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Posted: 22 Feb 2007 11:35 am
by Dave Mudgett
Donny - I agree that what constitutes "good tone" is subjective. But the original post asked "What component of the guitar contributes
the most to tone?" and "Generally speaking, is there one component that
makes the biggest difference? If there was one thing to change to affect the inherent tone of guitar, what would it be?" {Italics mine} The way I interpret it, the question goes to which design elements have the largest impact on tone, not the quality of the tones themselves.
It seems to me that those things should be quantifiable in some sense, and possible to get factual evidence for, and not have to rely on pure opinion. For example, one can, in principle, play the guitar and quantitatively measure the amount and character of change to the audio frequency spectrum content over the frequency range before and after various design changes are made, and then assess which design changes produce the largest spectral changes. Or one could use human listening tests to assess those same changes. If one is interested in "scientifically objective" evidence, I'd do the former. But if one is interested in how those changes are perceived by human listeners, I'd do the latter.
For instance, if the guitar doesn't produce the high frequencies desired, the pickup won't "sense" them, therefore there will be no output voltage, at those frequencies, from the pickup.
I can't see this. In vibrational frequency responses of excited distributed-mass systems like this, I have always observed
some frequency content at high frequencies - it's a matter of relative levels. As long as there is some high frequency content, it should be possible to build a filter to amplify that to make it audible. I admit, I haven't done these kind of measurements on pedal steels, but certainly have done this kind of thing with guitars, a long time ago. I just can't imagine why it would be conceptually different, but maybe I'm missing something.
Ed - I just saw your post. Of course, I agree that if it ain't there at all, it can't be amplified. But I have generally found that higher order modes of excitation are there, but often low in amplitude. For example, looking at your FSAs from the last tone thread -
http://bb.steelguitarforum.com/viewtopic.php?t=103050 - the difference between peak and high-frequency cutoff was on the order of 30-40 dB - certainly down at high frequencies, but not completely inaudible. I agree there are practical problems with high gains at high frequencies.
Posted: 22 Feb 2007 11:50 am
by ed packard
Dave M: To the extent that it is not there, it can't be "tweaked"...I stated the extreme to make the point.
-40 db (volts) as I recall is 1/100 of the reference...that by comparison is at least close to inaudible/descernable.
The noise floor of the test setup was about -80db. Boosting signals between -40 db and -80 db would have S/N issues to deal with.
(Added) The instrumentation is flat (when calibrated as it was) from 10Hz to 20kHz. Us poor humans hear up to 10KHz or so, even at my advanced age. The FSA charts indicate that there is little signal to deal with at 6Khz and higher = well within the abused hearing range.
Posted: 22 Feb 2007 1:27 pm
by Bob Carlucci
great discussion guys.. whoa.. I'll say this right now..This is the LAST time I go toe to toe with Ed... He's too damn smart for me to match wits with
!!! I did misunderstand him a bit but Mike Wheeler cleared it up for me..
I think most of us agree on a few basics..
First,Not all steels resonate equally... As with solid electrics, a resonant piece of wood should sound better [and longer] than a body with the resonance of a wet newspaper.
Second, you need a GOOD signal to "process".. A junk pickup will not give the desired input into the signal chain..
Many other items are subjective.. Does a twangy old ZB with a thin bright twang sound "better" than a modern steel with a big huge sound???. Well to me it does, but many guys here would say I'm a nut...
In any case, I have to keep one basic in mind, because I disregard it, and then complain about my bad tone... If I want my steel to sound sweet and ring long, I need to swap strings more than once a year...

bob
Posted: 22 Feb 2007 1:47 pm
by ed packard
Aw, come on Bob C.,it is all fun. Most apparent differences are usually a matter of terminology/semantics, perspective, or differences in background.
Posted: 22 Feb 2007 2:08 pm
by Donny Hinson
Mike Wheeler wrote:What Ed said was true. For instance, if the guitar doesn't produce the high frequencies desired, the pickup won't "sense" them, therefore there will be no output voltage, at those frequencies, from the pickup. "Tweaking the highs" will gain nothing, unless some kind of synth is added to artificially add them to the original signal.
Okay, let's look at that statement objectively. Ed Packard said...
The resonances of the “components” to which the strings are attached can only subtract from the energy of the excited string(s)…presented as a “fact”.
It is this subtraction that is different for different constructions and materials, therefore different “tones” for different instruments even with the same pickup conditions…presented as “fact”.
