Speaker 1: Welcome to text Stuff, a production from my Heart Radio.
Speaker 1: Hey there, and welcome to tech Stuff. I'm your host,
Speaker 1: Jonathan Strickland. I'm an executive producer with I Heart Radio,
Speaker 1: and I love all things tech. And here's a really
Speaker 1: cool thing about technology. Technology is the proof that science works.
Speaker 1: So you can think of technology is sort of the
Speaker 1: physical manifestation of our understanding of science. And as we
Speaker 1: learn more about how our universe works, we can build
Speaker 1: stuff that leverages what we've learned. We can even leverage
Speaker 1: how the universe works without having a full understanding of
Speaker 1: the scientific principles. Though in general, the better we understand
Speaker 1: those principles, the better technology we can make. And one
Speaker 1: subset of technology that I think really illustrates this well
Speaker 1: is musical instrument and so in this episode and in
Speaker 1: the next episode, I'll talk about the science behind music
Speaker 1: without getting too deep into musical theory that's its own thing,
Speaker 1: and how musical instruments are an example of physics and action. Now,
Speaker 1: in the past, I've done episodes on stuff like synthesizers
Speaker 1: and electric guitars and pickups and amplifiers, you know, describing
Speaker 1: how electronics gave musicians new ways to make sounds, including
Speaker 1: sounds that have never been created before. But honestly, the
Speaker 1: entire history of musical instruments kind of follows that path.
Speaker 1: It's just that some of those instruments are the kind
Speaker 1: that you plug in or that you connect to amplifiers
Speaker 1: or whatever, and some aren't. But they all relate back
Speaker 1: to science in some way or another. Music marries the
Speaker 1: scientific with the creative, and it's one of the manifestations
Speaker 1: of ingenuity that I really love. Case in point, the
Speaker 1: inspiration for today's episode came out of something I was
Speaker 1: genuinely curious about out myself. See, I'm not a musician
Speaker 1: by any stretch of the imagination. Though I do own
Speaker 1: a few musical instruments, I was never in band or
Speaker 1: orchestra or anything like that. So I was sitting there thinking,
Speaker 1: how the heck does a trumpet work? And I researched it,
Speaker 1: and then I thought, you know, I should do a
Speaker 1: tech stuff episode on this. But then I kept going
Speaker 1: down the rabbit hole and decided to do something a
Speaker 1: little more ambitious than how a trumpet works. So in
Speaker 1: today's episode, I'm going to talk more generally about music
Speaker 1: instruments and how they work. By explaining the physics behind
Speaker 1: the art of music, because when you get down to it,
Speaker 1: a musical instrument is really just taking what we understand
Speaker 1: about physics, building a real world object based on that understanding,
Speaker 1: and then putting it to use to make something beautiful
Speaker 1: or interesting, or, in my case, terrible. To understand all this,
Speaker 1: it's best to start with a scientific breakdown of the
Speaker 1: phenomenon of sound. And there's an old philosophical question that says,
Speaker 1: if a tree falls in the forest and nobody is
Speaker 1: around to hear it, does it make a sound? Now,
Speaker 1: one point of this question could be to say, if
Speaker 1: there's no way to observe something happening, can we really
Speaker 1: be sure that it actually happened, particularly something as ephemeral
Speaker 1: as sound, So if no one was there to observe it,
Speaker 1: can we say for sure that something observable happened. But
Speaker 1: another way that we could look at the same question
Speaker 1: is to say, is sound really a thing if there
Speaker 1: is no one there to perceive it? Because sound is
Speaker 1: really describing how our brains process incoming fluctuations of air pressure.
Speaker 1: In this case, we're not necessarily asking if the vibrations
Speaker 1: from the tree happened or not. It's more that if
Speaker 1: there is no one to experience that as sound, would
Speaker 1: we really say that a sound happened? Is the experience
Speaker 1: necessary to call it sound? Now I don't have an
Speaker 1: answer to that question, but I do want to talk
Speaker 1: more about what's going on with sounds. So at the
Speaker 1: very heart of it, sound comes from vibrations. Generally, when
Speaker 1: we talk about sound, we typically mean it comes from
Speaker 1: vibrations of air molecules, which gets to that fluctuation and
Speaker 1: air pressure that I was talking about. It's fluctuations and
Speaker 1: air pressure that ultimately are sound most of the time
Speaker 1: when we're talking about it. Sound can actually travel through
Speaker 1: really any physical medium. It's just that it travels more
Speaker 1: easily through some rather than others. And the way we
Speaker 1: usually encounter it is through the air. So let's say
Speaker 1: for a moment that you have the incredible superpower to
Speaker 1: zoom and enhance your vision, and you can also see
Speaker 1: air molecules, so you're actually looking at the air molecules
Speaker 1: all around you. Now, imagine that you see someone clap
Speaker 1: their hands, and as they clap their hands, they're causing
Speaker 1: a bunch of air molecules to bounce around into each other,
Speaker 1: and that creates a chain reaction that passes from the
Speaker 1: point of origin, that being the clapping hands outward like
Speaker 1: a ripple and a pond, almost but in all directions.
Speaker 1: Now you're paying really close attention, and you notice that
Speaker 1: as the collisions move outward, the reaction as a whole
Speaker 1: begins to appear to lose energy. So the further you
Speaker 1: out from the point of origin, the less you'll see
Speaker 1: those air molecules move, and eventually you'll be far enough
Speaker 1: out where the movement is imperceptible. And this is why
Speaker 1: sounds are louder when you're closer to the point of origin,
Speaker 1: which I admit is about as basic an idea as
Speaker 1: I can communicate. But the reason those sounds are softer
Speaker 1: when you're further away, assuming you don't have some interesting
Speaker 1: curvature of the acoustic area around you, the reason that
Speaker 1: they're softer is that the energy of that initial vibration
Speaker 1: gets diluted as the reaction passes outward. And you can
Speaker 1: think of it as the origin of the sound affects
Speaker 1: a relatively small number of air molecules and at least
Speaker 1: surrounding that point of origin, and it causes those air
Speaker 1: molecules to fluctuate. Those fluctuating air molecules cause a larger
Speaker 1: number of surrounding air molecules to fluctuate. But because you're
Speaker 1: talking about transferring energy from a smaller number of molecules
Speaker 1: to a larger number of molecules, the amount of energy
Speaker 1: transmitted to that second group of air molecules means that
Speaker 1: each individual molecule is getting less than the first group.
