SAT Part 4 Altering Stretch

[Jim]

This is #4 of 6

SAT Part4 Altering the stretch

In the first three articles we have discussed the effect
of altering the A4 stretch number of the three FAC's. One
can take this to an extreme, but I would suggest going no
farther than an additional 1 cent stretch, for this will
provide a single octave stretch of 1/2 bps or more. This
gets close to the limit which one can tolerate in the
sound of the center single octave.

If more stretch of the high treble is desired, then
altering the C6 stretch number is required. For an example
of this, let us create a Page 3 tuning using the FAC #'s
8.0, 8.5, 8.5.  We then find a comparison between Pages 1,
2, and 3 as follows:

                     C5       C6       C7       C8
   Page 1            3.0      4.0      13.8     43.8
   Page 2            3.2      4.2      14.7     44.4
   Page 3            3.2      4.2      14.7     46.6

Now please remember that in increasing the stretch of A4 by
..5 cents, it was necessary to reset the SAT on the sharp
side by .5 cents at the note C5 and another .1 cent at C6
so that the real values of the above should be:

                     C5       C6       C7       C8
   Page 1            3.0      4.0      13.8     43.8
   Page 2            3.7      4.8      15.3     45.0
   Page 3            3.7      4.8      15.3     47.2

Since the stretch is based on an exponential curve (steeper
and steeper climb to the right), There is not any difference
at note C7 in this example, but if one uses a higher addi-
tional stretch like 2 cents for C6, you will see a more
dramatic change in the numbers as shown in Page 4 where the
stretch numbers are:  8.0, 8.5, 10.0

                     C5       C6       C7       C8
   Page 1            3.0      4.0      13.8     43.8
   Page 2            3.7      4.8      15.3     45.0
   Page 3            3.7      4.8      15.3     47.2
   Page 4            3.7      4.7      15.5     54.0

For pages 2,3, &4 the corrective reset of .5 cents at C5 and
..1 cents at C6 have been included due to the change of the
A4 stretch number from 8.0 to 8.5.

Now for an extreme example, let us take a 1 cent change at
A4 and a 2 cent change at C6.  Our FAC numbers will now be
8.0, 9.0, 10.0 and we will program this on page 5.

Let us see first of all what the change in the A4 number
creates.  We will compare Page 1 with Page 5 in respect
to the locations where the partial being used changes.

               B4      C5    diff.    B5      C6    diff.
   Page 1      12.2    3.0   9.2      10.8    4.0   6.8
   Page 5      13.0    3.2   9.8      12.4    4.1   8.3
                            =====                  =====
                              .6                    1.5

As a result of this, it is necessary to reset the SAT at
plus .6 cents when you get to C5 and an additional 1.5
cents when you get to C6.  You can see the exponential
increase over the resets for the .5 increase of the
stretch number for A4.  Now let us apply this change to
the readings of Page 5 in the following comparison.

           FAC's        C5       C6       C7       C8
   Page 1  8 8   8      3.0      4.0      13.8     43.8
   Page 2  8 8.5 8      3.7      4.8      15.3     45.0
   Page 3  8 8.5 8.5    3.7      4.8      15.3     47.2
   Page 4  8 8.5 10     3.7      4.7      15.5     54.0
   Page 5  8 9   10     3.8      6.2      17.0     55.5

>From the above you can see that varying the A4 stretch
number makes more difference than varying the C6 stretch
number except in the upper top octave.

You can apply these above principles on any piano if you
desire to change the amount of stretching of the octaves.

There is one other type of change for the treble which
needs to be addressed and that is where you wish to
compress the octaves for some reason.  One example that
comes to mind is in taking the PTG test.  Since one of
the requirements for the top octave is that they be tuned
in simple 2-1 fashion, that is where the C7 is in tune
with the 2nd partial of C6.  For this purpose, one could
decrease the normal C6 stretch number which in turn would
decrease the cents especially in the top octave on an
exponential basis.  The location of C6 would normally
fall within the tolerance range anyway, but by choosing
a slightly smaller number for the C6 stretch value, it
would in effect tend to flatten out the normal exponen-
tial upward curve from C7 to B7.

Here is an example of decreasing the C6 stretch number
by 1 cent:
           FAC's        C5       C6       C7       C8
   Page 1  8 8  8       3.0      4.0      13.8     43.8
   Page 6  8 8  7       3.0      4.0      13.8     39.2

A much simpler way to tune the top octave for PTG test
purposes would be to tune C7 to the 2nd partial of C6,
and continue in like fashion up to B7. It is my opinion
that those who do the master tuning, should use this same
method since there is the ARBITRARY requirement that the
examinees be judged on this basis.  Aural tuning IN THIS
AREA brings with it more variance than does electronic
tuning.

In the next article, we will explore the possibilities
of varying the F3 stretch number and its effect on the
Bass and Tenor areas.

Jim Coleman, Sr.