Falbo Intension Bridge

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Re: Falbo Intension Bridge

Post by DarwinStrings » Thu Oct 06, 2016 2:56 pm

Oh and thanks for your time on answering questions Frank.
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Re: Falbo Intension Bridge

Post by lamanoditrento » Sat Oct 08, 2016 10:50 am

With this in mind, this is where I start to talk about phase linearity and the comb filtering
Damn, just when I had started to get my head around monopole mobility and frequency responses, another rabbit hole to climb into!
I can't stop someone from buying one to destroy, but its an expensive experiment. So it is cheaper for a company to just contact me, to discuss licensing under NDA
I would happily sign a NDA and licensing agreement :D

Frank, from an amateur maker point of view what is your recommendation about what to do with this information? Is this just something for the pros?
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Re: Falbo Intension Bridge

Post by kiwigeo » Sat Oct 08, 2016 1:40 pm

lamanoditrento wrote:
Frank, from an amateur maker point of view what is your recommendation about what to do with this information? Is this just something for the pros?
I'd focus on getting your head around The Books first...once you do that everything else will make sense :mrgreen:
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Re: Falbo Intension Bridge

Post by frankfalbo » Sat Oct 08, 2016 2:58 pm

Martin is right. Make some guitars the regular way for awhile. But yes I am open to licensing talks.

You are correct about the rabbit hole of phase linearity and comb filtering. It's something that occurs across the time constant. It's extremely difficult to produce any chart or graph that represents it. It requires driving the top in the same way string energy does (or just using the strings) and knowing how/what to measure.

For example (on a torqued bridge) I could place two contact transducers on the top, one near the sound hole, the other behind the bridge. (The dipole delta) Both will have a measurable frequency response. But more importantly, if I overlay them against one another, they won't be phase aligned. So there's a phase smearing across the time constant, compounded by the smearing of the box reflections.

With the torque neutralized, the two signals are more phase aligned. That means they push audio into the air and the box with greater linearity.

Incidentally this is the same reason Chladni patterns on a top without strings and tuned to pitch don't necessarily translate meaningfully to the finished instrument's response. Though they can serve to make known "likes" more repeatable.

But mostly in my case it's the reason I could post a response curve from two different guitars and it doesn't come close to telling the whole story.

Keep in mind I'm not one of those inventors who thinks their invention will change the game, or is "better". It's just different, and in ways that I think are great but it doesn't make 100 years of acoustic guitar technology "wrong". Please don't take anything I'm saying that way.

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Re: Falbo Intension Bridge

Post by hepikohetaniwha » Sun Oct 09, 2016 2:09 am

I was always under the impression from my old beaters that the top's distortion over time was mainly a buckling in front of the bridge from the mostly linear tension of the strings. The smaller rotational force on the bridge ensured that the buckling was a dip rather than a bulge. If you cancel the rotational force on the bridge, will some guitars buckle backwards?

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Re: Falbo Intension Bridge

Post by frankfalbo » Mon Oct 10, 2016 1:15 am

Not from neutralizing torque, no. But if you went past the balance point, then yes you could pull the top down behind the bridge. But at the balance point; just think of it as standing on a fence. The wood is at its strongest longitudinally.

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Re: Falbo Intension Bridge

Post by lauburu » Mon Oct 10, 2016 6:16 am

f I overlay them against one another, they won't be phase aligned. So there's a phase smearing across the time constant, compounded by the smearing of the box reflections.
Mmmmmmmmm. Think I'll take up knitting.
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Re: Falbo Intension Bridge

Post by lamanoditrento » Mon Oct 10, 2016 8:31 am

I'd focus on getting your head around The Books first...once you do that everything else will make sense
Oh yes I am. I have been tap testing as I build, working my way through online course on A level math and physics (masses on springs...) etc but I can wonder what a sparse falcate with a falbo bridge would turn out like
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Re: Falbo Intension Bridge

Post by simonm » Mon Oct 17, 2016 7:19 am

frankfalbo wrote:... a patent troll ...
.... I really don't think there is any guitar maker on the planet that needs to worry about patent trolls. They are not interested unless someone is selling 100's of millions worth of some product per year in the US market.

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Re: Falbo Intension Bridge

Post by simso » Mon Oct 17, 2016 11:31 am

I believe we are always trying to re-invent the wheel.