Speaker 1: You know, energy cannot be created or destroyed, so we're
Speaker 1: not getting rid of energy here, it's just we're spreading
Speaker 1: it out across a larger area, so each individual component
Speaker 1: is getting slightly less energy than the previous group. Now,
Speaker 1: of course, in the real world it's not quite so
Speaker 1: neat and simple as saying a circle of air molecules
Speaker 1: than affects and slightly larger circle that affects a slightly
Speaker 1: larger circle, and so on. But you get the idea.
Speaker 1: When we talk about vibrations, we mentioned stuff like frequency,
Speaker 1: and that word is all about the number of times
Speaker 1: a repeating event occurs within a given unit of time.
Speaker 1: So with sound, we usually refer to frequency in terms
Speaker 1: of units called hurts, h, E, R, t z. This
Speaker 1: tells us how many times this particular repeated event, and
Speaker 1: oscillation happens within the span of a second. Twenty hurts,
Speaker 1: which is generally said to be the lower end of
Speaker 1: the typical range for human hearing, would be a wave
Speaker 1: that's oscillating twenty times per second. Any vibration slower than
Speaker 1: that would be at such a low frequency that the
Speaker 1: average person would be unable to hear it. A twenty
Speaker 1: killer hurts sound, which is at the tippy top end
Speaker 1: of typical human hearing, would mean that the oscillating wave
Speaker 1: is oscillating at a speed of twenty thousand times per second.
Speaker 1: So that means if you had a string that vibrated
Speaker 1: at twenty hurts, you can set up a high speed
Speaker 1: camera on that string, and when you pluck the string
Speaker 1: and you're use that high speed camera to shoot video
Speaker 1: of it, you would see that for every second in
Speaker 1: real time that passes, you could count the string making
Speaker 1: twenty full cycles, which means going up and down past
Speaker 1: the camera that's one full cycle. Not just passing it once,
Speaker 1: it has to pass it twice. That would be twenty hurts. Now,
Speaker 1: we also tend to talk about sound waves, and this
Speaker 1: gets a little complicated because we can mean different things
Speaker 1: by sound waves. We could be talking about the actual
Speaker 1: physical wave of air fluctuations that propagates outwards from the
Speaker 1: origin of sound, or we could be talking about a
Speaker 1: visualization of the qualities of a sound. And this gets
Speaker 1: into a territory where it's tricky to explain this without
Speaker 1: visual aids, but we're gonna try. So we're gonna talk
Speaker 1: about the visualization without visual aids. So I want you
Speaker 1: to imagine that you have a piece of paper, and
Speaker 1: across the middle of this piece of paper, you draw
Speaker 1: a straight horizontal line from left to right goes all
Speaker 1: the way across the paper. And this law line in
Speaker 1: this particular representation is going to represent time. This is
Speaker 1: the X axis. So the left side of your paper,
Speaker 1: where you're starting point is, represents zero seconds. The far
Speaker 1: right sign represents some arbitrary point of time. We'll get
Speaker 1: to that in a second, because it all depends on
Speaker 1: the specific kind of wave you're drawing. So now let's
Speaker 1: just imagine drawing a nice sign wave, and we start
Speaker 1: on the leftmost side at the center point, so zero
Speaker 1: at the center horizontal line, and draw a nice gentle
Speaker 1: crest up and then we come back down cross that
Speaker 1: center line and then draw an equally gentle trough that
Speaker 1: is of equivalent size to the crest on the opposite side.
Speaker 1: And then once the line comes back up and crosses
Speaker 1: the horizontal line again, we've got one wavelength of a
Speaker 1: sound wave that this would be in what we would
Speaker 1: call the time domain. The reason we call it the
Speaker 1: time domain is that we are visualizing a sound wave
Speaker 1: with regard to the passing of time. That X axis
Speaker 1: again is showing the time is passing. So the wavelength
Speaker 1: describes the distance or the amount of time that passes
Speaker 1: between two corresponding points on a sign wave. So let's
Speaker 1: say we draw a series of these like we get
Speaker 1: twenty sheets of paper, and we draw equal sign waves
Speaker 1: on each of those twenty sheets of paper, and we
Speaker 1: put them all side by side, so we get a
Speaker 1: nice continuous wave all the way down these twenty sheets wide.
Speaker 1: And we say that each sheet represents one twentieth of
Speaker 1: a second, so that when we have twenty of them
Speaker 1: side by side, that represents one seconds worth of time.
Speaker 1: You would say I have twenty wave lengths that span
Speaker 1: one second. That means that this represents twenty hurts. This
Speaker 1: is a sound wave with a frequency of twenty Hurts
Speaker 1: because it takes twenty of these will pass a given
Speaker 1: point in space within the span of one second. So
Speaker 1: then we need to talk about the period of a wave,
Speaker 1: and this is the inverse of Frequency is the amount
Speaker 1: of time it takes for one wavelength to complete one cycle.
Speaker 1: So frequency is the number of cycles per second. The
Speaker 1: period of a wave is the number of seconds per cycle.
