Self-consistent eigenmode analysis

[hrhodes3]

Pleas help me I am trying to do Self-consistent eigenmode analysis of my washburn d27sc for my own cureiosity

[nylon rock]

Are you talking advanced mathematics?

 

What are your inputs?

What are your outputs?

 

Why don't you just learn how to play the silly thing?

[Queequeg]

try this-

(These vectors are eigenvectors, and the frequencies are eigenvalues.)

 

The first normal mode is:

 

egin{pmatrix} x_1(t) \ x_2(t) end{pmatrix} = c_1 egin{pmatrix} 1 \ 1 end{pmatrix} cos{(omega_1 t + phi_1)}

 

and the second normal mode is:

 

egin{pmatrix} x_1(t) \ x_2(t) end{pmatrix} = c_2 egin{pmatrix} 1 \ -1 end{pmatrix} cos{(omega_2 t + phi_2)}

 

well, you get the idea....

 

 

OK, I'm just pulling your chain. Geeze, I'm just a guitar picker. I didn't even know what the heck you were talking about until I looked it up.

And I looked it up and I still don't really know what you're talking about.

So for the benefit of maybe that one other guy out there who might not have a thorough understanding of quantum mechanics, and finding normal modes in harmonic oscillation using the strength of linear algebra and linear sets of differential equations where one can present the problem as a matrix-vector equation and then solve for its eigenvectors, you want to explain what the frick you're doing?

[hrhodes3]

I was just kidding

it worked

[Queequeg]

yeah? Well my formula contains an encrypted script which will infect your guitar far more menacing & diabolical than nanowebs & cotton shirts.

You're toast, hrhodes3.

fuhgeddaboudit.

[nylon rock]

My teacher of Ordinary Differential Equations told us one class that his daytime job working for Motorola had steered him toward eigenvalues and how cool they were.

 

To this day I don't know what he was getting at. I once tried to return to my ODE book, relearn the stuff up to the chapter on eigenvalues, but then ran out of focus to take on the challenge.

 

Suppose I'll die some day never knowing what they're about.

[Old_Joe_Clark]

Originally posted by hrhodes3 Pleas help me I am trying to do Self-consistent eigenmode analysis of my washburn d27sc for my own cureiosity

I don't know about the self-consistent part....but I did an eigenmode analysis for my cutaway Washburn EA Festival series. And I compared it to one I did on a non-cutaway.

 

[hrhodes3]

your the man

[knockwood]

 

Originally posted by Queequeg yeah? Well my formula contains an encrypted script which will infect your guitar far more menacing & diabolical than nanowebs & cotton shirts. You're toast, hrhodes3. fuhgeddaboudit.

 

 

Nothing is more menacing & diabolical than nanowebs & cotton shirts.

 

-The E.S.C.

[Sweb]

Now THIS is a great thread.

 

And, by the way, cotton is probably the better material to use with coated strings. Any poly blend will simultaneously combust with poly strings at the harmonic flashpoint, expressed in eigenvectors, and melt to your skin causing much more damage than cotton. Plus, poly gives up its electrons much more easily than cotton, on the eigenvalue scale, creating a greater potential of injury due to explosive separation of the string coating during electro-magnetic bursts from heavy strumming. Cotton has a higher flashpoint and is therefore the better protection when playing coated strings. This raises some serious questions about the safety of classical guitar strings.

[Old_Joe_Clark]

This shows the displacement of the 5th eigenmode of the non-cutaway. (red is large value, purple is small value)

 

 

It resonates somewhere on the high E string below A.

 

I have more if anyone is interested.

[Sweb]

Originally posted by Old_Joe_Clark This shows the displacement of the 5th eigenmode of the non-cutaway. (red is large value, purple is small value) I have more if anyone is interested.

 

Peter Max?

 

This depiction is representative of a guitar's sonic "pulse" (output)for a given (input) exitation frequency? Is that about right? As useless as this stuff is to me I'm still curious. Listen up hrodes3.

[JasmineTea]

 

Originally posted by Sweb Now THIS is a great thread. And, by the way, cotton is probably the better material to use with coated strings. Any poly blend will simultaneously combust with poly strings at the harmonic flashpoint, expressed in eigenvectors, and melt to your skin causing much more damage than cotton. Plus, poly gives up its electrons much more easily than cotton, on the eigenvalue scale, creating a greater potential of injury due to explosive separation of the string coating during electro-magnetic bursts from heavy strumming. Cotton has a higher flashpoint and is therefore the better protection when playing coated strings. This raises some serious questions about the safety of classical guitar strings.

This is true, but there is case after known case of cotten and coated strings causing deadly explosions.

 

The E.S.C. has conducted tests using dummies with guitars strung with Elixirs and nanos, and I gotta say, man those dummies are expensive!! Eventualy we'll document the whole thing, run a special on PBS.

 

We're starting see potential evidence that Elixirs we're designed to explode when contacting cotten and other common clothing material.

[Old_Joe_Clark]

 

Originally posted by Sweb Peter Max? This depiction is representative of a guitar's sonic "pulse" (output)for a given (input) exitation frequency? Is that about right? As useless as this stuff is to me I'm still curious. Listen up hrodes3.

 

 

well...no and yes.

