John is correct in this sense: when a piano is tuned, octaves are not
supposed to beat. The second harmonic of the lower string will beat with
the first harmonic of the higher string if the octave is not stretched.
Although it may be "subjective" that we don't want beats, once we have said
that, then physics dictates what has to happen to get rid of the beats.
On the other hand, musicians and psychologists and physics (sometimes the
same person) have done studies to determine what the average person claims
is an octave. These tests do not involve tuning two piano strings until
beats disappear. Rather they involve playing a lower note followed by a
higher note (or vice versa) and varying the frequency of the second note
until the listener declares the two sounds are one octave apart. In these
tests, most listeners will choose a stretched octave. I'm not sure why
other than some sort of psychological preference as Leigh says. I heard one
musician declare it was because so many times as people learn to sing in
choirs in high school, they keep having it drummed into their heads that
they must not go flat. Especially the boys are taught to "think high" or we
also hear "hit it from the top."
It is true (having listened to many high-school choirs) that the men have a
tendency to go flat and the director has to keep working to get them to
think higher. But I have also noticed that college choirs, if anything,
tend to go sharp. Perhaps, when singing a cappella they are taught to
concentrate so hard on not going flat that they actually go sharp.
Anyway, depending upon which type of discussion you are having, I think
there is ample evidence for both viewpoints expressed by John and Leigh.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817