Small gains can be made through re-designs, but would really need to be independently quantified to be valid.

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Re: Falbo Intension Bridge

Post by frankfalbo » Tue Oct 18, 2016 2:12 am

simonm wrote:
frankfalbo wrote:... a patent troll ...
.... I really don't think there is any guitar maker on the planet that needs to worry about patent trolls. They are not interested unless someone is selling 100's of millions worth of some product per year in the US market.
Sadly it happens regularly within the music industry, between companies. I should not give examples, but there are many products that you would all recognize, which have been stolen from their inventors. These are very real occurrences in which I have first-hand knowledge, not rumors. The internet is permanent and searchable.

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Re: Falbo Intension Bridge

Post by Deems Davis » Tue Oct 18, 2016 4:18 pm

frankfalbo wrote:
DarwinStrings wrote: So it's Trent's first post that is correct, in that my long dipole is reduced/cancelled in favor of the monopole. With this in mind, this is where I start to talk about phase linearity and the comb filtering present within an acoustic top driven by torque. Amplitude, frequency density, and projection are now (in my experience) no longer directly tied to pure excursion data.
.

Frank, with regards to phase linearity (let's save comb filtering for the moment) can you help me/us understand how this gets induced into a top? are you referring to the "normal" phase inversion present in the dipole? Or is this something different? I'm just trying to get straight in my head what the physics.mechanics is that causes/allows this.


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Re: Falbo Intension Bridge

Post by frankfalbo » Wed Oct 19, 2016 1:59 am

Well, for simplicity's sake you can limit the discussion to the long dipole, and talk about how that differs from the trapeze/bridge arrangement on jazzers, violins, banjos, etc. My guitars aren't targeting the latter. They don't sound like trapeze tops. But that's the easiest way to see the most obvious phase imbalance. Simple, 180° out of phase information in front of vs behind the bridge. We don't hear it as such because everything combines in the box, there are reflections everywhere, and the dipole isn't the only vibration transfer. But to discuss in isolation this is simple.

Next, the top isn't made of a consistent material. So it's strength, and transmission of vibrations isn't linear. As the multiple vibrations combine, there are all sorts of smaller, shorter phase arguments. Each pitch (wavelength) dependent, and when playing chords with dissonance, you can hear these phase anomalies in the way the top (and therefore guitar) modulates; the "beating" sound. Also it will affect whether a 6-note chord will quickly resolve to root/fifth, or whether the complex harmonic mix is replicated and all 6 notes sustain together. I'm not saying other great guitars don't have these qualities, just that it becomes obvious when you play test for certain things that the phase alignment of the extended harmonic content is absolutely contributing to this phenomenon. The top forms a feedback loop with the strings, and the decay teaches a lot of these things.

Each brace is a divisor of sorts, as well as a transmission trajectory. Not just because the brace laminations exist, but also because of what the pre-load looks like under 160lbs of string tension. The way a top transmits vibrations without string load is less meaningful as when under load and driven at the bridge by the string.

The comb filtering from phase anomalies are partially what makes the recorded guitar sound dramatically different if you move the microphone (or player) around. First, yes the guitar does produce different sounds in different locations. But beyond that, the microphone is picking up out of phase audio from other areas on the guitar. In other words it's not just thin-sounding off the 12th fret, it's made even thinner by phase arguments from other areas of the guitar reaching the mic, which are already convoluted by the way the top is driven. So you move a mic all around one of my guitars and you don't hear the "swooshy" watery, flangey sound of these arguments. In short, the result validates the cause.

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Re: Falbo Intension Bridge

Post by Deems Davis » Wed Oct 19, 2016 12:56 pm

Oversimplifying: If I understand correctly, your intensioned bridge "neutralizes" the phase shifts and produces a cleaner (less muddied) sound? I'm still trying to get my head around whether these phase irregularities are material enough to affect the instrument sound. If they are material it would seem to follow that they should be seen and measured in a freq response sample. Is there any emperical evidence I can digest to better understand this? If they aren't significant enough to be measured I'm struggling to grasp what how they somehow sum to something that is.