 

No in the following sense:

The eigenmodes resonate at select frequencies. Not every frequency has its own eigenmode. According to my analysis, there are about 16 eigenmodes for a typical guitar top between low E and the 18th fret of the high E string. Each looks a little different. Each resonates at some particular pitch. At any pitch, however, several eigenmodes will be partially excited and will be responsible for most of the vibration.

 

But Yes in the following sense:

At the very special pitch (the eigenvalue) that resonates the eigenmode, it will be primarily that eigenmode that is excited. So at that pitch, the top "pulses" like the picture shows.

 

 

I have a video someplace of an eigenmode vibrating....slowed down of course. I'll look.

[Old_Joe_Clark]

A real eigenmode...in action!!!! Depending on the wood, the thickness, etc etc...this eigenmode would be vibrating about 10 to 20% lower than a 440 tuning fork. It is very dependent on many factors.

 

This is viewed from an angle so that you can see the "pulsing" rising and falling. Of course, the amount of the "pulsing" is exagerated. The actual amount is probably fractions of a millimeter.

 

 

I cut the file down so that it doesn't take forever to load.

I have a better file http://home.stny.rr.com/musicbocs/gcuto.gif if someone wants it.

[Old_Joe_Clark]

Originally posted by hrhodes3 Pleas help me I am trying to do Self-consistent eigenmode analysis of my washburn d27sc for my own cureiosity

 

something tells me that you were not serious.

[Hudman]

This thread is so stupid that I'm sure I lost a few IQ points reading it.

[jackwr]

What do you expect?

 

Using your eyes to evaluate what your ears should be enjoying..........too much time on your hands?

 

HiHo HiHO it's off to pick I go:thu:

[nylon rock]

Originally posted by Old_Joe_Clark A real eigenmode...in action!!!! Depending on the wood, the thickness, etc etc...this eigenmode would be vibrating about 10 to 20% lower than a 440 tuning fork. It is very dependent on many factors. This is viewed from an angle so that you can see the "pulsing" rising and falling. Of course, the amount of the "pulsing" is exagerated. The actual amount is probably fractions of a millimeter. I cut the file down so that it doesn't take forever to load. I have a better file http://home.stny.rr.com/musicbocs/gcuto.gif if someone wants it.

 

So, show a similar image of a non-cutaway.

[Old_Joe_Clark]

 

Originally posted by nylon rock So, show a similar image of a non-cutaway.

 

 

I have an entire series of modes for both, differing only in the cutaway. I've posted them before and everyone goes Ho Hum. But I'll do it again......stand by.

[Old_Joe_Clark]

http://home.stny.rr.com/musicbocs/modes/eigenmode1.html

 

The twenty eigenmodes with the lowest frequencies.

[JasmineTea]

Originally posted by Old_Joe_Clark I have an entire series of modes for both, differing only in the cutaway. I've posted them before and everyone goes Ho Hum. But I'll do it again......stand by.

Well criminies, what's there to say? I remember when you posted those things (btw ) and all I could do was look at them. But I appreciated it.

 

If it was detailed images of specific bracing types like an OM with and without scalloped braces I'd find it a bit more interesting. Or a comparison of two of the same exact model that shows variences here and there. I don't know.

[Old_Joe_Clark]

Originally posted by JasmineTea Well criminies, what's there to say? I remember when you posted those things (btw ) and all I could do was look at them. But I appreciated it. If it was detailed images of specific bracing types like an OM with and without scalloped braces I'd find it a bit more interesting. Or a comparison of two of the same exact model that shows variences here and there. I don't know.

 

 

I wish I knew how to add bracing. I think the software that I have will do it but I don't know how. It's on my long term to-do list...adding bracing.

 

I have made some improvements since I did these runs. I've added the effect of wood grain...different properties in different directions of the wood.

 

But these pics at least show that the tonal difference of a cutaway top and a rounded top is not great. In fact, I'd have to say that the modes are even spread out a bit more, which would minimize dead spots. But, it's only one example comparison and it doesn't account for the different air volume inside the guitar. So I wouldn't want to draw a strong conclusion at this time.

 

I only posted them cause someone was bringing up eigenmodes.

[nylon rock]

OK, so follow up a little bit here.

 

I know A is 440, but what about the other notes. It seems that the cutaway has shifted its frequency of "strong" vibrations relative to the rounded shape.

 

What does this mean? Is it that playing in certain keys for one will have increased volume over the other. I like a guitar that rings well when I am in normal keys like C, D, E, G, A rather than C#, D#, F, G#, A#. Which guitar would I prefer based on this analysis?

 

What would be your conclusions so the the layman can understand what you see?

[Old_Joe_Clark]

 

Originally posted by nylon rock OK, so follow up a little bit here. I know A is 440, but what about the other notes. It seems that the cutaway has shifted its frequency of "strong" vibrations relative to the rounded shape. What does this mean? Is it that playing in certain keys for one will have increased volume over the other. I like a guitar that rings well when I am in normal keys like C, D, E, G, A rather than C#, D#, F, G#, A#. Which guitar would I prefer based on this analysis? What would be your conclusions so the the layman can understand what you see?

 

 

What I learned from my analysis is that the cutaway has minimal effect on the top's tone....just like what appears to be true when you play and listen.

 

So long as you have modes spread out over the frequencies that the strings can create (as well as the harmonics), a string vibration will be picked up and sounded by the top.