Understanding Guitar Resonance | Part 1 | The Most Important Factors

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Transcript

SPEAKER_01 0:00

Boom. And just like that, we are live once again, ladies and gentlemen. I am pretty pumped about this one because we are going to be doing something pretty ambitious here, which is having a multi-part live stream discussion and just as much as I can handle it, a comprehensive look at understanding guitar resonances. This is something that everybody wants to understand. There's immense interest and need for it. And um, you know, the internet has all kinds of uh opinions and theories on this type of stuff, but I really don't see any sort of comprehensive nuts to bolts beginning to end coverage of this topic, except in textbooks. There's lots of great books out there on the topic where you can understand this stuff, and that's where I got my understanding of it from, um, however complete or incomplete it is at the moment. And uh, we got John J. Long in the chat says, good morning, good morning, John. So, by the way, as I mentioned, this will be live. And so you might be watching this during the live stream or after the live stream, the replays, the more condensed, edited down version. Uh, but if you do want to join in on us live, uh, it's every Tuesday, uh, typically around 10 a.m.-ish, but because I have to prep these things, the the time is always variable. But if you're paying attention on Tuesday, you you can uh get involved with us here. And hey, if you have physics friends or other guitar maker friends who are really into this stuff, let them know about the live streams because uh I want this to be a dynamic event where uh lots of um you know people with thoughts on this, uh especially people in the know can get involved and we can have some really like high-level discussions. So the way this is gonna work, in the beginning of each one, I'm gonna give you my spiel, and then uh I will address the the chat and we'll we'll talk about all sorts of great things. So um before we get started, if you like what I do and you get a little something out of the lessons that I teach, you can go to Eric Schaefer Guitars. Hold on, wrong tab right there. There we go. Ericsshaperguitars.com, and there you will see the schedule of dates for my hands-on workshops. Um, I have one available workshop left for this year, and that's in November. The October workshop is totally full. Uh, but I am also creating the schedule for 2027 at the moment. So if you have interest in a workshop for next year, that's an opportunity for you to reach out to me and uh you can pitch a set of dates to me, and I might, if it works, I might add it to the schedule for next year. Um, also at Eric Schaeferguitars.com, you will find the online course Building an OM Acoustic over 60 full-length instructional videos from the beginning to the end of a guitar build showing you everything you need to know. Um, if you know you're not so much interested in these high-level acoustic design topics and you actually just want the nuts to bolt, that's what that course is all about. It's not really about understanding resonance, it's about actually going through the steps and building an instrument on your own at home. And then lastly, I now have the tone wood shop. And uh, so I've got a lot of different backs and side back and side material and top material, and even some uh neck blanks and bridge blanks and things like that in the tone wood shop. So check that out. And hey, if you want to get your tone woods from someone who is interested in the principles of vibration as I am, uh, well, hey, that might be a great person to uh to reach out to and and get some quality materials from. Okay, so uh talking a little bit more about what we're gonna be doing today. Um, so what's today about specifically? Because yes, long term we want to understand this very deep topic of resonance. Uh, but the way I want to start this out, I think this is the best way to start this out, is simply to give you guys a what I would consider a 30,000-foot view of what the guitar is doing. So I've titled this one the most important factors uh to consider. I'm actually I don't remember exactly what I titled it, but part one is the most important factors affecting resonance. And I've decided on four of them, and they are I would say in order too. I've I've ordered them in relevance too. So these four factors are going to be the material properties of the string itself, the scale length, the Helmholtz resonance, otherwise known as the main air resonance. It's basically the ratio of um the volume of your soundbox compared to the sound of your or the size of your sound hole, the volume of trapped air in your soundbox and the size of your sound hole that generates your Helmholtz resonance. And then lastly, the main top resonance, which I think is where a lot of the nuance uh gets involved. So we'll we'll talk about all four of those things. And so, um, like I said, any questions you have along the way, throw them into the chat. I try to address everything, but we're gonna go