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Re: Falbo Intension Bridge

Post by frankfalbo » Wed Oct 19, 2016 2:54 pm

Frequency response is a 3-dimensional occurrence. It's either a moment in time, frozen, or it's a composite of audio over time. When ignorant of the time constant it tells you very little. For example imagine you have a loudspeaker where the tweeter is poorly aligned with the woofer. I could put a mic in the room and maybe you'll see some convolution in the treble range. I could then ADD EQ to boost that, revealing "more" treble. But it would be ugly treble. Even though the frequency response chart would suggest that you've recovered the lost treble, its not the "same" treble.

Its like judging all race cars by their horsepower. Predicting that only the HP data matters. But there's how the car handles, the gear ratio, etc. The ADSR envelope includes so much more than the frequency response. So if I showed a response curve that had some lift here and there, some dips here and there, it would not be able to show you any of this phenomenon. For example I could show you a Martin at moderate playing volume. You look at the response chart and say "that looks fantastic" and then, you strum the Martin really hard and you say "that looks ugly. It sounds overloaded now" or I fingerpick softly and it looks weak, dark, anemic, etc. So there's no one singular response curve that tells the whole story.

My personal empirical evidence is from the play time I have on the instruments, plus what I know to be true of the physics. On one hand, you could say it's the most egregious form of confirmation bias, but I'm my own harshest skeptic. Proving out the things I see in my head is my highest priority even if it means I'd prove myself wrong. Playing a 6-note chord and listening to all 6 notes sustain for a long time, even with dissonance, even if the guitar is painfully out of tune, teaches the phase alignment as part of the feedback loop between the top and the strings. There's not another root cause.

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Re: Falbo Intension Bridge

Post by DarwinStrings » Wed Oct 19, 2016 3:16 pm

Deems asks
Deems Davis wrote: Is there any emperical evidence I can digest to better understand this?


Deems
I reckon this bit is your answer but I am having trouble understanding the way you write Frank
frankfalbo wrote:
My personal empirical evidence is from the play time I have on the instruments, plus what I know to be true of the physics. On one hand, you could say it's the most egregious form of confirmation bias, but I'm my own harshest skeptic. Proving out the things I see in my head is my highest priority even if it means I'd prove myself wrong. Playing a 6-note chord and listening to all 6 notes sustain for a long time, even with dissonance, even if the guitar is painfully out of tune, teaches the phase alignment as part of the feedback loop between the top and the strings. There's not another root cause.
So is your answer to Deems' question just simply a no?
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Re: Falbo Intension Bridge

Post by frankfalbo » Wed Oct 19, 2016 4:29 pm

I apologize for being verbose. Will a frequency response chart tell you something? Yes of course. But it doesn't prove out anything with regard to phase alignment, the main question he was asking.

If the question is, "how can we prove that your top is more phase aligned under string tension?" then it would be an extensive test with cameras and/or body sensors. It can also be modeled. But the simplest test (that does not illustrate all the complexities) is two body sensors across the dipole. One in front of the bridge, one behind. Play and record both simultaneously and look at the two wavs up close. Then do the same with a torqued bridge.

The fact that I don't make that available at this time, well...if that resulted in fewer guitar sales for now, then so be it. But I still try to explain what I can and apologize in advance for my shortcomings.

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Re: Falbo Intension Bridge

Post by Deems Davis » Wed Oct 19, 2016 5:43 pm

Frank, forgive me for being obtuse but one of the things that attracted me to guitar building is the recent work that has been performed that modeled and measured the fundamental physics/mechanics that are present within a guitar in a way that can predictably prescribe much of an instruments responsiveness. this notion of Phase Linearity is new to me and so I'm trying to digest and integrate it into what I've learned (learning). I found the following atricle http://www.phy.mtu.edu/~suits/phaseshifts.html that suggests that inducing some phase shift for a sinusoidal wave form results in no discernable difference in the sound that is heard. When listening to the 2 samples I cannot discern a difference. This seems in conflict with your experience.

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Re: Falbo Intension Bridge

Post by frankfalbo » Thu Oct 20, 2016 4:35 pm

I don't think you're being obtuse at all. The link you posted is referencing electronic signal, whereas what we're dealing with is more in the realm of loudspeakers, drum heads, in that the convolution occurs in the air in and around the guitar. In an electric guitar signal for example, if I have two signals and one is 180 degrees out of phase, when I combine them they will cancel. Meaning, I can have 12dB of signal A, plus 12dB of signal B, and together they produce 0dB; silence.