Speaker 1: So for a twenty Hurts frequency, the period of the
Speaker 1: wave would be one seconds per cycle. That's why we
Speaker 1: would need twenty sheets of paper with just one nice
Speaker 1: curvy wave on each piece to represent a twenty Hurts wave.
Speaker 1: Now you could just do this on one sheet of paper,
Speaker 1: you know, you just change the scale. So you change
Speaker 1: the scale so that every single wavelength represents of a second.
Speaker 1: You draw twenty of those on one sheet of paper.
Speaker 1: Will be much smaller than our original example, but that
Speaker 1: would still will be a twenty Hurts wave. It's all
Speaker 1: dependent on the scale of your representation. Wavelength and frequency
Speaker 1: are related, and we see that in an equation where
Speaker 1: we say velocity equals wavelength times frequency. So velocity describes
Speaker 1: the speed and direction. But we can ignore that for
Speaker 1: now of a wave as it passes a stationary point.
Speaker 1: So if we know two of those three factors, we
Speaker 1: can figure out the third. But just a little math, right,
Speaker 1: If we know the velocity and we know the wavelength, well,
Speaker 1: we can divide the velocity by the wavelength and then
Speaker 1: we have the frequency. Or if we know the frequency
Speaker 1: but not the wavelength, we can divide the velocity by
Speaker 1: the frequency. We get the wavelength. If we know the
Speaker 1: frequency and the wavelength, we multiply them together, we get
Speaker 1: the velocity. Pretty easy stuff. Now, speed of sound is
Speaker 1: not that difficult for us to to get our minds
Speaker 1: wrapped around, because we know what the speed of sound
Speaker 1: is generally speaking, so the speed of sound depends partly
Speaker 1: upon the medium through which the sound is traveling. Sound
Speaker 1: moves at different speeds through water than it does through
Speaker 1: the air, for example. But even in the air, stuff
Speaker 1: can affect the speed of sound, like the air's humidity
Speaker 1: and its temperature. Essentially, we're talking about density. The density
Speaker 1: of those air molecules will affect how quickly sound can
Speaker 1: travel through it. So when we talk about the speed
Speaker 1: of sound, we have to get more specific. So we
Speaker 1: tend to describe the speed of sound as being three
Speaker 1: hundred forty three meters per second in dry air at
Speaker 1: twenty degrees celsius. Now, for my fellow Americans out there
Speaker 1: who ain't got time to truck with no sensible metrics
Speaker 1: system or celsius or anything, this would mean sound travels
Speaker 1: at about one thousand, one twenty five ft per second
Speaker 1: when the air is sixty eight degrees fahrenheit. Sound at
Speaker 1: all frequencies will travel at the same speed through any
Speaker 1: given medium. So that means that a low pitch sound
Speaker 1: and a high pitch sound will both cover the same
Speaker 1: amount of space in the same amount of time through
Speaker 1: the same medium. But low sounds have low frequencies and
Speaker 1: thus longer wavelengths than high sounds, which are higher frequencies
Speaker 1: with shorter wavelengths. It will take the same amount of
Speaker 1: time for a high pitch note on a trumpet to
Speaker 1: get to you as a low blast note on a
Speaker 1: tuba that's played at the same distance, but the high
Speaker 1: pitched note will have a higher frequency and a shorter
Speaker 1: wavelength than the tubus note. Now I've used this analogy
Speaker 1: several times before, but imagine that you've got a two
Speaker 1: lane highway and you've got a line of buses that
Speaker 1: are in the right lane, and the buses are one
Speaker 1: right after the other. And in the left lane you've
Speaker 1: got a line of compact cars. And for every bus,
Speaker 1: you can fit three cars in that same length of space.
Speaker 1: And the front of the first car is in line
Speaker 1: with the front of the first bus. The rear bumper
Speaker 1: of the last car lines up with the rear bumper
Speaker 1: of the last bus. Both lanes of traffic are traveling
Speaker 1: at the exact same speed. Down highway, both lanes of
Speaker 1: traffic will cross a finish line at the exact same time. However,
Speaker 1: you have more cars in lane two than you have
Speaker 1: buses in lane one. Everyone's going at the same speed.
Speaker 1: That's kind of the way we have to think about
Speaker 1: sound waves and frequencies. If a sound is low enough,
Speaker 1: we may not hear it at all, But if it
Speaker 1: is a strong enough signal, meaning it has a great
Speaker 1: deal of amplitude, we could physically feel it. You remember,
Speaker 1: it's air fluctuations, it's actual air pressure. So typically we
Speaker 1: would perceive amplitude as volume, and in our sketch of
Speaker 1: a wave, it would mean that the peaks and low
Speaker 1: points would be really far out from that center line,
Speaker 1: you know, the taller those peaks are, the greater the
Speaker 1: amplitude or greater the volume. If you've ever been near
Speaker 1: a massive sub whiffer and you felt pressure, like in
Speaker 1: your chest, but you couldn't really hear anything, chances are
Speaker 1: it means the sub whoffer was blasting out vibrations below
Speaker 1: your threshold of hearing. Typically, when we talk about music,
Speaker 1: we talk a lot more about frequencies than we do
Speaker 1: about wavelength and that's because of this relationship between frequency
Speaker 1: and pitch. But wavelengths are also important as they will
Speaker 1: become a key component of stuff like resonance and harmonics
Speaker 1: and boyality. Let me tell you, preparing this section of
Speaker 1: the podcast was a heck of a thing all by itself,
Speaker 1: because this is stuff that's way easier to explain with
Speaker 1: visual aids. But stick with me because I know you
Speaker 1: guys are smart enough to suss it all out, so
Speaker 1: it really just falls on me to describe it clearly.