ahead and get started. Let's jump over to the bench. And so again, I want to start this discussion with the material properties of the string itself. And it might seem almost pedantic or too elemental to start there, but I think a lot of critical mistakes happen from making comparisons that are not really an apples to apples comparison. Um, and then definitely when we get into talking about the top and the main top resonance and the variety of modes that affect the top, it's going to be crucial at that point to understand the difference between classical guitar top bracing and steel string top bracing. And in order to understand that, it all starts at the string. So obviously, classical guitars have nylon strings, which nylon inherently wants to sound bassy and muddy. Um, and so we're always fighting with our top bracing, with the pattern, with the way we voice it, everything, we are fighting that inherent characteristic of the string and trying to bring out more of the trebly pop of that string, which it lacks. Alternatively, on a steel string guitar, generally speaking, we are doing the opposite thing because steel strings, not surprisingly, inherently want to sound bright, trebly, you know, metallic and brash, all of these different descriptors all describe the same thing, which is treble. And so, in order to fight that, we are going to have to have a different approach to our bracing pattern, as you can see right here with this X-brace, which we'll get into uh when we get into the uh last part, which is the main top resonance. Um, but then moving on from the string choice, which again we're gonna talk about more when we get to the main top resonance. The second factor to consider is your scale length. Very important. I always find this to be uh surprisingly the most overlooked thing. I remember, uh, just as a quick little anecdote, a little story. I remember I went to a um guitar show, not really a guitar show, but more like a um uh Luthery exhibition exhibit. And um as one part of the show, uh they had a professional musician there and a bunch of luthier. We all kind of got together in like a panel and passed around some guitars, a variety of very different guitars. And the uh very skilled musician played those guitars, and then we all, both the luthers and the musician himself, we all just kind of had a fun little discussion about the differences between those guitars. And um, a lot of smart people and came to a lot of very smart conclusions. But one thing that surprised me is um at one point we had a OM-sized instrument that was played and stacked up against a parlor-sized instrument. And after the instrument was played, immediately everyone in the panel started talking about the different woods that were used for the top. And to me, I thought that was such a uh misdirection there because we were talking about two guitars with extraordinarily different, not only body sizes, which we'll get into with the Helmholtz resonance, but with extraordinarily different scale lengths. So it literally is like comparing an apple to a fig or something. It's it's not apples to apples and not even close. And the reason why that matters is because the longer the scale length is, the higher the tension those strings are going to be at when you tune it up to pitch. And of course, we're assuming all of these guitars, which 99% of the time they are, all of these guitars are tuned to standard pitch, right? E A D G B E. And so when you have a long scale length, let's take a bass guitar as a dramatic example, in order to get to the same pitch as a shorter scale length, you're going to have to crank on those tuners a little more to give it extra tension. At pitch, the long scale will be at a higher tension. You can feel that when you play an OM compared to a triple O, long scale OM, triple O is short scale. You can always tell that difference naturally just by the feel of the strings, because the OM is always going to feel stiffer. It's going to be just a little harder to press down on those strings. And certainly, if you're the type of player that does a lot of bends, it's going to be more difficult to get a good solid bend out of a long scale string compared to a short scale, which by the way is why some people like the short scale, is just for the flexibility of the strings. It's more of a um uh a player choice, a uh playability choice rather than a tonal choice, because uh most people, not all, but most people find that the long scale delivers more of the tonal promise that they're after. And that's simply because that higher tension is going to give you more energy into the top, and so it's going to give you more of those things that you want, like projection and volume. Um and you know, if you just as an example too, we all kind of recognize this when you tune your strings. Here, I'll downtune this when you tune a string down really low, you not only uh change the pitch, obviously you you change the pitch, but you're also losing a lot of volume. So you listen to that, then as I tune it up, the volume really comes in, and so it then makes sense that