Okay, school me here...is it the strings, or the body of the guitar that produces the frequencies?
If I'm not mistaken, Ed is saying (above) that all the body and other components can do is "subtract selectively" from what the string itself creates. They do this by vibrating sympathetically, and this vibrating is actually taking away ("altering", if you choose) what the string itself is producing.
Is that about right?
Posted: 22 Feb 2007 3:14 pm
by David Mason
Can I have a steel made out of
THIS?
Atomic-Booger Guitar
Who CARES what it
sounds like - Whoo-Hoo! I glow in the
dark, Baby!
Posted: 22 Feb 2007 3:29 pm
by Bob Carlucci
"Aw, come on Bob C.,it is all fun. Most apparent differences are usually a matter of terminology/semantics, perspective, or differences in background."..
amen to that ED!!!.. If it involves pedal steel ,its all good!!.. but I still say you are too smart to argue with!!

... thanks for your very intelligent replies and posts... I always learn something from your writings!!! bob
Posted: 22 Feb 2007 3:36 pm
by Mike Wheeler
Donny, though Ed can probably explain it better than I ever could, I'll take a stab at it....
When the strings are excited, the bridge and nut will transmit these vibrations to the other components that make up the guitar...the body, frame, keyhead, legs, etc. All these various components can act as absorptive filters at certain frequencies (similar to a comb filter), thus diminishing the string's spectral content at those frequencies, while not absorbing at others. The pickup then translates the resulting vibrations into an electrical signal that represents this process. This signal will represent the timbre, or tonal character, of that guitar.
How's that?...my brain hurts!
Posted: 22 Feb 2007 3:49 pm
by Bobbe Seymour
Mike Wheeler, now your are getting close, but that's passive timbre, the backfeeding of the string is ACTIVE timbre!
Great go gettum!
Bobbe
Posted: 22 Feb 2007 4:03 pm
by Mike Wheeler
Ha, ha!! Bobbe, I love you, man. But, darn it, you're making me think some more....how much do you think this pea-brain of mine can handle?!?!?!
Excuse me, gotta go cogitate for a bit.

Posted: 22 Feb 2007 5:02 pm
by Martin Vigesaa
It may be simpler to point out what doesn't affect the tone, or what affect the tone the least. Like if you play with the lights on or off.. But then the heat from the bulb could be a factor too.
Or what you ate for lunch.. The 2 pounds you gained will transfer to the floor causing the vibrations of the steel throught it's legs to be absorbed or resonate differently than before.
I would say the most noticable changes are the materials where the strings contact (bridge and nut), and the material the body is made of. Replace your rollers with popsicle stick and take a listen. Strings and pickups make a difference and are fairly easy to test these yourself.
Pickups will change the sound but some of the guitars character will always remain.
Posted: 22 Feb 2007 5:08 pm
by ed packard
Good stuff chaps…I like the “energy” explanation for the “happenings”.
Any flaws, additions, alternatives are solicited.
To put the whole thing in terms of “energy”:
1. When you pick (excite) the string you impart energy to it.
2. Assuming no feedback from sound in the room, there will be no other source of energy imparted to it.
3. The “energy” in the string is used up performing “work”.
4. The “work” performed is:
A. Vibrating the string.
B. Overcoming the stiffness of the string.
C. Vibrating the mechanics at the ends of the string, and the bar.
D. Vibrating the body.
E. Overcoming the magnetic pull on the string.
F. Pushing the air surrounding the string.
5. A thru E have frequency dependent properties.
6. They each have several/many resonances (preferred frequencies at which to vibrate = “modes” of vibration).
7. Each interface has a property called “sonic impedance”.
8. This “sonic impedance” will be different for each frequency component found at the interface.
9. The spectral (frequency related) sonic impedances are different for different materials, for different shapes, and for different contact forces.
10. It is the frequency selective loss of “energy” that causes the change in harmonic content vs. time.
11. The lower the sonic impedances at the various interfaces, the greater the energy loss at that frequency at that interface.
12. When all energy is “drained” from the system, the string stops vibrating.
13. If there is enough external feedback, the string will vibrate longer.
14. Vibration of a “not so smooth“ bar will cause apparent sustain because of frictional excitement of the string…but also give increased string noise.
Danged formatting does not transfer from Word to the Forum!
