SAT-Learn aural tuning PartV

[Jim]

Dear list, Associates and others interested:

This is the 5th in a series of articles for those who have a SAT available
for help in using the Baldassin-Sanderson Tremperment.  Up to this point, we
have 6 contiguous 3rds tuned from A2 to A4 and the F3 to F4 Temperament is
complete.

Just as we originally divided 2 octaves into equal pieces, we now will
divide smaller areas.  In tuning below F3, we choose to tune D#3 next,
because immediately we can put the speed of the D#3 M3rd halfway between the
C#3 M3rd and the F3 M3rd.  We have available a 4th and a 5th above to help
zero in on the proper location of D#3.  I like to tune D#3 to D#4 as an
octave with zero beat first, then play the D#3 5th which probably has a
slight beat in the narrow direction.  Settle the D#3 gradually toward .5
bps and check with the D#3 4th to see that it is starting to beat.  I want
the D# 4th to beat just slightly faster than the D3 5th.   Now, play the D#3
M3rd to see that it is equally balanced between whole step neighbors.  When
this is balanced, we can then proceed to the M3rds on either side of it.

Next, balance in the E3 M3rd, utilizing the 4th and 5th as above to help zero
in, then see that the E3 3rd fits in evenly between the D#3 3rd and the F3
3rd.  You can also check that the parallel M6ths from F3-D4 on down to C#3-
A#3 decrease evenly in speed.  You can also use the outside-inside M6th-M3rd
test chromatically.  Utilize the same procedures and tests for locating the
D3 M3rd between the C#3 M3rd and the D#3 M3rd.

We have 3 more notes in the bottom of the temperament to do: C3, B2, A#2.
Pick the B2 first to balance between the A2 M3rd and the C#3 M3rd, using the
above procedures.  Then balance the C3 M3rd between the B2 and C#3 M3rds,
using the above type checks.  Then balance the A#2 M3rd between the A2 and
the B2 M3rds, also using the 4ths, 5ths, and 6ths as above.

Now we have just 3 notes left to fill out the top of the 2 octave tempera-
ment, namely: F#4, G4, and G#4.  Pick the middle one G4. Tune it as a pure
5th from C4.  This keeps you on the high side.  See if D#3-G4 fits in as a
good 10th between the C#3 tenth and the F3 tenth.  Correct if necessary and
then check that the 4th (D4-G4) is faster than the 5th (C4-G4).  Usually the
5th will be almost pure in this area, especially in this area and on up. The
M3rd D#4-G4 should also fit in evenly between the the C#4 M3rd and the F4
M3rd.  The parallel M6ths G#3-F4, A#3-G4, and C4-A4 must also fit together
evenly.

Now it will be a simple matter to fit in the F#4 and the G#4 using the above
principles.  From here on up remember to keep the 4ths down from the notes
you are tuning to be a little faster than the 5th down from the same note.
By keeping the 5ths almost pure you are preparing for the greater stretch
needed to help the piano as a whole fit together better.  Some will find it
easier to listen to the slower beats of the 10ths below the note being
tuned.  Also the 3rd-10th test as used in setting the A-A octave and the
F-F octave is important here as well.

This completes the tuning of the BST temperament.  Please stick with each
section of it until you can always tune within .3 cents of what the SAT
calls for, Then gradually try tuning larger portions by ear until you can
do the whole things right.

Jim Coleman, Sr.