Speaker 1: So another thing we need to understand before we jump
Speaker 1: into that, and we'll take a break before we get
Speaker 1: to resonance and harmonics. But one other thing I want
Speaker 1: to explain is the phase of a wave. A wave's
Speaker 1: phase refers to how it is offset from some specific
Speaker 1: starting position. And it really becomes important when you're talking
Speaker 1: about multiple waves. Because multiple waves can be offset from
Speaker 1: one another. They can be out of phase with each other,
Speaker 1: and that affects the sounds that we perceive. So, going
Speaker 1: back to our original sketch of a single wave, imagine
Speaker 1: that you draw a new wave using that same series
Speaker 1: of pieces of paper, but you use a different color
Speaker 1: for this new wave, and you offset it a bit.
Speaker 1: So instead of starting at the far left of the
Speaker 1: first sheet, let's say you start one inch in so
Speaker 1: it's offset from that first wave. Otherwise it follows the
Speaker 1: exact same trajectory. Well, these two waves would be out
Speaker 1: of phase with respect of each other. Why is this
Speaker 1: all important? I'll explain in a second, but first let's
Speaker 1: take a quick break. Okay, So before the break, I
Speaker 1: talked about the phase of a sound wave. Imagine you've
Speaker 1: got two of the same frequency of sound, but they're
Speaker 1: out of phase with each other. That would affect how
Speaker 1: we perceived the sound. It could get pretty noisy. Actually.
Speaker 1: If the two frequencies, however, are perfectly opposite each other,
Speaker 1: so that the crests in sound wave a match up
Speaker 1: perfectly with the troughs of sound wave B, and they're
Speaker 1: of the exact same frequency and amplitude, we wouldn't hear
Speaker 1: the sound at all because those two sound waves would
Speaker 1: cancel each other out. You can think of it in
Speaker 1: this way. Think of air molecule number one is pushing
Speaker 1: to the right on air molecule number two, but air
Speaker 1: molecule two is pushing just as hard on the left
Speaker 1: to air molecule number one, which means neither air molecule
Speaker 1: will actually move. This is how noise canceling headphones work.
Speaker 1: By the way, the headphones incorporate a microphone. It picks
Speaker 1: up the ambient sounds in your environment, and then speakers
Speaker 1: in the headphones generate the equal but opposite sound waves
Speaker 1: to cancel out the ones that you would otherwise hear
Speaker 1: as long as the latency that being the lag between
Speaker 1: detecting a sound and generating the opposite sound, As long
Speaker 1: as that latency is low enough, we humans are too
Speaker 1: slow to pick up on the difference, and our perception
Speaker 1: is really limited in that way. But the out of
Speaker 1: face stuff also matters a lot when we talk about
Speaker 1: things like resonance and harmonics as well. So I guess
Speaker 1: there's no time like the present to finally get into
Speaker 1: all that stuff. It is incredibly important with musical instruments,
Speaker 1: So the descriptions I've used so far really refer to
Speaker 1: pure pitches, which is something we can generate with electronics,
Speaker 1: but it's not typically what we get with musical instruments
Speaker 1: outside of things like tuning forks. A pure pitch describes
Speaker 1: a single frequency with no harmonics or overtones, so we
Speaker 1: don't get any other frequencies other than the base one,
Speaker 1: the fundamental frequency. We're getting a pure tone, which we
Speaker 1: could plot as a smooth, consistent sign wave with equal
Speaker 1: crests and troughs, nice and neat, kind of like the
Speaker 1: example I was describing at the top of this episode.
Speaker 1: But in the real world, the sounds we hear typically
Speaker 1: consist of more than one frequency. There are multiple frequencies
Speaker 1: going on here. We can still plot the sound waves,
Speaker 1: but they wouldn't look like those nice, smooth curves we
Speaker 1: were talking about earlier. They would be funk looking potentially,
Speaker 1: with little dips and bumps and the crests and troughs.
Speaker 1: And that's because we'd be representing a collection of frequencies
Speaker 1: in a single way. Visualization sort of the visual equivalent
Speaker 1: of how we would perceive the sound through hearing. So
Speaker 1: let's go through with an example. Let's say you're strumming
Speaker 1: a guitar string, and that string will vibrate and not
Speaker 1: just one frequency, but a few different frequencies all at
Speaker 1: the same time. All of these frequencies are resonant frequencies,
Speaker 1: meaning these are the collection of vibration speeds at which
Speaker 1: that string naturally experiences when it is strummed. However, human
Speaker 1: hearing is such that we typically only hear the pitch
Speaker 1: of the lowest resonant frequency in that bunch. This is
Speaker 1: the fundamental frequency. You can think of it as the baseline.
Speaker 1: In musical instruments. The additional resonant frequencies those higher than
Speaker 1: the fundamental frequency, higher in frequency, so more hurts. In
Speaker 1: other words, are typically, but not exclusively, harmonics of the
Speaker 1: fundamental and a harmonic is a whole number multiple of
Speaker 1: the fundamental frequency. So let's focus on that guitar string.
Speaker 1: It's a lot easier if we talk about a specific example.
Speaker 1: So we're gonna say that we're gonna play the A string.
Speaker 1: Why the A string, Well, because it has a fundamental
Speaker 1: frequency of one ten hurts. It makes it very easy
Speaker 1: for us to do multiples. So the fundamental frequency sees
Speaker 1: the string vibrate one hundred ten times per second. That
Speaker 1: means a full sequence of going up and down and
Speaker 1: returning to starting point on times per second. The string
Speaker 1: is anchored at either end of the guitar. If we
Speaker 1: could slow down time, we would see that length of
Speaker 1: string making that up down journey one ten times every second.
Speaker 1: But the string is also vibrating at other frequencies that
Speaker 1: are higher than the fundamental In general, we call these
Speaker 1: overtones together. The overtones with the fundamental frequency are called partials.