when you have that longer scale and you have to tune them up more to reach the appropriate pitch, you're going to get more punch and more volume and more just energy out of that system. So that's scale length, very, very important. Um, I brought a whole bunch of uh extra guitars here along with me just to explain a couple things. So on the table there, you are looking at an orchestra model, and here is a short scale parlor guitar. This is actually a very short scale guitar. And by the way, I'm not gonna play these guitars against each other because I have a lapel mic that we don't have a setup here for doing that sort of thing. And honestly, it's not what this video is about. Um, you know, if you like watching those guitar comparison videos, it's just a totally different thing. We're just talking about concepts here, and so this shorter scale is going to deliver a lot of things to the player that they might desire. The fret spacing is tighter together. So if you have smaller hands, the strings are at a lower tension, so you can bend them more easily, as I mentioned, um, and press them down to the fret wire a little bit more easily. Uh, but this is going the shorter scale instrument, whether it's a parlor or a triple O, is going to sound uh this is just going to have less power being delivered into the bridge, okay? Less energy. And then so that's scale length. Um, and then for our main air resonance, that's the Helmholtz resonance. That is very important. I wanted to start with the strings and the scale length, even though they're not red they're not resonances, they're just different factors that affect it, so that people are comparing apples to apples and they're not making critical design choices in the early stage that box them into something that they don't want. So you want to think about those things first, and then you can we can start getting into the real geeky stuff with resonances. So, what is our main top resonance, also known as the Helmholtz resonance? It is the ratio, the um difference between the volume of trapped air in the soundbox, so at the design stage, how large or how small you design your soundbox relative to the size of the sound hole. So the smaller the sound hole gets in comparison to the size of the soundbox, the more bass response you're gonna get. And vice versa, if you really open up that sound hole, you're going to uh it's gonna change a lot of things. You're gonna lose some projection from it, but you're also going to encourage less of that bass response and get more trouble. Okay. Um just to I have I brought something here, I'm looking for my prop. Here it is. Here's my prop. Um, just as a really easy demonstration of what Helmholtz resonance is, I have this nice bottle of uh champagne here. Um, and many of you guys have heard of this analogy before, but all you have to do to understand Helmholtz resonance is take a bottle and blow across the top. Not very good at doing that, but um what you're hearing is a result of the size of the bottle and the size of the hole. This is analogous to our soundbox size. This is analogous to your sound hole. So if I took a smaller bottle, which typically, like a beer bottle, has the same hole on the top, but a much smaller volume, it would sound very different when I blow on that. Oh man, I can I can taste some nasty three-day old champagne when I blow on that a little bit in my nose. Not pleasant. Another great example of Helmholtz resonance, just for the sake of understanding what it is, is think about a flute. Flute is basically an instrument that relies entirely on Helmholtz resonance to um to be played, to get the various pitches as you play it. Because what a flute is, is it's a cylinder filled with air that has a variety of holes that you block the holes with your fingers to generate different pitches. And what you're effectively doing is you're keeping with that flute, you're keep maintaining the same volume of air within the flute. That doesn't change, you're not changing the size of the flute, but what you are changing is the size of the sound hole by by blocking particular holes, and that gives you the musicality of it in the different pitches. On the guitar, of course, it's completely different. Um, we're not using Helmholtz resonance to create the musicality of the instrument and to change the pitches. It's a static thing here. Really, the Helmholtz resonance is just built into the amplification mechanism of the acoustic guitar. Obviously, electric guitars don't have this concept related to them at all because they don't have a soundbox, right? Um, so that is Helmholtz resonance. The arguably the most important resonance, that's something you figure out at the design stage when you have pen and paper out and you're just deciding what you're gonna build. If you want to dramatically affect the uh acoustic output of your instrument, you can play around with the that ratio between the volume of trapped air and the size of your sound hole. Okay, let's uh check out the fourth element here that I want to talk about. Uh let me put this guitar down first, which is