As normally tuned, they don't sound sharp. We say they are stretched
(frequency-wise) but we don't normally say they are sharp.
Sound sharp? Depends on who you ask. Some singers who say they have
"perfect pitch" hate what I call a properly tuned piano because they
think the high notes are sharp. They say so in exactly those words.
I've heard violinists say exactly the same thing.
"We" say stretched but not sharp? Define we. I am a pianist for 43
years and a piano tuner for 30 years. I have a Yamaha C7B in my living
room (>$20,000 piano). I can say sharp if I want to.
John also said:
There's an unshakeable consensus among musicians that the nominal
octaves
on a piano are indeed octaves. They aren't quite the same as the
octaves
on, say, a bugle -- but the thirds and fifths aren't the same
either. Life's tough all over.
And I bet those musicians are talking about the "octaves" near the
middle of a piano that aren't "stretched" much at all. Most piano
tuners won't do any stretching from C below middle C to C above middle
C, and some don't stretch another octave on either side of that. So
those middle octaves are usually tuned darn close to a factor of two.
Of course the thirds and fifths are not the same. The piano is tuned
to the equal-tempered scale (plus stretching). Singers, or instruments
where the musician can control the pitch while performing are only
approximations of equal temper. Sometimes this produces a standard
"accepted" sound. For example, when a string bass and a piano double
up on bass notes in a jazz ensemble, they're not playing the same
pitches... i.e. they are out of tune with each other. But that's the
way those instruments are "supposed to sound" when played in a jazz
ensemble. We're accustomed to that sound as "normal."
I said: I'll stick with the definition of an octave as a factor of two
in frequency.
John said: "That's a physics nerd's definition, not a musician's
definition."
I say... bull.
(1) I'm a musician. Maybe a physics nerd also, but that's beside the
point.
(2) Go to college and talk to Ph.D. musicians and see how they define
and/or teach octaves. Everyday I drink coffee with one or more Ph.D.
musicians and I can assure you they define an octave as a factor of two
(as well as those piano octaves, as well as so many notes apart in the
scale). They use all definitions. Many of them think they are the
same thing... they never learned the details. Those who did learn the
details still teach the factor of two because they're supposed to be
teaching "equal temper" but they know any particular instrument or
musician only approximates equal temper.
By the way, the piano waveform doesn't look exactly periodic on an
oscilloscope because "it's alive." The waveform is very dynamic, minor
beating coming and going, unison strings interacting with each other as
energy is coupled back and forth between the strings. But overall it's
basically periodic. It makes the dial on my "strob-o-tuner" stand
still just fine (watching the fundamental circle). But it is fun to
watch the harmonic circles advance and retard as the note is sustained,
while the fundamental stays pretty solid. If the harmonics of one
unison string are not exactly in-tune with another (typical), then the
waveform is very dynamic. I can see this as various tuner circles
moving differently and changing direction as the note is sustained, and
that's what I mean by "alive" and is probably what John means as "not
periodic."
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