Sat Part 3 of 6 Altering the Stretch

[Jim]

SAT Part 3  Additional stretch

In the last article we showed how to increase the A4 stretch # in
order to program a wider stretch not only in the A3-A4 octave, but
thoughout the entire tuning.  When this is done, it provides a
wider jump between B4 and C5 where the SAT switches from tuning by
the 4th partial to tuning by the 2nd partial of C5. We will show
how it is necessary to decrease this jump to keep smooth
continuity across this break.  This will require resetting the
pitch a little on the sharp side at C5.

If one programed page 1 of memory to reflect the tuning generated
by the actual measured stretch numbers and page 2 to reflect the
tuning generated by the altered stretch number of A4, then it can
be seen that there is a wider difference between the readings of
B4 and C5 on the second page. Here are the numbers taken from the
example from the Part 1 article:

                       F3   A4   C6
   Page 1 FAC #'s were 8.0, 8.0, 8.0   B4=12.2, C5=3.0  diff,=9.2
   Page 2 FAC #'s were 8.0, 8.5, 8.0   B4=12.9, C5=3.2  diff.=9.7
                                                         ========
                                                               .5
   The B4 readings are for its 4th partial.
   The C5 readings are for its 2nd partial.

In order for the C5 of page 2 to fall in line with the normal
curve of the change in page 1 from B4 to C5, it is necessary to
increase the sharpness of C5 of page 2 to reflect the difference
between B4 and C5 of Page 1.  The above figures in this case as
shown above will require a resetting of the pitch at C5 an amount
equal to the difference of the two differences ie. .5 cents.  It
just happens in this case that the amount for reset (.5 cents) is
the same amount that our A4 stretch number was changed.  It will
not always be the case however, but where the stretch numbers are
close to this example, you could just use the same reset value as
you used in your deviation of the A4 stretch number. In practice
it is good to write down these deviations or resettings so you
don't get confused.  In fact it is good to write these down on
your service record for reference the next time you tune the
piano.

There is another place in the treble where a change from using
the 2nd partial to using the 1st partial or fundamental to tune
occurs. This is between B5 and C6.  This, however, turns out to
be rather inconsequential as the numbers below show:

                 B5             C6       diff.
     Page 1      10.8           4.0      6.8
     Page 2      11.1           4.2      6.9
                                        =====
                                          .1

There is one other place where a change of partial occurs, and
that is between B2 and C3.  B2 utilizes the 6th partial for
tuning, whereas the C3 uses the 4th partial.  Where the stringing
scale is smooth thru this area, it is rather simple to reset the
SAT to accomplish a smooth transition when an alternate value for
A4 has been used.  Here is how the numbers work out:

                   B2             C3      diff.
     Page 1        1.4           -2.4     3.8
     Page 2        1.3           -2.4     3.7
                                         =====
                                           .1

Here again in this case is seems rather inconsequential.  But to
establish the principle it would be necessary to subtract the .1
cent correction.  In some cases where the three FAC numbers are
quite different, it may be necessary to do this type of change.
Just remember, at the 6th partial change, one should subtract
the difference as computed above or in your own example.  At the
change from 4th partial to 2nd partial at C5 one should add the
corrective amount.

In the next article we will discuss the altering of the C6
stretch number in order to provide extreme sharpening thereby
making the triple octaves sound better.  This will also help the
octave-5th and the double-octave-5th at the expense of the wider
single octave and double octave sound.

Jim Coleman, Sr.