Posted: 22 Feb 2007 6:12 pm
by Eric West
Ed. Since it was mentioned, and I think most of us can agree (to quote somebody) that new strings have a remarkably more distinct, and brilliant tone, have you done any analyses of the differences between them and older strings?
Is it simply more treble, or is there something else at work in them?
EJL
Posted: 22 Feb 2007 7:02 pm
by Mike Baldwin

I just tried play'in my Dekley without any strings, it did'nt have any tone at all !! I believe strings are very important
Posted: 22 Feb 2007 7:26 pm
by Dave Mudgett
Every time I've seen a spectral analysis of a vibrating distributed, flexible body, the higher modes had significantly lower amplitude than the lower, midrange frequencies. I think that, in general, higher modes of oscillation vibrate at lower amplitudes in mechanical systems like this. So my point is that to bring the high frequencies of a vibrating body that is "relatively dead" at high frequencies to the level of one that is "very live" is nothing like 30 or 40 dB. So I don't think it's totally crazy to think that one can equalize different guitars in the high frequency range, as many like Bob C. and Donny H. have suggested. I already agreed that real high gains at high frequencies have signal-to-noise issues, but I don't necessarily think that's an issue here.
If I'm not mistaken, Ed is saying (above) that all the body and other components can do is "subtract selectively" from what the string itself creates.
The way I see it, there's an interchange of energy between the body and the string. The body can, in principle, selectively take energy from the string, but the body can also supply energy back to the string, and so on.
Man, this stuff is so complex. I have a close friend and colleague that teaches solid structure mechanics at Rutgers, and we've talked about his kind of thing many times relative to my interest, which is the control of systems, including flexible mechanical structures. One important point about this is that this is a distributed mechanical system and has an infinite number of degrees of freedom and intensely complex possible behaviors. Any little bloody thing can affect the behavior, and the level of diversity in responses is unbelievable. But even with that micro level of diversity, I'm always amazed at how similar guitars (my experience here is with 6-stringers) of similar general design may measure a bit differently, but still sound to human ears as being very similar.
Of course, another issue mentioned is the way the strings are excited. This is critical, and different methods of excitation may produce very different responses. Personally, I think it's very difficult, if not impossible, to control
all the variables in such a system - and yet, I am somehow amazed at the ability of a real skilled player to manage to control it enough to make it sound like "it's in the hands". This does not deny inherent nominal tonal differences between instruments, but to be amazed at how some people can shape the forced response to their desires.
And all of this without every mentioning the feedback between the amp and the guitar - think Jimi Hendrix. One thing I agree with Kevin on is that a bit of microphonicity in the pickups can be a good thing, as long as it doesn't start howling like a banshee.

Posted: 22 Feb 2007 8:15 pm
by David Doggett
Ed and Bobbe are now talking about something I am puzzled about - the effect of body resonance on a solid-body electric guitar or steel guitar. We also discussed this a couple of years ago. With an acoustic instrument, of course the resonance properties of the body top are very critical to the sound. The strings themselves have long sustain, rich overtones, and very little volume. They don't move much air. It is the vibrations imparted from the stings to the top that move air and create most of the sound we hear. In general, the the lighter and more flexible the the top, the more volume we hear, and the less sustain. That's a banjo. It creates a very loud pluck, with almost no sustain. Somewhere in between are resonator guitars. The thin metal resonator gives a lot of volume, with some sustain. A standard wood top acoustic guitar has less volume, and more sustain. In this continuum, you generally swap off between volume and sustain. By draining off vibrational energy from the string to the top, you create volume at the expense of sustain. In order to capture the tone of the resonator or top, acoustic pickups are attached to the top or saddle.
Now a magnetic pickup is a completely different animal. These pickups can be microphonic and pick up some body vibrations. Most people consider that a bad thing, but in previous discussions some people actually liked the tone they get with a certain amount of microphonics. But aside from that, a magnetic pickup captures only the vibrations of the string, not the body, top or resonator. In this situation, the body subtracts vibrational energy from the strings. For this spectrum, at one end we have a big box archtop jazz guitar, which has a very mellow sound without a lot of sustain. The sound is mellow because the high overtones are the fastest to die out and the quickest to drain off into the body. This leaves the mid and low overtones and the fundamental in the string vibrations to be captured by the pickup. At the other extreme is a solid plank of a body, like on a lap steel. The thick hard body absorbs very little string energy, and so the strings are mostly left with their natural high overtones and long sustain to be captured by the pickup. Any loss in volume is not very relevant, because we just crank up the amplifier - that's sort of the whole point of a magnetic pickup. So the volume/sustain swap off we are familiar with in acoustic instruments, for all practical purposes doesn't really apply with magnetic pickups. We can use a hollow body, and subtract off the high overtones, or a solid body, and keep the high overtones, and can use amplification to keep the volume constant.
