- 9/20/2024
Lutherie Demystified is a video series hosted by Garrett Lee that explores the world of classical guitar building--from techniques and theory to commentary and perspectives about the instruments, players and lutherie profession. www.GarrettLeeGuitars.com This is Episode #16 and is a Guest lecture for PHY 115, Physics of Music at Wake Forest University, April 9, 2024.
Category
🎥
Short filmTranscript
00:00Hi, it's Gary, and in this video, I want to bring you something a little bit different.
00:06This week, I had the pleasure of giving a guest lecture for the Physics of Music course
00:10at Wake Forest University, which is an interdisciplinary type of physics course designed for undergraduate
00:18non-physics majors, bringing together the worlds of music and physics, which is a perfect
00:27combination because, as you know from the Luthier Demystified series, we talk a lot
00:33about how physics rules what we can do as guitar builders.
00:40And so I wanted to give a flavor of how what we do as guitar builders is constrained by
00:47the laws of physics, but also bring in some ideas of how luthiers work with guitarists
00:54to build an instrument that works for not just the player, but the audience, and also
01:03something that a luthier can actually accomplish within the rules dictated by physics.
01:11You'll hear some ideas that we've presented in past episodes of this series, and then
01:17some new material that, in future episodes of Luthier Demystified, I'll actually talk
01:23in more detail.
01:25So I want to thank Dr. Jack Dostal of the Physics Department, and Dr. Marco Sartor of
01:31the Music Department for the kind invitation, and the Interdisciplinary Arts Center for
01:37making this talk possible.
01:40So I hope you enjoy it.
01:41Hi, it's Gary, and I want to welcome you to my workshop.
01:45I'm in New Jersey right now, about 20 miles west of New York City, and we're going to
01:50have some fun.
01:51I want to share with you something that you've probably not been exposed to, even though
01:56guitars are very popular, you've probably not been exposed to how they're built.
02:02Guitars can mean a lot of things to different people.
02:04To the players, it's a means to express something that is not able to be expressed through words
02:13or pictures, but only through the magic of music can you express something so deep, and
02:20a guitar is often a tool for that expression for their artistry.
02:27In terms of craft, some people view a guitar as a work of art, although I tend to think
02:33of it as more of a tool, since it has a function, rather than art, but they have an aesthetic
02:39quality that is very nice, and for me, as a trained scientist, I see a guitar as a system
02:48that's really interesting in terms of physical study, so we'll talk a lot about that, but
02:55I'm what people would call a luthier.
02:58A luthier is a stringed instrument maker, and the term goes back several hundred years
03:05when lute builders were the big thing, and as lutes became less popular and violins became
03:13popular, then even violin makers were called luthiers because they were converted from
03:21the lute world, and so I build classical guitars as my specialty, and these are the type of
03:29instruments that I make.
03:33Classical guitars originated in its most modern form from the 1800s in Spain.
03:40They had gut strings back then, three treble gut strings, and since the 1950s, we now use
03:49nylon, which came out of the fishing line industry, and then three metal wound bases,
03:57and the metal increases the mass, so you can reach lower pitches for the same string length
04:02and tension.
04:04Here's some pictures of my workshop, and my wife says I run my workshop like a lab, and
04:10that's probably because my training is in a lab.
04:14I'm trained as a research scientist in biochemistry, and while many people think that luthiery and
04:20biochemistry probably have very little in common, I think they really do, and here's why.
04:28Biochemists have a fascination with what's known as structure-function relationships.
04:34For example, how does this protein's shape make it so good at moving muscles?
04:42And in much the same way, I also ask, how does this guitar's structure make it successful
04:48at taking the player's instructions and push sound waves to our ears with nuance of frequency
04:56and different levels of strength?
05:00Both examples are constrained by the rules of physics, and within these boundaries, we
05:05must learn how they work if we want to develop them, such as finding cures for diseases or
05:10making better-sounding guitars.
05:14And this is the world in which I live.
05:18I live somewhere sandwiched between what the player wants and what the laws of physics
05:25allow me to do.
05:27The good thing is that physics is always more predictable than guitars.
05:33So here I am in the middle trying to satisfy both conditions.
05:38Well, the reality is that playing the game where the rules of physics define your moves
05:44means there are a lot of compromises when you build a guitar.