Speaker 1: Now I'm going to focus on harmonics first because they
Speaker 1: are the easiest to grasp. So we've got our a
Speaker 1: string with a hundred ten hurts frequency. That's our fundamental
Speaker 1: tone or first harmonic. The next harmonic would be twice
Speaker 1: the frequency as two is the next whole number. It's
Speaker 1: the next integer in the sequence. We start with one,
Speaker 1: but any number of times one is itself. We go
Speaker 1: to the next integer, that's two. So now we multiply
Speaker 1: our frequency hurts by two, we get two hurts. That's
Speaker 1: still an A. It's still the note A, but it's
Speaker 1: an octave higher than the original a note that we played.
Speaker 1: So hypothetically, this also means if you've got a string
Speaker 1: that's tuned to one hurts and you shortened the length
Speaker 1: of that string by half, so you made it half
Speaker 1: as long, you would produce the two D twenty Hurts
Speaker 1: tone when you strummed the half as long string. You
Speaker 1: shortened the wavelength by shortening the string. Thus you increase
Speaker 1: the frequency because remember we remember velocity is wavelength times frequency.
Speaker 1: Velocity is constant, so if we have the wavelength, we
Speaker 1: have to double the frequency. At least that's what would
Speaker 1: happen in an ideal realization of this principle, But in
Speaker 1: reality it gets more complicated because the oscillating wave in
Speaker 1: a guitar string doesn't propagate all the way from one
Speaker 1: anchored end of the string all the way to the
Speaker 1: other end of this string. Instead, there's actually a small
Speaker 1: length of string that's close to the anchor points that
Speaker 1: doesn't move. It's something that people tend to call the
Speaker 1: dead length of string. Now, the amount of dead length,
Speaker 1: like the length of that non moving part of the string,
Speaker 1: depends on a lot of factors, like how thick the
Speaker 1: string is, so there's no hard and fast rule of
Speaker 1: how long the dead length will be. In general, this
Speaker 1: actually means that the actual halfway mark down a string
Speaker 1: doesn't necessarily correspond to doubling the vibrational frequency of that string.
Speaker 1: But we'll get more into that in the next episode,
Speaker 1: I hope. So we're gonna put it aside for now.
Speaker 1: That's a future Jonathan problem. So the next harmonic would
Speaker 1: be three times the fundamental right, we just did two hurts,
Speaker 1: so three would be that's right, three thirty hurts, which
Speaker 1: we would perceive as an E note if we could
Speaker 1: hear it over the fundamental frequency, and so on. We
Speaker 1: would go up the harmonic scale. The fourth harmonic at
Speaker 1: four or forty would get us back to another A
Speaker 1: note at a higher octave uh five fifty For the
Speaker 1: fifth harmonic would actually be close to a C sharp,
Speaker 1: but not exactly C sharp. It would be a little
Speaker 1: off by just a few hurts. Now, overtones aren't necessarily
Speaker 1: at harmonic frequencies. We tend to design musical instruments that
Speaker 1: produce harmonics as overtones because we find them more pleasing
Speaker 1: to the ear. Typically, but different instruments will produce different overtones.
Speaker 1: At different intensities, So some might really emphasize the third
Speaker 1: partial or third harmonic, others m really emphasize the fifth harmonic.
Speaker 1: And this is why we can hear the same note
Speaker 1: played on two different types of musical instruments, and we
Speaker 1: experienced two different qualities of sound, two different experiences of sound.
Speaker 1: So a G played on a banjo sounds different from
Speaker 1: that same G note played on a guitar, and that
Speaker 1: sounds different from that same G note played on a
Speaker 1: piano or a G on a trumpet. Each of these
Speaker 1: instruments produces overtones of varying degrees of intensity. And while
Speaker 1: we don't necessarily perceive the pitch of those overtones, we don't,
Speaker 1: you know, distinguish those other pitches. The overtones shape the sound,
Speaker 1: It affects the timbre of the note. So we can
Speaker 1: tell the G on a banjo and the G on
Speaker 1: a guitar are the same pitch, they're the same note,
Speaker 1: but they don't have the same quality of sound. If
Speaker 1: they did, there'd be no reason to make different musical
Speaker 1: instruments because they would all just produce the exact same sounds.
Speaker 1: There's something else I need to say about resonance and
Speaker 1: it involves adding energy into a system. One way to
Speaker 1: think about this is with a swing set, So you know,
Speaker 1: and you're a kid, or if you're me an adult
Speaker 1: and you're swinging on a swing set, if someone gives
Speaker 1: you a push just as you were about to start
Speaker 1: your downward swing, you go a little higher on your
Speaker 1: next swing because that push was adding to the natural
Speaker 1: frequency of your swing. You're adding energy into the system.
Speaker 1: So objects will resonate at certain frequencies, and if you
Speaker 1: add energy at the regular intervals of that frequency, it
Speaker 1: boosts the amplification. You get more volume, you get more energy,
Speaker 1: And it depends on a load of factors, such as
Speaker 1: what the physical stuff is made up of, how much
Speaker 1: of it there is, the tension that's on it, and
Speaker 1: lots of other stuff. But resonance is going to play
Speaker 1: an important part in how some specific instruments work. So
Speaker 1: if a musician subjects an instrument at a resonant frequency
Speaker 1: in some way, the sound creative and the instrument will
Speaker 1: be a louder one. The classic example of resonance is
Speaker 1: using a crystal champagne glasses fundamental frequency to shatter the glass,
Speaker 1: and it's a neat trick, so The first thing you
Speaker 1: gotta do is determine what the glass is fundamental frequency is.
