SAT in low bass

[Robert Scott]

Ted Simmons wrote:

>I was called in to tune a
>spinet that I had never seen before.  I set up my SAT for this piano
>and began the tuning.  As I got into the lower bass the SAT
>indicated that the notes were very flat and had to be adjusted
>upwards.  When I got to the lowest B, however, the  SAT indicated
>that it was only slightly flat and so I merely tweaked it a little.
>I was puzzled by the fact that among all of those "very flat" notes
>was one that was almost on pitch.  So I did some aural checks and,
>while striking the lowest B, I played notes up from it one at a
>time and discovered that this B was in unison with D1.  Instead
>of being flat, it was sharp by a great amount!  I love my SAT and
>it performs well for me, but it fooled me down in the low bass.
>I've been leery of its bass capabilities ever since.  Can anyone
>explain why this happened and how the SAT can be used to home in
>on the correct pitch for these low notes?

Here is what I think happened.  The SAT uses the 6th partial in
this region.  That means it has a narrow bandpass filter set
around the frequency that is 6 times the nominal fundamental
frequency for B1.  Any frequency that falls inside that narrow
band will be displayed in the lights.  Now look at D1.  It is
a minor third above B1.  A minor third is nearly a 6:5 ratio
in frequencies.  Therefore the 5th partial of D1 is nearly the
same as the 6th partial of B1.  The SAT can't tell the which
partial it is listening to.  It only knows individual frequencies.
So it displays the 5th partial of D1 as if it were the 6th
partial of B1.  Now why were you drawn to the 5th partial in the
first place?  Perhaps the 5th partial was much stronger than
the 6th partial on that string.  In any case, I am surprised that
the B1 string did not break when tuned 300 cents sharp.

Bob Scott
Ann Arbor, Michigan