05:50A guitar is much like a tool to the player that uses it to express music, and all the
05:59musicians here can think of the important things that a guitar or whatever your musical
06:05instrument is, what it needs to be able to do in order to express music, which is such
06:11a deep and complex thing.
06:14Master musicians can be very picky, and rightly so, because high-level music is often about
06:25the nuances that must be communicated to elicit something so emotional.
06:31They need an excellent tool to do that job.
06:35And if you ask a guitarist, what would you like me to build in your guitar, and they'll
06:42typically say, oh, I want it to have good volume, sustaining notes, play in tune, maybe
06:55have a variety of tonal colors, and easy to play.
07:01But it turns out that what they really want is something like this.
07:07The list can be endless, and often it can't be articulated.
07:15Subtle things like, I want the notes to have a strong fundamental and a very pleasant and
07:22interesting set of overtones, or I want it to sound good at a distance, such as in a
07:29concert hall, but also close up, so you can record with a microphone.
07:38And we want it to look good.
07:41The truth is that most good guitarists will select a guitar based on how few deficiencies
07:46it has, rather than how many good qualities it has.
07:51In other words, the simple knife is not enough, and this is the challenge that I love, though.
07:59But the reality is that I can't give them everything they want.
08:03Many of their desires are physically opposed, such as, I really want a loud guitar, and
08:11I want the notes to last forever.
08:13Well, I'm sorry to report that in this universe, there are things like friction and conservation
08:21of energy, and that just doesn't bode well for a string that is plucked and not bowed.
08:29So my job is to decide on the best compromises, and to try to pull out as much efficiency
08:37out of the system.
08:39This is why it's important to understand how the system works.
08:43And in truth, I'm not exactly sandwiched, because it's really this physical reality
08:49that envelops all of us in this endeavor, and it's physics that sets the rules.
09:00So let's start to look at some structure now.
09:04The architecture of guitars is fascinating on its own, such as in this inside view, which
09:12few people get a chance to see.
09:15And just from this photo on a macroscopic level, we see some important design elements.
09:23Inside this room, we have the roof above, which is the soundboard, which is often called
09:28the top, which is attached to the strings via the bridge.
09:34When the soundboard vibrates, it will pump air pressure waves to our ears.
09:39And while everything works as a system in a guitar, the top is the most important part,
09:45and is the real transducer of the guitar that has the gears that determine the overall efficiency.
09:52And we'll talk in depth about that in a moment.
09:56But as you can see, this soundboard and the back, which is actually the floor in this
10:02room type of view, are strengthened by beams called braces.
10:09And you might think that this room is empty, that there's nothing there, but it's actually
10:14filled with a column of air that has mass, which can also vibrate and send pressure waves
10:21to the outside via the sound hole, which you see the light coming through.
10:27Now remember I told you that there are many qualities in guitars that we want that are
10:31physically opposed, and the example I gave you is loudness versus sustain.
10:38Infinite sustain means that the note never dies.
10:42Sustain can be crucial for maintaining a melodic line, for example.
10:48So we're talking string motion here, and when we first learn about oscillating strings,
10:54we usually think about the ideal case, like what we're seeing here, where the ends are
11:00fixed to something rigid and heavy, like a wall, where all the string energy gets reflected.
11:07It would be something like this.
11:09And you already know this is not a good idea.
11:12You know you're not going to hear much because the strings can't move the brick, and therefore
11:18the brick won't push air to our ears, plus the fact that the strings don't have much
11:23surface area to push air to our ear.
11:27But this is a great system for sustain because the strings will keep oscillating for a long
11:31time because the brick is not draining any string energy.
11:35And this is what happens in an electric guitar, that is if you don't plug it in.
11:40You don't hear much because most electric guitars are huge blocks of heavy wood, and
11:47it's only because it has electromagnetic pickups that sense the metal strings and convert the
11:52movements to current that can be amplified.
11:56Now doing thought experiments at the extremes is good, so let's consider the other extreme,
12:02a guitar of our imagination that has a paper soundboard.
12:07You can imagine how all the string vibration will easily and quickly transfer to make the
12:12paper flap, but then it will be all over because there's no reflectance.
12:19In the real world, if we could apply enough tension to this system without it ripping
12:24the paper, we'd get a loud but non-sustaining note.
12:29And that's the design and character of a banjo.
12:33It's a membrane that is stretched around a rim, and when you play it, it's really loud,
12:40but very short and almost percussive.