Speaker 1: Typically you do that by tapping it lightly, and you
Speaker 1: would listen to the tone it produces, and you would
Speaker 1: analyze that tone. Then you would subject the glass to
Speaker 1: that same frequency of sound. The glass will begin to
Speaker 1: vibrate in the presence of that fundamental frequency all by itself,
Speaker 1: so you don't have to strike it or anything. It's
Speaker 1: as if the glass has been struck. It will resonate
Speaker 1: along with that frequency. It will also do this, by
Speaker 1: the way, if you're doing one of the harmonics of
Speaker 1: that frequency, but at a lesser degree. So if the
Speaker 1: incoming frequency is strong enough, it will cause the glass
Speaker 1: to vibrate to the point that deforms enough to shatter.
Speaker 1: And there are a lot of stories of opera singers
Speaker 1: who had perfect pitch who could managed this. They would
Speaker 1: listen to the tone and replicate it perfectly, and with
Speaker 1: their training, they would produce in a volume loud enough
Speaker 1: to shatter the glass. These days, it's a lot easier
Speaker 1: to do this because you just use a digital device
Speaker 1: capable of dialing into a precise frequency, and then you
Speaker 1: pump that frequency out to some speakers that can blast
Speaker 1: out the sound at a sufficient volume and the glass
Speaker 1: will just shatter itself. But uh, we're not done with
Speaker 1: the hard stuff yet. Now we have to talk about
Speaker 1: Furrier transforms. And who knew that music was so darn complicated?
Speaker 1: I mean, Bach did, but you know you get what
Speaker 1: I mean. Back in the eighteenth and early nineteenth centuries,
Speaker 1: we had this smarty pants named Jean Baptiste Joseph Fourier,
Speaker 1: or Old Joe as i'll call him. So. Old Joe
Speaker 1: was a physicist and a mathematician born way back in
Speaker 1: seventeen sixty eight, and he was really interested in explaining
Speaker 1: the flow of heat between adjacent molecules. But his work
Speaker 1: would lay the foundation for other smarty pants assess is
Speaker 1: to build upon net, leading to what we would call
Speaker 1: the Furrier transform. Not many people called the Furrier transform,
Speaker 1: so I'll just say Furrier. But what the heck does
Speaker 1: this have to do with music? Well, remember when I
Speaker 1: said if you wanted to depict a true sound wave
Speaker 1: as a type of sign wave, it would look really
Speaker 1: funky because the presence of all those overtones, it would
Speaker 1: make all these different dips and peaks, and it would
Speaker 1: just look very odd. It wouldn't be those smooth curves
Speaker 1: we were talking about originally, Well, we humans wouldn't hear
Speaker 1: all those frequencies as distinct pitches, but a meter could
Speaker 1: pick up all those different frequencies together. Basically, the Furrier
Speaker 1: transform describes how these multiple frequencies all combine into that
Speaker 1: one wave, which in our sketch means it creates that
Speaker 1: single wave visualization that incorporates all the frequencies at their
Speaker 1: respective amplitudes into a single, unbroken visualization of a wave.
Speaker 1: Furier showed that a continuous function could be produced as
Speaker 1: an infinite sum of sign and cost sign waves. The
Speaker 1: resulting plot of the function as a wave isn't necessarily smooth,
Speaker 1: and the shape of it will depend upon a lot
Speaker 1: of factors, including the phase of each constituent wave, the frequency,
Speaker 1: the amplitude, all that kind of stuff. But Furry and
Speaker 1: those who followed him described how this collection of individual
Speaker 1: components combine to make a whole. This applies in lots
Speaker 1: of areas of physics, not just in sound, and in
Speaker 1: fact we can visualize sound waves in a different way.
Speaker 1: There's more helpful when we try to understand this. So
Speaker 1: we've used the time domain method. Right, we've been using
Speaker 1: that in order to describe the the wavelength and frequency
Speaker 1: because those are really easy to visualize in terms of
Speaker 1: of span of time. However, it gets confusing when we
Speaker 1: want to talk about overtones and the shape of the
Speaker 1: wave goes all funky. So we can do this by
Speaker 1: looking at it not by the time domain but by
Speaker 1: the frequency domain. So in the time domain, that horizontal
Speaker 1: line or x axis relates to the passing of time,
Speaker 1: but in the frequency domain, the x axis refers to
Speaker 1: the range of frequencies, lower frequencies being on the left side,
Speaker 1: higher frequencies being on the right side. So you would
Speaker 1: plot where the frequency is on each of those overtones,
Speaker 1: and the fundamental frequency uh and the y axis is
Speaker 1: still amplitude, so it's still volume. So you would have
Speaker 1: the loudest frequency, which would be the fundamental, plotted at
Speaker 1: the highest point on the y axis, and then you
Speaker 1: would see the overtone frequencies at their respective places, and
Speaker 1: you would see, if you were to analyze through Furrier
Speaker 1: analysis each musical instrument, that those overtones are slightly different
Speaker 1: between things like guitars and banjos and harps and pianos
Speaker 1: and flutes and trumpets, etcetera. Uh, and other things like
Speaker 1: like whether or not you were plucking a string versus
Speaker 1: bowing a string. All of these factor into it. Now
Speaker 1: I get that all of this is really confusing without
Speaker 1: visual aids, So I do recommend checking this stuff out
Speaker 1: on the internet to get a better grasp of it.
