Sustain

[Jim Sliff]

I’m also willing to accept that string 10 played on fret 20 played on string 10 will sustain longer than string 3 at fret 20, strictly based on the mass of each string.

Actually, (and I don't have any data on this) it would seem to be the opposite - a wound string would have more counter-vibrating elements working against each other (minute winding friction and more parts - not a single contact point - touching the bridge and nut) plus additional stiffness.

I might do some "kitchen testing" on a wound and plain .020 or .022 and see if there's is noticeable difference just with the wound string.

[John Billings]

Jim, I read somewhere that Jerry Byrd used the same gauge string for the first three strings. Hmmm,,,,,,, Mighta been a good reason for that!

[ed packard]

Jim S...you might enjoy talking to Gene Fields of GFI re dead spots on basses etc. Along with his PSG designs at Fender, he also did a good amount of work on the solid body/neck basses...different shapes and materials. You might look up some of his work via GOOGLE PATENTS.

Bruce...Nice outline. The Constructive/Destructive wave interference is covered in the acoustic impedance and energy loss view of the problem...Impedance is made up of resistance and reactance. The reactance part is the part with the "phase shift" function...in phase is constructive, out of phase is destructive.

The velocity of sound in a material is a function of the materials density and Modulus of elasticity (can be found in a materials properties handbook). Sound travels differently in the body than in the string than in the changer and nut/headstock...so it may return to the transfer point(s) with different phase relationships to the string vibration = constructive or destructive.

Just to complicate things...the non string vibrations are in several modes = along the element (body etc), across the element, Z axis of the element, and several modes of each of these directions. These can be solved via Finite Element Analysis programs (FEA).

From the above, it should be apparent that some of the strings vibrational frequencies will return at different times and amplitudes than others = some of the spectrum more or less constructive than others = tonal change with time after exciting the string(s)...the highs fall off first(look at the charts for 33 PSGs on my PHOTOBUCKET site...It can be found via a Forum search. Some day I will put the FEA results up also.

OK, so the highs fall off first, and the constructive/destructive wave interference changes the tone because it is frequency selective.

The energy source is the picked string. After the picking, energy can only be lost until the string is excited again. It can be lost "selectively" re frequency via the constructive/destructive summations at the interface between string and the other elements.

If NO energy were to be transferred from the string to the other elements then NO frequency selective feedback (positive and negative = constructive and destructive = in phase and out of phase) could occur.

So how much string vibrational energy goes across the boundaries of the elements? Different materials have different sonic (acoustic) impedance's. The vibrational energy from the string can only be transmitted or reflected. How much is a function of the acoustic impedance at the material interfaces. How much is also a matter of the orientation of the materials (angles and force vectors involved). Now we come to the angle of string wrap across the fingers etc. for the force vectors....you don't want to go there!

For most designs, most of the string vibration energy reaches the body, so not much tone/sustain shaping is available via "feedback"...BUT, what is available can only subtract on a frequency selective basis from the initial energy.

Interesting to some, and boring to others.

Edited to add:

John B...JB knew what he liked, and he did not like string noise! He used a very small bar, and beat up on folk that left hand blocked. The same string gauge also meant string top planarity for those strings. JB used a lot os slants...try slants with different bar pressures and hear the sound difference.

[Gary Cosden]

Ed - your posts are always great. With regard to constructive/destructive wave interference is it possible that a given body would focus more on, say odd order harmonics than even order harmonics? Do you think it possible that the hole in a cabinet for tone control(s) might be a factor in this phenomenon?

[John Billings]

"he did not like string noise!"
I do recall reading that Ed. But it also seemed possible to me that he liked the commonality of tone and sustain given by plain strings. I do not use wound third strings on my lapsteels, resos, or bottleneck guitars for that same reason.
In regards to the planarity issue, isn't that solved by simply adjusting the depths of the slots in the nut?

[Rick Collins]

sustain is a verb

sustainment is a noun

[Donny Hinson]

For most designs, most of the string vibration energy reaches the body, so not much tone/sustain shaping is available via "feedback"...BUT, what is available can only subtract on a frequency selective basis from the initial energy.

Hmm...interesting. Ed, the above seems to indicate that any back-feeding of energy actually reduces the sound or signal that might otherwise be available.