Contrast that with an identical signal going into a 2x12" speaker cabinet, with one speaker out of phase with the other. Together they do not produce silence, because they are separated by distance, and the sound waves are coming together in the air in front of the cabinet. They are also convoluted inside the cabinet. One speaker is pushing while the other is pulling. So the air resistance (impedance) inside the cabinet is completely different. The internal air impedance basically zero's out. If the speakers were in phase, there would be air resistance as both speakers would pump and retract at the same time. So if the cabinet were ported, the port would breathe. If the two speakers were out of phase it would be more stagnant.

The speaker cabinet is the better analogy than the electronic signal. A torqued bridge and dipole vibrations are introducing out of phase information into the top. The information combines in two different ways. First, in the air around the guitar; what we (and mics) hear. Second is in the top wood itself. The vibrations are crashing into one another in the wood. This is more similar to the way waves in water will go out, come back in, and bump into one another. Together with the string they create a feedback loop that affects how the string decays. The string vibrates the top, which in turn manipulates the way the string continues to vibrate. It's all subtractive. The top doesn't add vibrations to the string beyond the energy from the initial strike. But how it communicates with the string influences the damping immediately after it's struck. This is why, a major 7th chord for example, will often resolve to just one or two notes quickly. On my guitars, all the notes coexist and ring out more together. Again a torqued bridge guitar can exhibit similar qualities, but that quality is generally a divider between good and great guitars.

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Re: Falbo Intension Bridge

Post by DarwinStrings » Thu Oct 20, 2016 7:05 pm

frankfalbo wrote:I don't think you're being obtuse at all. The link you posted is referencing electronic signal, whereas what we're dealing with is more in the realm of loudspeakers, drum heads, in that the convolution occurs in the air in and around the guitar. In an electric guitar signal for example, if I have two signals and one is 180 degrees out of phase, when I combine them they will cancel. Meaning, I can have 12dB of signal A, plus 12dB of signal B, and together they produce 0dB; silence.
Okay, that bit I get. Easily demonstrated with a unboxed speaker heard from the side. That is, noise out the front, 180 degree out of phase noise out the back but in the middle nothing.
frankfalbo wrote:Contrast that with an identical signal going into a 2x12" speaker cabinet, with one speaker out of phase with the other. Together they do not produce silence, because they are separated by distance, and the sound waves are coming together in the air in front of the cabinet. They are also convoluted inside the cabinet. One speaker is pushing while the other is pulling. So the air resistance (impedance) inside the cabinet is completely different. The internal air impedance basically zero's out. If the speakers were in phase, there would be air resistance as both speakers would pump and retract at the same time. So if the cabinet were ported, the port would breathe. If the two speakers were out of phase it would be more stagnant.
Easy enough and I guess relates to the difference between a cross dipole and monopole on guitar where the cross dipole moves the air plug in the port less than the monopole.
frankfalbo wrote:The speaker cabinet is the better analogy than the electronic signal. A torqued bridge and dipole vibrations are introducing out of phase information into the top.
Yep can see it but get a bit lost after that, so can I get back to something more simple because you talk a lot about the long dipole.



In this vid at about 5.30 you talk about removing the rotational force on the bridge and being left with a "up down" movement which sounds like you are describing a monopole mode. But I can't see how that lack of torque could stop a long dipole from occurring, surely the top using your design will still have a long dipole? right? so how is your long dipole any different?


youtu.be/

EDIT: Oh another question. You mention in another youtube that your guitars won't need neck resets. So if you have remove bridge rotation to stop bellying what do you do to stop the neck pulling into the body?
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Re: Falbo Intension Bridge

Post by seeaxe » Thu Oct 20, 2016 8:23 pm

At the end of the day, if he is building these guitars and people like them enough to buy them, then good luck to him. He has my appreciation for taking the time to talk to us about what he is doing, he doesn't have to do that and I cannot see a big upside in it for him.

And whether we agree with him or not, I think he deserves our respect for being prepared to have his designs put under a fair bit of scrutiny by a bunch of very well meaning mostly antipodean sceptics : Remember he is not claiming his guitars are better than anyone else's, he just talking about what he thinks is a good idea.

Having said that...

Mr Falbo doesn't help himself much as he is mixing up his terminology. Torque is torque, it's either positive or negative. There's no rotational torque. In structural terms it is bending moment. He also talks about energy in the string when the reference is apparetly to force, tension in this case.