In modern electric steel guitars, we are only talking about solid bodies. So let's think about that. Do we want any resonance at all in the body? Imagine if we had a body so hard and rigid it subtracted off essentially no vibrational energy - say a block of diamond with carved bridge and nut. Then the pickup would capture all the overtones, and the sound would be very bright, with long sustain. At the other end of the spectrum would be a mushy body that absorbed most of the vibrational energy of the string very quickly - say a body made of something soft, like wet clay. Loose attachment of the bridge and nut would also work like that. Somewhere in between those extremes is the typical 3/4" piece of tone wood, typically rock maple. I think a lot of people mistakenly carry over the above thinking about acoustic top resonance, and expect the steel guitar body resonance to somehow "create" or at least translate the string energy into volume, sustain, and tone. But that kind of resonance in a solid-body moves very little air, and only creates the sound you hear with the guitar unplugged. Yes, in a quiet room, you can put your ear to an unplugged tele, strat or steel guitar, and hear a little acoustic sound from the body. But that is totally swamped out when the guitar is plugged in and amplified. What you hear is not the air movement of an acoustic instrument, but instead you hear what cannot really be heard on an acoustic instrument - the actual vibrations of the strings alone, captured and amplified by the magnetic pickup and amp.
So I think we all agree that on electric guitars, body resonance mostly affects tone by what it subtracts from string vibrations heard by the pickup. So body resonance has a very different role than in acoustic instruments. But maybe it is not that simple. Bobbe and some others claim that the body resonance can "feedback" into the strings and accentuate certain overtones. If that occurs, would it be good or bad? By analogy, in a bass speaker cabinet, the resonance of the cabinet must be controlled very precisely to smoothly boost the shoulder where the bass frequencies begin to fall off, without creating unwanted narrow resonance around a particular frequency that causes particular notes to "boom." Can the resonance of a solid-body electric guitar be controlled like that to benefit tone? I'm not sure.
Obviously instrument makers manipulate solid-body shape and material to get different tones in solid-body guitars. They use mahogany, maple, swamp ash, grain patterns, solid wood, laminated wood, etc. Are they only working with subtractive manipulations, or are they also manipulating active supportive resonance of certain frequencies? Maybe it doesn't matter, because it is only the end results that we care about, and we don't care how they get the results. But to me this is an intregueing question, and I'd like to hear any thoughts. Maybe right now we only have thought experiments, but it sure would be nice to hear about any real experimental evidence. Ed? Bobbe? Anyone?
Edited: Dave M. posted while I was writing. We have the same questions, but it seems like we have both stated the question without any answers.
Continuing with the discussion
Posted: 23 Feb 2007 5:21 am
by Donny Hinson
ed packard wrote:
1. When you pick (excite) the string you impart energy to it.
2. Assuming no feedback from sound in the room, there will be no other source of energy imparted to it.
Does this mean the body and part resonances (sonic impedances) can actually
add nothing to the original waveform? (Note: I mean "add" in the strictest and most scientific sense of the word.)
Posted: 23 Feb 2007 6:04 am
by Mike Wheeler
Mike B. Some have said I'd sound MUCH better without strings!
So, in that case "tone is in the head"! But then, my timbre would come from Home Depot? (just wondering)

Posted: 23 Feb 2007 8:33 am
by ed packard
Dr West..Sir!...Eric…I have looked at the difference between an “old” string and a new string (just the G#) on the BEAST. The “old” string was only about a year old, and had not “P Franklin mileage” on it by a long shot. The type of presentation that I looked at is below. I should have taken more data but that look was just in passing.
In general, the “treble” falls off more quickly on an old string, and the rolloff point moves to the left faster…I.E. less sustain of the highs. The FSA can split a db if needed. The reason (my excuse) for not looking more closely at defining string life/sound is that folk can change them if they don’t like the sound that they get…while the instrument is another story. The shot below shows the harmonics present in my one year old G# on the 30” scaled BEAST, at some second or so after excitation. Excitation was a thumb pick at the 12th fret. The string was open. The object of the shot was to provide evidence of the harmonic content of a single open string
Dave M==> "Every time I've seen a spectral analysis of a vibrating distributed, flexible body, the higher modes had significantly lower amplitude than the lower, midrange frequencies."