your main top resonance. And actually, what I want to do here is take an opportunity to understand top resonance. Um now eventually we're through the other videos that I'm gonna do, the other live streams, we're gonna start from the beginning and get all the building blocks necessary to truly understand what's going on with the modal movements of the top and different bracing patterns and how all that works and the the uh physics of plates and uh compared to the physics of a string, compared to the physics of a beam. All of that is very important. Those are all the building blocks that are truly necessary to understanding this. But again, just to give you guys a 30,000-foot view explanation, um, what I'm gonna do is start again start with the string material and how that affects our choice of what we're gonna do for the bracing pattern, and then how that relates to modes and what modes actually are. Okay, but we're gonna keep this simplified. So, starting from the string, like I mentioned earlier, different strings have different inherent characteristics, and so we need to uh and so they bring inherent challenges to the table for a bracing pattern. For nylon strings, a classical guitar, we have not this bracing pattern, but a fan bracing pattern. I don't have a uh prop for that right here, but I'm just gonna explain the difference as far as what that would look like. Your transverse bar, which is right up here, this big beefy thing, instead of being above the sound hole, your transverse bar would be down below the sound hole. And you would have instead of the X, you would have simply what's called fan braces, which go more or less longitudinally along the length of the top rather than going at these angles across the top. Okay. And so if we're trying, if we know that the strings want to sound bass, uh bass heavy, and we want to fight that and introduce some treble to the situation, we need to encourage the modes that produce uh treble. And discourage or mute modes that encourage more base. Okay. And so though just to give you a brief layout of what those modes are, there are many modes, but to understand this, we only need to talk about two specific modes. And that's uh maybe three, but the the main two are monopole and cross-dipole. And that's because monopole mode is what encourages bass response. Cross dipole basically encourages treble response. And then long dipole, which don't worry, I'll explain what all these are in just a second. Long dipole is a bit more complicated. It uh encourages more project, it gets you more projection out of your out of your guitar. And um, I do think it's helpful to understand long dipole in this discussion just for the purpose purposes of understanding what to mute in order to generate the mode that you want. So modes are simply ways that a plate vibrate. Okay. So if I were to excite this plate in some way, either by strapping a bridge to it and plucking a string, or by um even just putting it close to a speaker cone and letting the speaker vibrate this, what's gonna happen is this is going to vibrate in a variety of ways and all at once. So some of those ways, it's gonna vibrate flutter side to side like this, it's gonna flutter front to back longitudinally, like this, and it will also pump uniformly, so all at once, like this, all together. This side to side fluttering, this is all by the way, in relationship to the bridge. So when I say side to side, you can think of the bridge as the central axis about which these modes are moving. And that's because, for obvious reasons, the string signal is going to start right where the bridge is. It's not starting up here or evenly everywhere across the top, it starts right here. So when I say a side-to-side fluttering, that's going to be like this about the bridge, and that is called cross-dipole. And cross-dipole encourages treble response. So with a classical guitar with its nylon strings, that sound bassy, we want to mute the long dipole, which is a fluttering in this direction. And when you mute one mode, the energy has to go somewhere. Don't think of it as like you're just simply deleting that mode. You are actually taking all the energy from that mode and moving it to a different mode because the energy, again, has to go somewhere, conservation of energy. And so if we restrict the movement in the long dipole, it's going to then put more of its energy into the cross dipole, which again gives us those, you know, lovely bright trebles that we all love, you know, especially on the classical guitar, where it's hard to you know pull that out of a nylon string. And that's why we see fan bracing on a classical guitar. Those braces, again, are going more or less in a longitudinal direction, which, if you put big beams going this way, you're strengthening it or stiffening it, I should say, in that direction, um, and thus muting the long dipole. Prior to putting those braces on, it was going like this. Once you put those big beams on there, it's gonna stiffen up in that direction, and the energy is gonna go this way, giving you cross dipole. Um, so now getting to a