Speaker 1: There are numerous websites and videos on the matter, and
Speaker 1: one really helpful one relating to what I was just
Speaker 1: talking about is on Mark Newman's YouTube channel. It's titled
Speaker 1: Preview how the Furrier transform works Lecture number two Sound
Speaker 1: as sign Waves. Check that out. It will really help
Speaker 1: clear things up. But when we get back, I'm gonna
Speaker 1: wrap up the physics bit. Then we're gonna talk about
Speaker 1: some biology. But first let's take a quick break. So
Speaker 1: Furrier analysis, where we can determine the amplitudes of individual
Speaker 1: overtones and harmonics and a played note, gives us the
Speaker 1: scientific explanation of why the same note played across different
Speaker 1: instruments produces a different kind of sound. The collection of
Speaker 1: those overtones is different for every instrument. But how about
Speaker 1: how we actually hear and perceive sound? What is the
Speaker 1: science behind our experience of sound? Well, we'll start with
Speaker 1: the physics and those moving air molecules what go into
Speaker 1: our ears. So we're really talking, like I said about
Speaker 1: fluctuating air pressure. Here, those changes in air pressure hit
Speaker 1: our ears and they pass into the external auditory canal,
Speaker 1: so that's open to the outside world on the inside
Speaker 1: in our heads. It ends with the tympanic membrane, also
Speaker 1: known as the ear drum. So this is a very
Speaker 1: thin membrane and it's at where we would say the
Speaker 1: outer ear begins to transition to the middle ear. On
Speaker 1: the other side, the inner side of the tympanic membrane
Speaker 1: is a series of three tiny bones. There, the malleus,
Speaker 1: the incas, and the statepies or the hammer, the anvil
Speaker 1: and the stirrup, so called because of their shape, and
Speaker 1: as the membrane moves due to these fluctuations of air pressure,
Speaker 1: as it's being pushed and pulled upon, the bones also move,
Speaker 1: So the hammer pushes impoles on the anvil, which pushes
Speaker 1: impolls on the stirrup. The stapes or stirrup connects to
Speaker 1: the oval window. That's a section that's part of the
Speaker 1: cochlea that's an organ in the inner ear. The cochlea
Speaker 1: is a spiral shaped organ and there are three parallel
Speaker 1: chambers filled with fluid inside the cochlea. The vibrations on
Speaker 1: the oval window cause waves to flow through this fluid.
Speaker 1: This in turn causes another membrane called the basilar membrane
Speaker 1: to move. And it's the basilar membrane or basil or
Speaker 1: if you prefer, that gives us the ability to differentiate
Speaker 1: the pitches that we hear. Different sections of this membrane
Speaker 1: respond more readily to certain frequencies of sound. Then you
Speaker 1: have the organ of core time, which is the receptor
Speaker 1: organ of the ear, and it detects the vibrations of
Speaker 1: this basilar membrane through special cells, and the special cells
Speaker 1: have little hair like protrusions on them. It acts kind
Speaker 1: of like a brush that just rests against this membrane.
Speaker 1: So as the membrane vibrates, the hair cells pick it up,
Speaker 1: and then they pass along the message to the brain
Speaker 1: through neurotransmitters, and it gets super complicated from there. But
Speaker 1: I figured this is deep enough already. At the end,
Speaker 1: our brains taken these incoming signals and then interpret it
Speaker 1: and we experience it as sound. Now you can also
Speaker 1: transmit vibrations to the tympanic membrane through stuff like bone conduction.
Speaker 1: That's where the vibration passes, not through air molecules that
Speaker 1: are going through the ear canal, but rather through the
Speaker 1: bones of the skull itself. So just remember that again,
Speaker 1: sound is one way we experience vibration, but not the
Speaker 1: only way. I mean, obviously, if a vibration is strong enough,
Speaker 1: we're gonna feel it. And some vibrations occurrent frequencies that
Speaker 1: again are too high or too low for us to
Speaker 1: perceive through sound through hearing it, but we might be
Speaker 1: able to feel it. So the basilar membrane won't vibrate
Speaker 1: at frequencies that are above or below the human range
Speaker 1: of hearing, or an individual's range of human hearing, because
Speaker 1: when we say twenty to twenty killer hurts, we're really
Speaker 1: talking about the range of the typical human. Some people
Speaker 1: are atypical. So you could say if a tree falls
Speaker 1: and the vibrations that cause were above or below the
Speaker 1: level of perception, it doesn't make a sound because sound
Speaker 1: is dependent upon us experiencing it. You could also argue
Speaker 1: the opposite. It all just depends on your way you're
Speaker 1: defining things. So when a musician strums a string on
Speaker 1: a guitar, that string vibrates, it causes the air molecules
Speaker 1: around the string to move. Thus you get a fluctuation
Speaker 1: of air pressure that matches that vibrating frequency. This spreads
Speaker 1: outward from the source and the air molecules all around vibrate,
Speaker 1: and if you're close enough, if you're within hearing distance,
Speaker 1: that fluctuation will be strong enough to move your tympanic membrane,
Speaker 1: which then is going to through the bones put pressure
Speaker 1: on that oval window of your cochlea, which in turn
Speaker 1: will cause the basilar membrane to vibrate at the particular
Speaker 1: area on the membrane that corresponds to that frequency. The
Speaker 1: hair cells will pick up that vibration and then emit
Speaker 1: neurotransmitters that our brains then say, oh, I recognize that
Speaker 1: that's in agata da vida boom. We've just heard some music.
Speaker 1: So when you get down to it, musical instruments are
Speaker 1: all about creating vibrations at specific frequencies. Music itself is
Speaker 1: all about establishing rules which can occasionally be broken for
Speaker 1: the arrangement of those frequencies in ways to achieve various effects.
Speaker 1: Those rules aren't just about which frequencies play well with others.
Speaker 1: It's also about stuff like amplitude. Levels of volume are
Speaker 1: really important and play into a song's dynamic range. Dynamic
Speaker 1: range explains the difference between the loudest versus the softest
Speaker 1: parts of a piece of music, and the limitations of
Speaker 1: human hearing also play an important part. So, for example,
Speaker 1: it's very hard for humans to pick up on a
Speaker 1: soft sound that immediately follows a loud sound, much like
Speaker 1: we really only hear the fundamental frequency played on a
Speaker 1: musical instrument. So if you wrote a piece of music
Speaker 1: that has a really loud moment followed immediately by a
Speaker 1: very soft one, chances are no one would ever hear
Speaker 1: the soft part. This also plays a big part in
Speaker 1: strategies that revolve around audio compression. If you've listened to
Speaker 1: my episodes about the MP three format, you know that
Speaker 1: some forms of compression rely on what's called a lossy formula.