12:44But there's a material and design that's somewhere right in the middle, and that's using wood.
12:52Through history, wood is recognized as the best solution, such as alpine conifers like
12:57spruce and western red cedar.
12:59Wood is a really miraculous material.
13:03It's light and extremely strong for its weight, so it can resist the tension of the string
13:07so your guitar won't collapse.
13:10And it rings like crazy if you activate it.
13:13And importantly, it has the right ratio of flexibility and weight to give a good balance
13:19between volume and sustain.
13:22The downside is that wood is a natural product that comes with a lot of variability in terms
13:27of stiffness and weight.
13:30And that's even if it's from the same log.
13:33But if it was uniform, I could simply build every guitar to the same dimensions, but since
13:39they're not, I have to do a lot of compensations and things like thickness in order to produce
13:45a consistent sound.
13:48Okay, so here's my prototype with a box of air.
13:53And then here's the finished product.
13:56It's a highly evolved instrument over history.
13:59Turning to the soundboard, the soundboard is like the guitar's energy transducer.
14:05It's the intermediary between the string energy and the pumping of airwaves to our ears.
14:11And it needs to be lightly built and moderately flexible so the strings can easily move it.
14:18It's an illusion that they're sturdy, actually.
14:21And because they're actually built on the edge of collapse, they're like potato chips
14:25with bracing.
14:28And here's a soundboard plate without bracing.
14:32And it's very thin.
14:34It's about two millimeters thick at this point.
14:38Super flexible, very light.
14:40It's about 100 grams.
14:42And if I tap it, it's kind of resonant, makes some very nice sounds.
14:53It has a fundamental pitch and some overtones that you can hear, but still pretty raw.
15:03And the flexibility is important because that determines a lot of how the pitches come
15:10out, and we'll talk about that.
15:17Here's a soundboard that has bracing, and it's much stiffer.
15:27It's about twice as stiff, even though the braces don't add much more weight to it.
15:36And if I tap it, because it's stiffer, the pitch is higher.
15:46And the braces give it more focus, but a higher pitch.
15:51The braces, you can see, have directionality, and I can use that directionality to change
15:59the character of the top in terms of how it moves and how it sounds, and we'll talk more
16:05about that, too.
16:07Now braces are an incredible invention because they add a lot of strength without adding
16:12much weight, which is why we use them in things like floor joists.
16:18Braces know that it saves a ton of weight to add a bunch of beams to give strength instead
16:22of having to increase the thickness of the floor itself, which would get so heavy that
16:28it becomes weak again.
16:31So on a top like this, I can double the strength of the plate and only add about 15% more weight
16:37in braces, and I'll take that trade-off any day.
16:42The braces are glued to the soundboard on this deck, and instead of using clamps, I
16:46use an old method of jamming sticks between the roof of the deck and the braces.
16:54Here's another classic engineering move.
16:56I've added a tiny bit of arching where the braces meet the soundboard, and this arching
17:02also adds stiffness without adding any weight.
17:06And you already know how arches are fantastic in things like bridges, and the Romans definitely
17:11knew how to take advantage of the incredible strength of arches.
17:17But you can overdo the stiffness, and that results in a very aggressive-sounding guitar
17:21that is maybe too treble-oriented and has some very annoying-sounding overtones.
17:28I shave the braces to really fine-tune the stiffness in different areas.
17:33I like to think of this process as carving away stiffness to introduce more flexibility.
17:39And by now, you're probably getting the picture that my whole job as a luthier is to control
17:43stiffness and weight and spatial distribution of those two things.
17:49I'm trying to achieve the right balance of the flexibility in the top plate and marrying
17:54it with the right amount of bracing, and this all determines the eventual sound character
18:00of the guitar and how it will perform in a large range of pitches that the player is
18:07going to instruct the guitar to play.
18:13So with our energy transducer soundboard finished, then we close the top, gluing it together
18:21with a million clamps, and then we have a completed body fully capable of resonating
18:28if we energize it in some way.
18:32And it doesn't even have to be with strings, and this is where I challenge you to stick
18:35with me because what follows is what people might call the whole enchilada.
18:42If you get this last part, you'll get the real essence of building musical instruments.
18:47So if you're ready, let's go.
18:51Now with this completed body, most of the acoustic capabilities are pretty much baked
18:55in if we activate it with energy.
18:59Of course, if we added the neck and strings, we could activate it with very specific string
19:04energy.