[Dave Mudgett]

For most designs, most of the string vibration energy reaches the body, so not much tone/sustain shaping is available via "feedback"...BUT, what is available can only subtract on a frequency selective basis from the initial energy.

Hmm...interesting. Ed, the above seems to indicate that any back-feeding of energy actually reduces the sound or signal that might otherwise be available.

It makes sense that if string vibration energy reaches the body, not much would come back to the strings. There are so many other places it can be dissipated at that point.

As far as how that vibration energy reflected back interacts with the string vibrations - it seems that this would depend on the phase relationship. I have trouble imagining why that would be sufficiently coherent to always guarantee subtractive interference. Seems to me like it would be more random, with some frequencies/strings subtractive, and others additive. I dunno, I guess one would have to measure it. Maybe Ed has.

The "feedback" I was talking about in earlier posts was, as Ed said, acoustic feedback from the amp/speaker. That certainly can add energy to the string or directly couple to the pickup via microphonics. When I'm playing a fairly loud gig and have my amp fairly close, it can have a very noticable effect and cause a significant increase in sustain. I don't generally play so loud to get completely self-sustaining or unstable oscillations, but the note decay time is sometimes lengthened significantly.

[Jim Sliff]

sustain is a verb

sustainment is a noun

Not anymore - and certainly not in this context. Wixtionary now has the word also in a noun category.

Common usage dictates the "verb vs" noun" rule anyway. Even Oxford folds to common use...eventually

"Sustain" in this context is a noun.

[ed packard]

Donny...Good catch...It could have been worded better. Perhaps removing "feedback" and replacing it with the "Reflective/Transmissive" type terminology (the sum of reflected and transmitted must equal one) and leaving "feedback" to refer to the external = from the room etc. energy (Dave's useage).

After passing thru several material interfaces, and rattling around in the body and associated structure any return vibrations will small (compared to that from the initial picking), and to a great degree phase random re the starting string vibrations. Those vibes on the in phase side of the ledger will constructively interfere, those on the out of phase side will subtract. The add will increase sustain, and the subtract will decrease sustain. Either or both will change the spectrum of(harmonics contained in)the string vibrations = tone shaping.

Because we are NOT dealing with a single sinewave, but a complex waveform this phase relationship of the returning energy must be in phase for all or most of the harmonics in the original waveform (string vibration) = highly unlikely, hence the "only subtract" comment was used. Probably the "only" is a bit too much...what happens is a statistical nightmare, but I feel that the net result is a subtraction of energy.

I might go back and modify the subject post later.

Dave...as for measuring it, the closest that I have come is to place the PSG in a box with a speaker, sweep the frequency driving the speaker, and using the FSA on the resulting pickup signal = one step above slapping the body and listening to the output.
One day I would like to do the external excitation frequency sweep to the 33 PSGs that we did measurements on at Jim Palenscar's shop.

JS..right on...common useage prevails. Sustain is not the first, nor will it be the last "verb" to be morphed into a noun, and beyond. My favorite annoyance is the D# and F# strings in E9 being called chromatic.

[Rick Collins]

Sustain is a verb.

Bastard English does not make it a noun.

[John Billings]

Well, "founder" and "flounder" have come to have the same meaning through common usage.

[Dave Mudgett]

Language always evolves to meet new needs. All it takes is a critical mass of people to agree on the terms. No amount of appeal to the past will stop the future.

Ed - I agree that the phase interactions would probably be very complex, to the point of nightmarish. I also have trouble visualizing how one would measure this, since the frequency content of what's coming back off the body depends explicitly on what was input to it via transmission from the strings, changer, etc. Externally exciting the body might be quite different. Maybe I'm wrong, but that's the way it seems to me.

After thinking about it, since we're talking about relative phase between the outgoing and incoming vibrations, one way to measure this would be to find a way to stop the reflections without interfering with the string vibrations, measure the amplitude and phase spectrum that way, and then measure with the reflections. Then one could look at the difference frequency response.

However, it doesn't seem so easy to surgically separate these two responses in situ. To me, it makes more sense to do this with the guitar in various stages of assembly. Even this seems fraught with problems - one need some structure just to suspend the strings at the required tension. Perhaps one could put some kind of absorbing material between the top/changer and the rest of the body/legs and so on, and then measure with and without.

