single vs. three string unisons (long)

[FSSturm@aol.com]

In a message concerning the "Tune-off", Jim Coleman, sr. mentioned Virgil
Smith's contention that a three-string unison is flatter in pitch than its
individual strings, and said that Virgil convinced him it was true. With due
respect, I beg to differ, or at least to state my skepticism.

When Virgil wrote on the subject about a year ago in the PTJ, I was skeptical
from an aural tuning point of view. I had never experienced the phenomenon,
and I was utterly unable to duplicate it myself. I assumed Virgil was
referring to a psychological attitude rather than a physical fact, and that
he really just wanted to make octaves wide of what would normally be
considered "beatless" in an aural sense in order to prepare for beatless
triple and even possibly quadruple octaves (I have my doubts about the
quadruple ones, except maybe on pianos with really low mid range
inharmonicity, like Kawais).

Just to verify my conclusions, I decided to test the notion with the help of
my SAT. At first, I was surprised to find what seemed to be evidence in favor
of Virgil's contention. Further testing, however,  has led me to doubt it.

There are several possible scenarios with SAT readings. When strings are
pure, it is possible to tune so as to "stop the lights cold." When this
occurs for all three individual strings of a unison, my experience shows that
the unison will have lights "stopped cold" as well, and at the same pitch.
Whenever I have met with an exception, I have rechecked the individual
strings and found that one or more was "slowly creeping" (it was really
reading slightly sharp or flat, whether because my initial reading wasn't
careful enough or because the pitch had changed). When this was corrected,
the three-string unison registered the same as the individual strings. It
only takes the tiniest discrepancy of one string to override the readings of
the other two. When a pitch raise of one cent is done, often pulling the
second and third strings up will cause the first string to go flat by one or
two tenths of a cent - not enough to make the unison objectionable, or even
noticeably have a "wow", but enough to make the lights rotate.

Unfortunately, pure strings like this are relatively rare in the upper
regions of pianos, and the movement of the lights has to be interpreted.
There are two main behaviors: 1) lights jump forward (sharp), then rotate
back (flat), and 2) lights jump in one direction or the other, skipping one
or two pairs of lights. Actually there is a third behavior, when a string is
really wild, where the lights seem to dance at random, but let's ignore that
one. (And to be precise, there are all sorts of in between conditions as
well).

In case 1, I believe the difference between prompt and sustain pitch is what
is being read by the machine. This occurs especially in the top octave and a
half. Normally we tune the prompt (at least I do), playing the note rapidly
in successive blows to get a "stable" reading. When all three strings are
played together, the sustain is longer and more prominent, so it shows up
more clearly than with each individual string. At least this is my experience
and interpretation. In other words, we can get a clearer reading of a longer
sustained tone from the three strings together, and it reads flatter than the
prompt tone we tuned. But if we play the three strings with as rapid a
repetition as we played the singles while tuning them, we'll mostly get
consistent readings for both individual strings and the three string unison.

Case 2 is difficult to interpret in many cases. I think it is a stroboscopic
phenomenon like when old movies showed wagons with spoked wheels, that
appeared to rotate  backward as they slowed down. It is often hard to tell
which way the lights are jumping. Are they jumping two lights to the east, or
one to the west? Often they seem to be stationary, just alternating by one
light from right to left and back, when really they are skipping two lights
and rotating in a particular direction. Sometimes I'll tune two "jumping
light" strings and think I am interpreting them the same, but when I play the
unison I find that I was mistaken on one or even both of them. At any rate,
when there is one or more "jumping light" strings in a unison, this can skew
the way the three strings read together. I think in a majority of cases the
three strings together read flat, but quite often they will read sharp. I
think flat beats out sharp in about a 60/40 ratio, but I am not sure that
this is not caused by my own interpretation of the lights.

When I look at the whole picture, go through a piano very carefully, checking
and rechecking each string and comparing their readings with their respective
three string unisons, I am unable to find any consistent evidence for the
pitch difference phenomenon that can't be explained by the foregoing.

So there is my two cents worth on the subject. I write mostly because I hate
to see something like this become a commonly accepted "fact", and fail to be
questioned further, just because somebody with authority and respect has said
it was so. After writing that, I want to say that there is probably nobody
whose opinions I respect more than Jim Coleman's. So Jim, can you explain a
little further how you became convinced? And anyone else have thoughts on the
subject?

Fred Sturm, RPT
Albuquerque, NM