19:05By specific, I mean the player will select the note on the fingerboard, and then that
19:11will specify the fundamental frequency and all the associated sets of higher frequency
19:17overtones depending on how the player strikes the string.
19:23But without a neck, it's still acoustically very interesting because I can activate it
19:27by tapping and listening to the output similar to how you would ring a bell and listen.
19:35Unlike the case where the player plays the string with a specific note, by tapping it
19:41with a hammer, I can activate almost every possible pitch the box can radiate.
19:47It won't sound great, but it will radiate a large number of pitches.
19:51In other words, it's showing me its potential to support each note on the fingerboard once
19:56it's on.
19:58Some notes will be better than others, and it's my job as a builder to equalize that
20:02potential.
20:05So here's the completed box, and I've got this hammer, and I'm going to tap it in different
20:10places and listen.
20:22Now I can hear a lot of different pitches, but I can't hear all of them.
20:28My brain can't resolve all of the pitches that are coming out of this soundboard.
20:34But if I have a microphone and a laptop, I can use that to pick up the vibrations off
20:42of the box and then use an algorithm to tell me what pitches are being heard.
20:51And here's the output with the frequency on the x-axis, and the relative strength of the
20:56output on the y-axis.
20:59The peaks that you see are the different pitches that the microphone heard when we tapped.
21:04It kind of looks like a big mess of peaks all jammed together.
21:08And it looks very different than when you tap, say, a bell, which is tuned to a certain
21:13pitch and radiates a very ordered set of frequencies.
21:17But for tapping a guitar, we see a big pile of peaks jammed together so that there's a
21:22lot of area under this curve and no gaps that hit zero.
21:28And having a lot of area under this curve is important, and let me show you why.
21:34Let's consider a situation where I take my guitar and I play A220.
21:49Sounds like this, and the computer hears this.
21:53Here's the fundamental at 220 hertz plus some overtones.
21:58If there's no potential for the box to support these frequencies, you won't hear them because
22:04the box physically can't vibrate at these frequencies.
22:08But fortunately, in this guitar, they do, and this relative mix of fundamental plus
22:13overtone sounds really pleasant.
22:17So bringing back the box's potential in the lower panel, you can see what needs to happen.
22:23There has to be area under the curve in the bottom panel at the pitches being played by
22:29the string.
22:30The player and the string instruct the frequencies, and the question is, can the box vibrate at
22:36that frequency to obey the string's command?
22:40And if the answer is yes, you will hear those frequencies.
22:44Let's consider a hypothetical case where there's a gap in the box's output potential shown
22:49in red down at the bottom, meaning that the soundboard just can't vibrate at that frequency
22:55to generate the sound.
22:57Maybe the top is too stiff or it's too heavy, and the sound profile in the top panel might
23:03look like this in red.
23:05The relative abundance or orchestration of the different overtones will have changed,
23:11and we would hear what we would call a different tonal color for that note.
23:16This is, in essence, how different guitars can wind up sounding different depending on
23:21the landscape of the guitar's output potential in that lower panel.
23:28And this is the whole enchilada.
23:30My job as a luthier is to move these peaks left or right, or try to equilibrate the heights
23:37of these peaks to give a smooth landscape which results in a smooth sound.
23:44And it all comes back to manipulating spatial distribution of stiffness and weight.
23:49My sonic recipe must take into account things like material choice, material thickness,
23:56and bracing size and direction.
24:00And if that was the whole enchilada, then what I'm going to tell you next is the super
24:05enchilada with all the fixings, and then we'll end our session.
24:11Resonances are movements in vibrating objects that happen at high efficiency at specific
24:17frequencies.
24:18In other words, it's easy to get the top to vibrate at those frequencies.
24:22They are all those peaks you saw.
24:26So here's a video that I made for you last night to show you how this works.
24:30Ernst Chladni was a German physicist and musician who is considered the father of modern acoustics.
24:36In the 1780s, he wrote a treatise on how vibrating plates move.
24:40You probably know of his famous demonstrations where he sprinkled sand on metal plates and
24:45got the sand to move by activating the plate with a violin bow.
24:49The sand settles in lines called nodes because those are the boundaries where the plate is
24:54motionless, whereas the vacant areas indicate areas of motion.
24:57Today we know that these patterns are formed the strongest when the plate is activated
25:02at resonant frequencies, and we refer to them as modes of vibration.