steel string guitar, again, steel strings, we've got plenty of high uh harmonic content from those steel strings. It's gonna sound plenty bright. So we don't want to encourage cross dipole. What we want to encourage is monopole, and again, or actually, I don't know if I mentioned it yet, but monopole is that uniform pumping that I talked about. Okay, that's how you get your bass. And uh it's one of the harder things to encourage because the way that you get a uniform pumping of a plate is by evenly bracing the plate more or less in all directions. Um, because if we now simply, let's say we want to eliminate the cross dipole, okay, so let's just put ladder braces going straight across. Yes, that will mute the cross dipole, but then it's just going to put all of its energy into long dipole. And that's not really uh what we want either. So what we need to do is something like the X brace. That's why this looks the way it does. You can see how this is reinforcing or stiffening, I should say, the top relatively even in both directions, which more or less forces it to pump. We still get some cross dipole and some long dipole. And honestly, we want to because um having a guitar that only moves in one mode actually wouldn't sound very good. It would sound uh, it wouldn't have the richness and the complexity that you get from having a little bit of the other modes as well. So you can't get too um rigid about these concepts and you know try to try to force it to only do one thing. Not that you'd be able to anyway, because pretty much all objects want to vibrate in a variety of modes no matter what you do. So, anyway, um, but more or less the general concept is we want to encourage more of that pumping on a steel string guitar to counteract the inherent brightness of steel strings. Uh now let me just explain, just because I think this is always helpful for people to understand from the outset, I'm gonna explain to you guys what all of these individual braces are doing, what their role is. Because you might, after that brief discussion there, you might um uh come to the conclusion that, hey, uh, if you really want to encourage more monopol, like what's this one doing across here, right? And um, why wouldn't you do just like a lattice pattern all the way across? And really the answer is simply that there are other structural requirements for a top that also have to be met uh simply so that it doesn't endure some structural damage, right, from the tension of the strings. And so um I always like to start with the transverse bar. Um and it's important to understand the transverse bar first because the transverse bar sets the vibrational footprint of your top for you, and this is true pretty much with any bracing pattern. Uh, when you're analyzing any bracing pattern, for the most part, you can look for this big beefy bar that runs straight across the top, and that will always tell you where the vibrational footprint of the top begins. And so for a X-braced steel string guitar, the vibrational footprint begins right here, and it's everything south of that transverse bar. All of that is what you are considering acoustically when you're voicing a top. Everything above the transverse bar you can think of as essentially acoustically inert. Um, meaning you can put a nice beefy block in here for the neck joint, which we do, right? There's a big block in there. You can you can brace this up a little more if you need to, and it doesn't really meaningfully affect the tone because this bar is essentially like a barrier. Okay, it's doing the same function as the sides, in that it is simply a perimeter wall to restrict the vibrational footprint to a smaller area. So that's the transverse bar. Um, it's also, of course, I think most of us know that the transverse bar is resisting the uh cantilever effect of the neck as the fretboard tongue pushes down on the guitar top. If you didn't have a transverse bar on a steel string guitar in this location, then you would uh very quickly experience some dramatic sinking and splits and things like that in the upper bout location. So it's it's holding up a lot of that tension and it's uh creating a strict barrier for your vibrational footprint. And then on this little demo sample piece I have here. I don't actually have a bridge plate on here, but the bridge plate is important to understand. The bridge plate is basically a first and foremost, uh a hard-bearing surface for the ball ends of your strings. It's usually a piece of hard maple in here that uh provides a good surface for the ball ends of the strings to rest against. If you didn't have it, the ball ends of the strings would just eat through the softwood uh pretty quickly. So you need a hardware surface right there. But it's important to keep the bridge plate very thin because once you've satisfied that requirement, you don't really need extra weight and um mass and thickness in that location. Uh, it's just gonna you know add too much mass to your bridge. So keep that thin. Uh, the other thing that the bridge plate is doing, you'll always notice that the bridge plate is