SAT-Learn Aural Tuning II

[Jim]

At the request of John Piesik, I'm continuing with the process of
learning Temperament with the aid of the Sanderson Accutuner since
many of our Associates have that or a similar ETD.

In the previous article I neglected to explain HOW to tune the con-
tiguous 3rds accurately in the Baldassin-Sanderson Temperament.

Once the A3-A4 is established, a trial F3-A3 third may be tuned.  If
F-A comes out to about 6 bps or approx. 12 cents, and a similar
octave stretch is used for the F4 as was used for the A3-A4, the
upper F4-A4 will also be about 11-12 cts wide.  To complete the 3 con-
tiguous 3rds of the F3-F4 octave, one needs only to fit in the C#4
so that there is a smooth progression of the F3 3rd, the A3 3rd
and the C#4 3rd.  There is only one place to put the C#4 to satisfy
that requirement.  And, when doing so, that is exactly where it be-
longs. The progression will be even, although the F3 3rd is too
slow and the C#4 3rd is too fast. Now, when you consider the 3
contiguous 3rds of the A3-A4 octave you'll find that the C#4 3rd is
too fast in relation to the F4 3rd, sometimes it is actually faster.
This tells us that the F4 needs to be lowered so that there is a
smooth progression from the A3 3rd to the C#4 3rd to the F4 3rd.
When you fix the F4, you will need to also fix the F3 3rd by
lowering the F3 to make a good octave with the F4 and also to fit back
into a smooth progression of the F3, A3, C#4, and F4 3rds.

Eventually your guess for the speed of the F3-A3 3rd will improve and
you will not need to do all of this rechecking.  Aim at almost 7 bps
on your first try.  If you set a metronome at 104 and count 4 wavers
or beats per tick of the metronome, you will have 6.9 bps.  If
you have trouble knowing where to listen for the beats, get the
Coleman Beat Locator (sorry for the commercial) and follow its direct-
ions.  Once you can estimate the starting beats well and your 5 notes
F3, A3 C#4, F4 and A4 are all within .3 cents of where the SAT says
they should be, you can set these notes with the machine first on
future pianos on which you practice, and concentrate on the next major
hurdle, ie locating the B3.

Tune in tomorrow for Part III of this series.

Jim Coleman, Sr.