His system will alter how the top is stressed internally to counter the external forces applied. But the applied moment (torque) is 200 lbs multiplied by the height of the saddle above the top. It is all resisted by the top in bending because that's all there is to resist it. End of story. You cannot chose to resist some and not the rest....

With his bridge design If you resolve the string tension forces in two directions where they impact the guitar, there is a downward vertical force at the saddle and an upward vertical force at the rear anchor point. These must be equal and opposite as there are no external applied forces perpendicular to the top. (Assuming the strings are parallel to the top, which they are, close enough anyway). So while he is talking about the torque applied by anchoring the strings below the sound board bending the lower bout in a concave fashion, he is apparently ignoring the forces on the entire bridge system that are doing exactly the opposite.

So I think John is right, once you are south of the rear anchor point, it's not much different to a normal bridge system. And I also think that you are right too Jim in that it will have a long dipole mode and resonance. That would be easily demonstrated by a response curve or chladni test, if you ever get to do it. It might well be reduced by the design, but I was under the impression that was not necessarily a good thing.

The other aspect of all this is that most of the benefits claimed for the design (amplitude, sustain, clarity of notes, changes in vibrational modes) can all be fairly easily measured. So why not just measure them and prove the point? Maybe it's not the whole answer but it would go a long way wouldn't it?

My two cents worth.
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Re: Falbo Intension Bridge

Post by DarwinStrings » Thu Oct 20, 2016 11:26 pm

seeaxe wrote: My two cents worth.
I'll have to give you 5¢ unless you take Eftpos Richard.
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Re: Falbo Intension Bridge

Post by frankfalbo » Fri Oct 21, 2016 3:40 pm

DarwinStrings wrote:Okay, that bit I get. Easily demonstrated with a unboxed speaker heard from the side. That is, noise out the front, 180 degree out of phase noise out the back but in the middle nothing...and I guess relates to the difference between a cross dipole and monopole on guitar where the cross dipole moves the air plug in the port less than the monopole.
Right. But to clarify the quality of sound from an acoustic guitar is not dependent on the air exchange through the soundhole. That's a byproduct of a lot of things. With all the things I AM saying, I don't want to inherit things I'm NOT saying. :)
DarwinStrings wrote:In this vid at about 5.30 you talk about removing the rotational force on the bridge and being left with a "up down" movement which sounds like you are describing a monopole mode.
Correct. And for those of you correctly pointing out that I use "dumb guy" terms to describe it, like repeating "rotational torque" when all torque is rotational, you are 100% correct. The purpose, however of that video was (is) to engage everyone, including those who have never heard terms like this. That video was the first piece of marketing material ever presented to the world. It needed to transcend language barriers, education barriers, etc. I needed to get my point across to all who would listen. Many people, you say "torque" and they think it's related to the power of a pickup truck, like horsepower.
DarwinStrings wrote:But I can't see how that lack of torque could stop a long dipole from occurring, surely the top using your design will still have a long dipole? right? so how is your long dipole any different?
First imagine a trapeze tailpiece. There is no long dipole to speak of, correct? There is technically with the string vibration a push and pull, especially after the transient into the early decay. So it could be argued that there's a "rocking" at the saddle. But it's not driven by the string tension load, as is when strings are anchored in the center.
DarwinStrings wrote:EDIT: Oh another question. You mention in another youtube that your guitars won't need neck resets. So if you have remove bridge rotation to stop bellying what do you do to stop the neck pulling into the body?
Only robust and pre-stressed bracing there. The X is pre-stressed to bloat the top into the neck angle...basically the neck area is overbuilt. I get so much drive from the "circle" around the bridge, to the point where stifling the neck and upper bouts isn't an issue.
Anecdotally, my cutaway vs. non-cutaway guitars sound more similar to one another than any other guitars I've tried. It's not that I'll never have any neck cave, just that if I have a little bit of neck cave but I don't have bridge belly then it's all within the available saddle motion. My bridge is also very tall, and can be safely lowered as a last resort.

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Re: Falbo Intension Bridge

Post by frankfalbo » Fri Oct 21, 2016 4:48 pm

seeaxe wrote:At the end of the day, if he is building these guitars and people like them enough to buy them, then good luck to him. He has my appreciation for taking the time to talk to us about what he is doing, he doesn't have to do that and I cannot see a big upside in it for him.