quite a bit larger and wider than your actual bridge footprint. And that's because uh it is essentially um acting like a graft that spreads the torque, the torque that the bridge experiences from the strings, it's spreading that torque over a larger area so that you don't get a dip in front of the bridge and a bulge behind the bridge. Now, we many of you uh have probably seen guitars with the classic bulge behind the bridge and the little sunken concavity in front of the bridge. Um, it's not necessarily because they didn't do the bridge plate right, although it could be. Uh often that's just the case with very old guitars that um that are left at tension. Over time, uh it's it's really just a lot of torque that um over time can deform the top. Now the X-brace. The X-brace I always like to think of as the main arteries of our structural system. On this sample top here, uh the ek none of these braces are carved out, the tapers aren't carved or anything like that, so you just have to imagine that they are. But um with your typical X-brace, these ends get tapered down to a very small tucked most of the time gets tucked into the kerfing so that it's structurally connected to the sides themselves. And this the structure of the X-brace is really what holds up the rest of the top against the tension being pulled on that bridge and keeps um, you know, basically the guitar from folding on itself over time. Very important structurally, it needs to be there. Okay. All of these other braces, the finger braces and the tone bars, in the end, when they get carved out, these do not connect into the kerfing at all. They just get carved down to nothing and they kind of disappear into the top. And so they're actually not, strictly speaking, structural because they're not actually connected into the sides. So what are they doing there? Essentially, they are helping to encourage that monopole mobility that we talked about, that monopole mode of the top. Because if you didn't have these six braces here, which I like to think of as like capillaries coming off of the main artery of the X, if you didn't have these, then what you would have on your top is pockets of extreme stiffness, like right here at the center of the X, and pockets of uh extreme looseness, like down here, if these tone bars weren't here. You know, a lot of uh guys online in forums and such, I've seen um this you know posted, have learned that hey, you can actually remove the tone bars, and um and I've seen people encouraged to reach into their soundbox and remove the tone bars, which you know, if you're after a certain sound, you can do that, but I think a lot of people are doing it under the mistaken notion that these aren't really doing anything, and your top is going to um vibrate more and it's gonna sound better ultimately if you remove these. Now it might vibrate more, but it's probably not gonna sound better, and that's because what we want is it to vibrate in the modes again that we're most interested in. And so what these are doing is they are again extending out like capillaries from the main artery of the X-brace, borrowing some of that stiffness and essentially stiffening out an area that would otherwise generate a lot of cross-dipole fluttering because you'd have pockets of stiffness and looseness. Because again, to get that monopole mobility, we need a very uniformly braced surface. And with that, actually, I didn't talk about the um fretboard graft, but it's not very meaningful or interesting for a uh resonance discussion. The fretboard graft is simply there to prevent. Uh, there's a common problem if you didn't have something like this, to prevent splits along the sides of the fretboard, because the fretboard is always a different wood from the top, a very different wood. It's usually ebony, and the top is let's say sit the spruce. And so the um one, the torque that's on the fretboard tongue, but then also just the different shrinkage rates of those two different woods, um, which are glued to each other, mean that if you just leave this without the fretboard graft, then you are very likely to get uh splits as the guitar ages. And so the fretboard graft, because the grain is running across in the uh 90 degree direction to the prevailing grain of the top, the fretboard graft is uh preventing splits. Um, so anyway, let me uh actually before I jump over to the chat, which I will in just a second, I know everyone's gonna want to know about the back, or maybe not. Maybe you guys are satisfied. I don't know. But um, I I'm not really including the back. I want to mention it briefly here, but as far as like the most important factors, I think those four things are a good jumping off point. The back is um still important, but definitely less important than your main air resonance and your main top resonance. And that's simply because the top is directly coupled to the string signal. When you pluck those strings, that energy goes physically or directly into the top, whereas the back is only indirectly excited by the string signal exciting the top, which in turn excites the the volume of