In the structures that I have looked at (PSG bodies included while designing the BEAST) using ANSOFT software modeling, I have found your observation to be true. There may well be exceptions, but they are not common to my experience.
RE the string(s): their vibration is sensed/detected by the mag pickup according to the “rate of change” of the flux = higher frequencies of vibration provide a higher rate of change for the same amplitude of vibration than the lower frequencies, hence more pickup output for a given amount of displacement. This occurs until the pickups resolution (sensing area) cannot “see” the range of vibration above it….for a number of possible reasons.
DD==>I agree with the premise that the acoustic instruments use the “soundboard” as the major source of their tone. I concur that such is not the case with electrified 2X4s (including PSGs) using magnetic pickups. The body, and associated mechanics DO have a contribution to the string vibration…MOSTLY a subtractive one. An interesting system to consider is the arch top with a mag pickup.
DONNY H==>One can induce an “ADD” into the PSG string vibration via the body/mechanics from external sources such as band stand noise, amplifier output etc. The amount of this will depend upon the sonic impedances connecting the body to the strings. If the impedances are low, there will be more string vibration caused than if the impedances are high.
As a system, the PSG (sans amp etc.) has “feedback loops”. Feedback loops come in two basic flavors = positive and negative. Positive is an “in phase” feedback, and negative is an “out of phase” feedback. Positive feedback is what gives the microphone squeals when the mic/PA or similar (J HENDRIX trix) has a gain of greater than one at the frequency(s) of squeal = oscillation.
My list re energy stops at the pickup output. The materials in the body/mechanism ARE part of a feedback loop built into the PSG, therefore they effect the string vibration. In one sense, they may be found to contribute positive feedback to the strings at some frequencies…this would ADD (enhance) to the strings vibrations at those particular frequencies. The gain of the PSG system to my knowledge is always less than one, hence no oscillation squeals, and the net is an energy LOSS…more at some frequencies than at others.
What determines the phase relationship between the string vibration and the body/mechanism feedback? The velocity of sound traveling through the mechanism/body materials. Different materials = different velocities = different phase relationships re feedback = different string vibrations = different pickup outputs. How big is the difference? Depends upon the sonic impedances coupling the strings to the mechanism and body….low impedances = body/mechanism feedback effect is greater, high impedances = body/mechanism feedback is less.
Short question, long answer.
Mikes==>My PSG sounds best with the strings on, but with someone else playing it!
Posted: 23 Feb 2007 10:19 am
by Fred Shannon
Continuing with thoughts generated by Ed's last post, and the discussions I've had with him relative to frequency, time, wavelength, etc., one cannot discard the fact that the wavelength of the different frequencies change with each note. However, because wavelength is directly related with time it also has to be related to distance.
For instance the wavelength of the 3rd string G# pulled up a half to A is one of the highest open frequencies on the PSG. That A is the fundamental frequency of the A at 440 hz. The wavelength for the 440 freq is 30.9 inches or approx 0.78 lambda (wavelengths) in free air. The lowest note, the B on the standard E9 tuning has a frequency of 123.4 hz or it's wavelength occupies 109.8 inches or 0.22 lambda (wavelength) in free air.
In either case, if one used say a 24 inch neck between the nut and the changer, neither of the frequencies produce a wavelength for the wave to be completely perfect to prevent a reflected wave on the string.
There will be reflections of the incident wave that will produce standing waves on the string which will cause deterioation of the basic frequency vibration, thusly possibly less sustain than a wavelength that is exactly 24 inches in length.
A decent website to show this can be located at:
http://www.physicsclassroom.com/Class/w ... estoc.html
Clik on the Animation at the bottom of the pages.
I'm certain, as Ed states, the material of the strings, composition of the guitar body, and certainly the neck length can cause the reflected waveform to be more or less in amplitude, and perhaps thats some of the reasons that makes one axe more responsive than others.
But in any case the sound if classified good or bad is in the ears of the cat that's listening to it. Period.
Edited to correct errors. You bet I make 'em too. Sorry
Phred
Posted: 23 Feb 2007 11:01 am
by Dave Mudgett
One thing that Phred's post on wavelength and scale-length reminds me I forgot to mention is the effect of the steel bar on all of this, which changes all of these parameters significantly. As I and others have mentioned several times in some of these "tone threads" - in most playing, this is a "forced" dynamical system, not a freely decaying one - especially considering the use of the bar and its sliding and vibrato movements.
