I watched the video and was particularly struck by how differently physicists and musicians think about sound. In the grand scheme of things, sounds waves are a very abstract section of physics. Many of the other subjects that are studied in physics can be seen by the naked eye. We can see gravity at work, centripetal force, momentum, etc. without needing any special equipment. Sound waves cannot be seen; just heard. Scientists came up with drawings and diagrams long ago in order to give sound a more visual approach. Assigning numbers to the different aspects of sound (i.e. frequency, amplitude, wavelength, etc) also makes it a much more tangible concept. Musicians definitely have to keep all of these things in mind while we play, but we also tend to avoid thinking too heavily about most of this information simply because it can get in the way.
Before I go any further, I just want to say two things:
1) I am not a physicist. Everything that I say here has either been verified by my mother or her colleagues as being accurate or I was able to verify the information with websites made available by Virginia Polytechnic Institute and Princeton University. These are all conclusions and paraphrasings of my own.
2) This is what I was taught. I am also coming at all of this from the perspective of a brass player. I briefly discuss harmonics as applicable to string players, but I don't stay on that subject long, seeing as I am not a string player myself. If string players have any corrections to make, please let me know and I will be happy to make corrections. I am certainly doing my best to not convey incorrect information. Much of this is information taught to me by musicians combined with my own knowledge of physics, as verified by actual physics teachers. If you believe that anything I say here to be incorrect, please provide me with a reputable source that contradicts me and I am happy to revise my research. You just disagreeing with me doesn't count. I need something in print that has been peer reviewed in order to consider any revisions.
After reviewing the video embedded above, this is what I sent in response:
"I finally had a chance to watch the video (which was great, by the way) and I was actually kind of amused by my train of thoughts as I listened and watched. I kept hearing myself say things like "That's an octave" and "That's the fifth above it" (speaking in terms of the tonal intervals from the fundamental pitch). It was particularly amusing to think about how differently scientists and musicians approach the physics of sound. The scientists like to think in numbers and pictures, whereas musicians think in terms of the sounds (or soundwaves) themselves.
When
I blow into the mouthpiece, my lips vibrate and create a "buzz" sound
that is amplified by the instrument (it's really just a really fancy and
expensive funnel when you think about it properly). As a brass player I
am much more aware of the tendencies of the natural overtone series
because the entire function of my instrument depends on it. Without
using any of the 4 keys available to me, I can play any of the following
notes at any point in time without changing anything except for the
speed of the lip vibration:
Which
valve (if any) I have depressed determines which harmonic series is
available to me because each valve combination changes the fundamental
of the instrument (there are 12 different fundamentals, therefore 12
different sets of overtones [some instruments are instead restricted to 7]). You can kind of see on the staff above
where things start to get a little hairy and the overtones stop
following the mathematical rules. Each bracket is highlighting an
interval between 2 pitches and each one is labelled with the kind and
quality of the interval between the 2 pitches. The higher you get, the
more adjectives are needed to describe the intervals because they no
longer follow the math. In order to play these pitches in tune with the
fundamental, I have to actively bend the pitch one way or another
(speed up or slow down the vibration) or use a different partial from
another overtone series with a different fundamental. Granted, I try to
not think too hard about any of this when I'm actually playing. That's
a lot of information to have to process when you only have a half a
millisecond to figure out what you're supposed to be playing next. I'd
lose my mind.
Back to the video....
So when he was
describing/drawing each of the harmonics, I was sitting here thinking
"2nd harmonic, 1st overtone, that's just an octave." "3rd harmonic, 2nd
overtone. That's the fifth above that." etc. This also reminded me of
the fact that string players have a completely different idea of what
harmonics are compared to brass players. By dividing the strings with
their finger tip at specific intervals, without completely depressing
the string to the finger board, string players have the ability to
actively play multiphonics (multiple pitches at once) on a single
string. Dividing the string actually multiplies the fundamental itself,
creating a very ethereal sound when only the "pure" harmonics (in-tune
overtones) resonate. It's really pretty cool to hear when it's done
well. When it's not, I suggest running away.
Here's a graphic showing how the strings can be divided to produce these harmonics:
Non-string players can kind of do the same thing,
but we can't do it alone. We need a buddy to produce the second tone
for us. For example: If 2 horn players play an interval of a perfect
fifth, and that perfect fifth is perfectly in tune, the sound waves will
actually produce a sympathetic overtone and you can audibly hear the
next overtone in the series (a perfect fourth above the top note) as well as the major third above the bottom note being played, making it sound as if there are 3 pitches being played instead of 2.
Other overtones are also present, they are just inaudible to the human
ear at the particular frequencies that they occur.
Something else that came to mind during the video was his comment about nodes and open-ended instruments. I don't believe that woodwind players (flute, clarinet, oboe, etc) are as concerned about nodes as brass players are, or at least as brass players should be. When the vibrations move through the funnel of a brass instrument, the sound waves bounce back and forth against the inside of the pipes and are amplified as they gradually move from a small area in the lead pipe to the much larger area of the bell of the instrument. The locations of the nodes change depend on the speed of the vibration, the fundamental being used (valve combination), and the exact overtone being used in that series. If we get a dent in the body of our instruments, it can drastically change our ability to play in tune because it causes a variation in the placement of the nodes. The sound waves can no longer move evenly through the instrument, which makes it much more difficult to play accurately."
Hopefully this wasn't too terribly confusing for anyone. I actually had a fantastic time with the conversations that resulted from all of this over the last few weeks. All of the graphics used above are courtesy of Wikipedia.