trapped air, which then in turn that excites the back. And so the back, while still very meaningful, I always encourage uh new builders to just forget about the back for a while and really if you want to dial in tone to focus on the top first and foremost. Honestly, if you didn't think about the back at all and you just did um the simplest, most obvious thing ladder bracing, and you didn't worry about the species too much and the thickness, uh, as long as you were focusing on the top, I think you would still be creating just amazing guitars that you know musicians would love. Um, and then if you want to, you know, add that extra 1% of oomph to your guitar, you can you know geek out on the the back a little bit more. But again, it's indirectly uh excited by the volume of trapped air. And so um we don't have to uh we don't have to dive into that just yet. I think later on um in future videos we'll get into this. But yeah, most backs are simply ladder braced, which is partially just for the simplicity of that. Um but also it's you know the the market has sort of determined that it produces uh a good, meaningful um it's able to turn the back into a resonator, and you could also turn the back into a reflector if you want with ladder bracing. But again, resonators and reflectors, that's a back discussion for another time. I think um let's focus on the material properties of the strings, the scale length, the main air resonance, also known as the Helmholtz resonance, and the main top resonance for now. And um, I'm gonna jump over to the chat. Let's see what's going on, guys. Okay, we got Carl Mills in the chat. Carl Mills uh took one of my workshops last year and he writes, I'm excited for this series. And um, okay, we got John J. Long writes, I have the Trevor Gore books. A lot of what I'm talking about, by the way, is based off of the Trevor Gore books. So I should mention those right now. If you guys um want to concurrently with this series, uh do some deep diving yourselves, um, I would get those Trevor Gore books. They're very expensive, they're sold at like textbook prices. If you remember, you know, that scam going to college and paying uh $200 for a textbook. I'm not saying that his is a scam, it's actually uh very high-quality material that I'm happy to pay that much for. And it's a two-book um collection. One is on the stuff we're talking about, all this design, um, geeky acoustic stuff. And then the second book is, which I actually haven't read, is about um actual build techniques, guitar building. But at the very least, get the first book and read that. Uh, it's I will, fair warning, it is extremely um dense and uh there's a lot of math in there, which honestly I just skip over. Um, I think the math is only there to provide proofs for the theories that he's talking about. Um, so if you just kind of skim past all the math problems and read the conclusions, you'll get the most out of that book. Uh, but let's read the rest of John's comment. Uh I have the Trevor Gorber books, but I haven't read them yet. This is some of what he covers in depth in those books. Yep. Someday I may actually read them. Until then, this is good info. Yeah. Yeah. I'm hoping this will um this could, you know, maybe supplement that. And uh I may get some things wrong here, too. So uh this is again, this is what the live part of this is all about. All right, good morning. Uh, from Tom Casty. Welcome. Um, expensive and they ship from oh, he's talking about the book. They ship from Australia. Oh my man. Uh Australian shipping rates are absurd if you're in the United States. Tons of math in the Gore books, but definitely worth a read. Oh, we got Larry Kuhn in the chat. He goes, uh hey guys, looked on YouTube and found a live stream. Coincidentally, I I just got back from a full week learning with Trevor Gore. Amazing week. Oh, that's awesome. Well, that's great. So, Larry Kuhn, hopefully um you will uh ride along with us for a lot of this, and um, we can borrow some things from your head as well. Okay, well, I think that'll be a good jumping off point. So, in in uh, if you stay tuned to next week and the week after. So, again, Tuesdays, I'm gonna be doing this. Um, we will be talking about uh, I believe the in the next one, we will simply be talking about what sound waves are and just a simple discussion of sound waves. That's a that's a great building block. Um, and then again, like I mentioned before, some other building blocks like the physics of beams, the physics of strings, and uh ultimately the physics of plates, which is what we're most interested in because that's what guitar tops are. Plates. All right. Okay, and like I said, if you like what I do and you get a little something of the lessons that I teach, go to Derek SchaeferGitars.com, check out those uh the hands-on workshops that are coming up, the one in November, and um look forward to the new dates coming up for the hands on workshops in 2027 starting in the spring. All right, guys, thanks for tuning in.

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I'll see you in the next one. Bye for now.