SAT Part 6 Altering Stretch

[Jim]

Here is the last of this this series.

SAT Part 6 Altering the Stretch numbers

In previous articles, we have shown controls by both increasing
and decreasing the normal FAC stretch numbers of a piano.  In
this article, we will investigate combinations of the two types.

A Lester spinet might be an example where one would wish to
compress the temperament and upper Bass section and yet have a
wider deep Bass.  The decreasing of the A4 number would have the
effect of tightening up the octaves of the upper Bass and Tenor,
while the expanding of the F3 number would have a greater effect
on the lower Bass where more stretch is needed on this piano.
The Lester spinet which has triple unisons in the top Bass section
cannot tolerate a 6-3 type octave.  A decreased number for A4 would
help accomplish this.  If it were accompanied by an increased F3
number which would not affect the upper Bass much at all as shown
in previous articles, but WOULD increase the stretch downward in
the low Bass, we could have the best of both solutions.

Here are the actual numbers for a Lester spinet:

F3         A4         C6
12.8       5.8        8.2

Let's make this Page 12. On Page 13 we will decrease the A4 and
then make the pitch correction and the break correction.

                               Pitch       Break - -
             F4   A4  C6       A4          B2      C3     Diff.
   Page 12   12.8 5.8 8.2      7.2         1.6    -2.1    3.7
   Page 13   12.8 5.3 8.2      6.6         1.6    -1.9    3.5
                              =====                      =====
                               +.6                        +.2

Actual SAT reading for Page 13:

              F4   A4  C6     A0    A1    A2    A3    A4
   Page 13    12.8 5.3 8.2   -12.4 -3.6   0.9   0.9   6.6

Pitch Corr. for Page 13 = +.6  Break Corr. = +.2 below C3

              F4   A4  C6     A0    A1    A2    A3    A4
   Page 12    12.8 5.8 8.2   -13.2 -4.0   0.8   1.0   7.2
   Page 13    12.8 5.3 8.2   -11.6 -2.8   1.7   1.5   7.2


Now, let's widen the low Bass by increasing the F3 number.

                               Pitch       Break - -
             F4   A4  C6       A4          B2      C3     Diff.
   Page 12   12.8 5.8 8.2      7.2         1.6    -2.1    3.7
   Page 14   15.0 5.3 8.2      6.6         1.6    -2.2    3.8
                              =====                      =====
                                .6                        -.1

Actual SAT reading for Page 14:

              F4   A4  C6     A0    A1    A2    A3    A4
   Page 14    12.8 5.3 8.2   -13.4 -3.8   0.9   0.9   6.6


Pitch Corr. for Page 14 = +.6   Break Corr. = -.1 for below C3

              F4   A4  C6     A0    A1    A2    A3    A4
   Page 12    12.8 5.8 8.2   -13.2 -4.0   0.8   1.0   7.2
   Page 13    12.8 5.3 8.2   -11.6 -2.8   1.7   1.5   7.2
   Page 14    15.0 5.3 8.2   -12.9 -3.3   1.4   1.5   7.2

An analysis of the above 3 lines will show that the A3-A4 octave
is tightened up in Pages 13 and 14.   The A2-A3 octave is
tightened in Page 13, but less in Page 14.  Octave A1-A2 is only
tigntened by .3 cents in Page 13 and only by .1 cent in Page 14.
Octave A0-A1 is narrowed by 2.8 cents on Page 13 and by only 1.0
cent on Page 14. So, in general we can say that this is a way to
tighten the center of the piano and keep the low Bass about the
same.

WIDENING THE CENTER

A similar thing can be done for the treble where one may wish to
widen the center of the piano, but curtail the widening in the
Bass octave.  A suggestion would be to widen the A4 stretch number
by perhaps .5 cents and decrease the F3 stretch number by 2 cents.
By following the above principles, you can experimentally find out
what works best for your particular situation.

My last topic for this series is one which involves what Dean
Reyburn has called para-inharmonicity.  In Bass strings, as well
as treble strings, there can be some irregularity in the way in-
harmonicity works. Some of the factors we know about are: down-
bearing effect, fit of the strings around the bearing points,
uneven string loading or windings, the proximity to soundboard
edges., the effect of bridge aprons, bridge undercutting, bridge
notches, end of bridge affects, etc.  Drs. Dave Roberts and Al
Sanderson have contributed greatly to our understanding of the
affects of the unwrapped lengths of Bass strings.

We have already noticed changes in our FAC numbers from before a
pitch raise and after a pitch raise.  When we have studied this a
little more completely we will share some generalities and a few
specifics.  Until then, you can argue with me about what we have
already written.

Jim Coleman, Sr.