Speaker 1: As the name implies, lossy compression is able to reduce
Speaker 1: file size by ditching some of that data, you lose
Speaker 1: some of the information. The goal of lossy compression is
Speaker 1: to get rid of data without perceivably changing the quality
Speaker 1: of the sound file or reducing any perceivable quality as
Speaker 1: much as possible. The first way to do that is
Speaker 1: to identify any sounds that theoretically should be imperceptible to
Speaker 1: the average person and then just getting rid of them,
Speaker 1: because if you can't hear it, why would you keep it.
Speaker 1: But as we've learned, stuff like overtones are also important.
Speaker 1: They are what characterized the quality of a particular musical instrument,
Speaker 1: even though we don't directly perceive the pitches underneath those
Speaker 1: overtones as distinct notes. So lossy formats have to take
Speaker 1: that into account, or the compressed file is just gonna
Speaker 1: sound weird. Guitars won't sound like guitars, for example. So interestingly,
Speaker 1: there's a lot of psychology that goes into audio compression
Speaker 1: by combining our understanding of physics, even if it was
Speaker 1: a limited understanding or perhaps more of an observation without
Speaker 1: full understanding, with our appreciation for which frequencies are pleasing
Speaker 1: to us, and the limitations that we have as human beings.
Speaker 1: We can construct various instruments to play into all of this,
Speaker 1: but it all comes down to how can I construct
Speaker 1: something that will vibrate and make those vibrations sound good.
Speaker 1: I'd love to give you history of musical instruments, but
Speaker 1: humanities relationship with music dates back before our relationship with
Speaker 1: written language. Among the oldest instruments ever discovered where flutes
Speaker 1: from European caves. These flutes were made out of bird
Speaker 1: bone and mammoth ivory and they were built more than
Speaker 1: forty thousand years ago. And keep in mind I said
Speaker 1: these were the earliest ones that we've discovered. Who knows
Speaker 1: when humans first made musical instruments. If I had to guess,
Speaker 1: I would wager that percussion instruments like drums were among
Speaker 1: the earliest. But there are a lot of other ancient examples,
Speaker 1: and one I want to talk about is particularly interesting.
Speaker 1: I want to close out with this ancient musical instrument
Speaker 1: because there are people who still use it today and
Speaker 1: it's super cool. It's called the bull roarer. It's hard
Speaker 1: for me to say that word, being Southern bull roarer.
Speaker 1: I just want to make it a two syllable word.
Speaker 1: But these were used as far back as the Stone Age.
Speaker 1: Typically these consist of a slat of wood, and it's
Speaker 1: usually shaped so that there's an edge on either side
Speaker 1: of the slat of wood. So think of like a ruler,
Speaker 1: but you've you've shaved the edges of the ruler down
Speaker 1: so that it's kind of like the propeller on an
Speaker 1: old prop plane. And you wrap a chord around one end,
Speaker 1: or you may drill a hole, loop the cord through
Speaker 1: the hole and tie it off, and then you give
Speaker 1: the cord a little bit of a twist, and then
Speaker 1: you hold the other end of the cord and you
Speaker 1: start swinging the bull roarer in a circle. As it swings,
Speaker 1: the cord begins to untwist, and then it continues twist
Speaker 1: in the opposite direction before reversing the process. So the
Speaker 1: bull roarer moves along the path of the circle, and
Speaker 1: as it's doing so, it's turning because of the cord
Speaker 1: twisting and untwisting, And this movement through the air creates
Speaker 1: the vibrations that travel as sound. Several factors can influence
Speaker 1: the pitch of that sound. That includes the length of
Speaker 1: cord ear using, which obviously determines the diameter of the
Speaker 1: circular path that the bull roarer is taking. Also the
Speaker 1: frequency with which you are swinging this in a circle,
Speaker 1: the amount of twists that was in the cord, and
Speaker 1: even the plane of rotation, whether it's vertical versus horizontal.
Speaker 1: For example, bull roarers were used by many ancient peoples
Speaker 1: as a means of communication by varying the pitch, which
Speaker 1: again you could do in all those different ways I
Speaker 1: just mentioned. You could send simple messages several miles away
Speaker 1: because the sound would just travel so far. Those low
Speaker 1: frequencies travel pretty well. The fact that you're talking about
Speaker 1: longer wavelengths um and and lower frequencies, the energy is
Speaker 1: much more efficient at far distance travel, and so these
Speaker 1: were used by early civilizations for thousands of years as
Speaker 1: a way for people to send distant messages back and forth.
Speaker 1: Pretty simple messages, but distant ones that could be very
Speaker 1: helpful for early civilizations. In the next episode, I'm going
Speaker 1: to go into more detail about how specific types of
Speaker 1: musical instruments actually work, how they create the sounds they make.
Speaker 1: I'm going to focus on the musical instruments found in
Speaker 1: Western orchestras, because to cover all musical instruments would require
Speaker 1: its own podcast series, and if I were to cover
Speaker 1: how bagpipes works, I would probably need a therapist. But
Speaker 1: I hope you guys enjoyed this overview of the science
Speaker 1: of producing sounds. If any of you out there have
Speaker 1: any suggestions for future topics I should cover, whether it's
Speaker 1: a specific technology, a type of tech like I'm doing now,
Speaker 1: a company in technology, or a very important person in tech,
Speaker 1: or anything along those lines. Let me know. You can
Speaker 1: reach out on Facebook or Twitter. The handover both is
Speaker 1: Tech Stuff HSW and I'll talk to you again really soon.
Speaker 1: Y tex Stuff is an I heart Rate deo production.
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