25:07But back then, Chladni's contribution was a glimpse into a completely unseen and poorly
25:12understood process of how plates move.
25:15Fast forward to today, and we know that we can replicate Chladni's experiments with
25:19our guitars, but instead activating them through space with sound waves, which physically are
25:25air molecules.
25:26You've already experienced this phenomenon when you're holding your guitar and it starts
25:30to vibrate when someone talks to you or plays in front of you.
25:34All of this is now made easy with a computer directing sound to a speaker, and this is
25:39what we're going to do.
25:42Let's try some Chladni analysis to look at some top movements, and I think it'll help
25:45you understand what these resonance peaks mean physically.
25:49So what I have is my guitar body, I have some tea leaves to act as an indicator, I have
25:55my laptop which can run pure sine waves of any frequency that I want, and then I have
26:01my Bluetooth speaker to send these sound waves, and I have some hearing protection.
26:07And let's start at this big peak at 178 hertz.
26:12And for you guitarists out there, 178 hertz is near F or F sharp on the fourth string,
26:18so if you're playing any notes in that vicinity, then this is the top movement that would be
26:23predominantly made when you play those notes.
26:37What's happening at this frequency is a relatively simple movement where the big middle area
26:51moves up while the periphery moves down, and then it flips where the middle area moves
26:55down and the periphery moves up.
26:59And this repetitive flipping happens at 178 times per second.
27:05Let's move up in frequency to 211 hertz and you'll see that the patterns start to get
27:10more complex as we go to higher pitches.
27:24Moving up again to this resonance peak at 322 hertz.
27:40Now I want to show you how braces can dramatically alter the movement of the top depending on
27:45direction.
27:47Of course there's already bracing underneath this top, but I'm going to tape an additional
27:51brace which adds stiffness.
27:54And let's try it again at 322 hertz.
28:03Notice what happens when the brace directly opposes the flipping action of the sectors.
28:09I can almost completely kill the movement at this frequency, which will have an effect
28:13on the sound because notes near this frequency may not be well represented if we tried to
28:18play them.
28:20But if I turn the brace 90 degrees, what do you think will happen?
28:32It turns out not much at all because the direction doesn't oppose the flipping motion of this
28:37resonance and now you can appreciate how bracing is not only a structural element, but also
28:43a device to control top motion and therefore sound characteristics.
28:50So we've come to the end of today's session and I really want to thank you for sticking
28:54with me because I presented and challenged you with a lot of complex material.
29:00And it's okay if you didn't grasp everything because guitar builders have been building
29:04guitars as we know them for about 200 years at least, and they certainly didn't understand
29:10all the underlying physics.
29:13But I do know that the concepts and the analytical tools that I showed you today do help me to
29:18build a better guitar in the sense that I can make predictions and know how the guitars
29:23are going to sound or fine tune them long before I ever string them up.
29:29So here are just a few things that I hope you take with you.
29:34Wood is a great material for acoustic guitars.
29:37It's light but strong and gives good compromise between volume and sustain.
29:43Bracing provides good stiffness for very little weight.
29:47It provides strength to resist collapse, but is also a good tool to control sound.
29:53A guitar needs many resonances to support the frequencies instructed by the player and
29:58the string.
29:59You can think of each resonance like a gear in a car.
30:03You need a collection of gears to go different speeds, but in our case it's to drive different
30:07pitches.
30:10Each resonance corresponds to a motion.
30:17And finally, the builder can change the resonances to change the sound.
30:23Before I leave you, if you're interested in exploring more, there are two places you can
30:27visit.
30:29My website, GarrettLeeGuitars.com, where you can hear what the guitars sound like played
30:33by some world-class players.
30:36And my YouTube series called Luthiery Demystified, where you can learn more about the craft of
30:41guitar building.
30:44So thanks again.
30:45It's a real privilege to spend time with you, so why don't we answer some questions now?
30:51I hope you enjoyed that presentation as much as I enjoyed putting it together and working
30:55with the students.
30:56It wasn't meant to be comprehensive, but I wanted to put together an introduction of
31:01the world of luthiery and how luthiers work with players and try to satisfy the rules
31:07of physics.
31:08And in upcoming videos, you'll see me further characterize more thoroughly the resonant
31:14peaks in that impulse spectrum, so I will see you on those videos.
Recommended
4:14
|
Up next