Of course, I suppose that one can consider the bar external to the "PSG system", but I consider it part of it, similar to the strings. Most of what I consider to be "tone" of, especially, a PSG is how it reacts in the barred positions, not the open positions. I spend a low fraction of the time playing open strings, and my sense is that this is true for most other PSG players.
I guess, as a player, I am interested primarily in answers that relate physical tonal performance of a PSG to practical playing considerations, rather than theoretical issues applied to a lightly strummed open-string guitar, even though they are also interesting to me as an Electrical Engineer/Scientist with strong interests in vibrations and systems.
Posted: 23 Feb 2007 11:19 am
by ed packard
PHRED...that is a phine repherence that you phound phor us...thanks.
Dave M...re open string strum as an index to the instruments tonal posibilities...it is a basic starting point upon which the same approach/instrumentation/measurment method may be understood. The method may then be applied to analyze any other more complex situations that tickle ones fancy...all the way through Sound Power level in the room....You knew that.
To any and all...here is a little experiment that you can easily perform that addresses the bar's effect, hence indirectly the mechanics at the end of the string:
If you have a drill bit set, take a small one and use the shank as a bar. note the tonal result. Repeat with a larger bit. Repeat again with a still larger bit. You should have noticed a tonal progression re bit size = how big a steel bar is big enough for you?
Now take the small bit again, but put your steel bar on top of it...what happens? What does this tell you?
If you have copper, or brass rods, or ? rods/tubes repeat the experiment and compare the results. What does this tell you about the mechanics upon which the strings are terminated?
Posted: 23 Feb 2007 12:09 pm
by David Doggett
Fred, I'm puzzled by a couple of things you said. I'm looking at Winnie Winston's book on p. 17 where he shows the relation of E9 strings to a piano keyboard. He has the 3rd string pulling to A above middle C, which I thought would be 440, not 880. I confess to always being confused about this, which is why I looked it up in his book. Is his book wrong? Or am I wrong, and 440 is A below middle C?
The other thing I am a little confused about is your equating wavelength to string length in discussing reflective overtones. It is not clear to me that wave length and string length have that kind of simple relationship. Wavelength refers to the length of the wave in air, not the string length. A string of a fixed length can produce many wavelengths, depending on string mass and tension. So it seems to me that scale length does not have the simple effect on reflective overtones that you seem to describe.
Ed, without making me go down in the basement and dig out some drill bits, what is your point? Maybe I'm just too lazy, but often I wish you would skip over the raw data and just tell us in plain language what your experiments show.

Posted: 23 Feb 2007 12:46 pm
by Fred Shannon
David, you're absolutely right on the notes vs. frequencies. I was using some notes I took back in 2005. I'll edit the post to reflect the proper freqs and distances.
I used free air wavelength because I have no way to obtain the string mass, density, or material. In any case the ratios would be the same. The reflected wave will still be there dependent on the distance from the nut to the changer, and the frequencies involved. Do you agree?
Thanks for calling this to my attention MY BAD.
BTW I got to chasing this after a conversatiion with Bobbe on overtones back in 2004. The method by which the changer is attached to the body, the body (material, length, type of string connection etc.) are just a couple of things that have a definite effect on the enhancement (more or less) of the feedback. Just my opinion.
Phred
Posted: 23 Feb 2007 1:24 pm
by David Doggett
Phred, thanks for clearing that up about a above middle C being 440.
Now...umm...about scale length and reflectance, I guess I'm not clear on your meaning for the term "reflective." I thought you might be talking about nodes being caused in the string vibration pattern that break up the fundamental vibration of the whole string length, and what effect scale length has on that. The fundamental is always a vibration of the whole string, unbroken by nodes - the only nodes are at the string ends. So regardless of the frequency and wavelength in air, the the length of the fundamental wave on the string is always the length of the string. All the different fundamental pitch frequencies on the 10-14 strings of a pedal steel guitar have exactly the same length on the strings, even though they each have a different frequency and wavelength in air. So in that sense, the scale length is not relevant.
But you may be talking about the reflectance of body resonance feeding back through the changer to the strings and reinforcing certain frequencies of overtones. I'm not sure what scale length has to do with that either.
So I can't really say I think you have said anything wrong about that, rather I'm not sure what it is you are saying regarding scale length.