And whether we agree with him or not, I think he deserves our respect for being prepared to have his designs put under a fair bit of scrutiny by a bunch of very well meaning mostly antipodean sceptics : Remember he is not claiming his guitars are better than anyone else's, he just talking about what he thinks is a good idea.
That's a genuine thank you from me. It's true I don't have something to gain. I don't begin with the premise that anyone here on a luthierie forum is a potential customer. Rather I enjoy talking about it, and with other luthiers. (sick, right?) No one to date has inverted torque and manipulated the long dipole in this way, with the string tension such an integral part of the motor.
seeaxe wrote:Having said that...
Ohhhh boy, here it comes :lol:
seeaxe wrote:Mr Falbo doesn't help himself much as he is mixing up his terminology. Torque is torque, it's either positive or negative. There's no rotational torque. In structural terms it is bending moment. He also talks about energy in the string when the reference is apparetly to force, tension in this case.
Correct. See above where I apologize, but don't really apologize for the dumbed-down terminology. The un-plucked guitar possesses stored energy, so once you start playing, the way that stress has manifested itself onto the instrument will influence the transients, the ADSR envelope, etc. It's what makes some guitars better at low volume fingerpicking, and others sound dull and muffled until you drive them hard. It's how much inertia you need from the string to hit the guitar's sweet spot.
seeaxe wrote:His system will alter how the top is stressed internally to counter the external forces applied. But the applied moment (torque) is 200 lbs multiplied by the height of the saddle above the top. It is all resisted by the top in bending because that's all there is to resist it. End of story. You cannot chose to resist some and not the rest....

With his bridge design If you resolve the string tension forces in two directions where they impact the guitar, there is a downward vertical force at the saddle and an upward vertical force at the rear anchor point. These must be equal and opposite as there are no external applied forces perpendicular to the top. (Assuming the strings are parallel to the top, which they are, close enough anyway). So while he is talking about the torque applied by anchoring the strings below the sound board bending the lower bout in a concave fashion, he is apparently ignoring the forces on the entire bridge system that are doing exactly the opposite.
No, I am relying on it. If the top were made of rubber you would see the two torque moments folding the top at the halfway point. But it's not. The longitudinal strength of the spruce, plus the bridge plate, plus the bridge and string receiving entity on either side all form a "lock" of sorts. It's what couples the moments in such a way as to turn the majority of the motor action into the up and down excursion, driven by the greater bridge "area", not two small torque moments driving localized energy.
seeaxe wrote:So I think John is right, once you are south of the rear anchor point, it's not much different to a normal bridge system. And I also think that you are right too Jim in that it will have a long dipole mode and resonance. That would be easily demonstrated by a response curve or chladni test, if you ever get to do it. It might well be reduced by the design, but I was under the impression that was not necessarily a good thing.
This is an excellent point. When torque reduction is discussed on a normal, torqued bridge design, you are correct that many people conclude that it's a net negative in the desired tone from a guitar. And let's define what is the traditional torque reduction understanding: It is when the bridge/saddle are lowered, and the string is brought closer to the body. This truncates the motor. And we're not talking about break, angle at the saddle, we're talking about the height away from the top. Allen Carruth talks a lot about this, here's one place: http://www.acousticguitarforum.com/foru ... 888&page=2 For example if we imagine a recessed neck, and a bridge that is as flat as a pancake, strings are 1mm from the top. Playing those strings does not drive the top with as much energy. As you raise the bridge/saddle, you are leveraging torque to drive the motor (better) but that is where I conclude that (with a design like mine) that trading dipole for monopole gives an advantage to all the things we generally like.
The other aspect of all this is that most of the benefits claimed for the design (amplitude, sustain, clarity of notes, changes in vibrational modes) can all be fairly easily measured. So why not just measure them and prove the point? Maybe it's not the whole answer but it would go a long way wouldn't it?[/quote]I have response curves that prove my point, but its a hornet's nest if I just post them without the support it needs for people to understand it all. The best vehicle will probably be a video series with images AND audio simultaneously, so I can show people what they're about to hear, and they can hear it in real time.

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Re: Falbo Intension Bridge

Post by seeaxe » Fri Oct 21, 2016 7:29 pm

Thanks once again for the detailed response. I'll need to read through that a few more times.
Cheers
Richard
Richard

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