last two notes
of the F-F octave, and then the next day on how to complete the two octave
temperament.  It is amazing how much this is a self-adjusting temperament.
You really don't have to remember any beats, just make everything fit as the
piano talks back to you.

Jim Coleman, Sr.