Just some ramblings.

[P Gleespen]

Okay, I went to the library and took out a copy of "The Acoustical Foundations of Music" as had been suggested.

I had some difficulty with it because:

a) I'm incredibly stupid

and

b) the guy that wrote it's stick is WAY further up his butt than the guy that wrote the book we used for this same subject in college ("Musical Acoustics" I think it was called...it's been a while).

Now, first of all, I have to say I DO agree with Jim Sliff's "Basic Laws of Physics" arguments on this subject of sustain.

That being said, I feel compelled to point out that this book doesn't cover the specific questions asked by Dave Mudgett regarding a steel bar on a string imparting energy to that string, so it's really kind of silly to keep pointing to this book and saying it does.

Also,

Sustain is a verb.

Sustain is a noun.

Sustain is a verb.

Hold it you two, Sustain is a desert topping AND a floor wax!

[Dave Mudgett]

For the purposes of any discussion we could have on this particular problem, any laws of physics needed to derive any physical model of such systems can be derived from

E = mc[sup]2[/sup] where E is energy, m = mass, and c = speed of light.

But the devil is in the details, and there are a lot of details involved in figuring out how to analyze any given physical situation and get answers to specific questions. No book covers every physical situation, set of boundary conditions, or question. I believe that, to get answers to the kind of questions I posed, someone would need to build and analyze a detailed physical model, do experiments, or both. I think experiments would be easier and more definitive on "what", but wouldn't necessarily answer "why".

Probably good fodder for future discussions - if we have some models or experiments to talk about. But I have never seen a book or paper that discusses the problem I posed specifically, and I have looked somewhat at least. The relationship between action and reaction are far from intuitive in some physical systems - hard analysis and experiment is the only way I know to deal with that.

In the meanwhile, I think we're gonna have to live with "anecdotal evidence". Which I think often works just fine in musical practice.

Patrick - I seriously doubt the issue is that you are stupid. The problem is that there are a lot of levels to look at these kinds of problems. One can do it very descriptively with minimal formal math, physics, and engineering - I'd guess that's probably what most music programs do. One can be very scientifically rigorous, and build detailed theoretical models and measure things via experiment to corroborate or falsify. Or one can take a middle approach, which is what I think this book does. IMO, it requires at least a basic college level of mathematical and scientific/engineering background. Without that, I imagine this book could be very annoying to read.

[P Gleespen]

Patrick - I seriously doubt the issue is that you are stupid.

We've obviously never met. (rimshot)

Actually, I think of myself as rather smart. I was just making a joke, which I'm hoping you already knew. (I know, I probably should have included a wink or a smile, but I always think those wreck the joke.)

In fact, I was surprised at how much of it I remembered from college. (I'm a college gradjamitt, don'tcha know. ...but it was Berklee, so it doesn't count! )

[Bob Simons]

To me, it's all touch, fresh strings in tune, and my Zumsteel.

Does anyone have an opinion on the Hilton or Goodrich sustain units?

[Bruce Atkinson]

One question that has been rattling around in my head for a while is this:

Does the tension on a string affect the duration of sustain?

Obviously, a "really loose" string won't sustain very well, as it has to be tight enough to not only set up a sine-wave but to continue "waving", so to speak. Tightening it up not only raises the pitch, but at the same time reduces the length of the wave itself, which is the very cause of its pitch.

Now then...add to that the possibility of the two endpoints of a vibrating string being exactly at the length of the wave for a given note...or twice the length, etc. Certainly the sustain when that occurs would be greater in duration than when the note is not an 'exact harmonic' of the length of the string.

Am I talking about a 'natural resonance' here? Sort of like Ella Fitzgerald breaking a glass with her voice? (remember the Memorex commercials?). Logic says there is a natural resonance to not only the string, but every part of the guitar, and, as a whole, the entire guitar itself.

Somehow, I think we're starting to get into some mathematical calculation that could go on and on and on and on coming up with more variables and expressions...

[Dave Mudgett]

Patrick - I was pretty sure it was a joke. But teaching math a lot, I run into a lot of math anxiety. Reassurance is a kneejerk response born from the frustration of many hundreds if not thousands of students over the years.

Bruce - On tension, I expect there is an optimum tension range where sustain is longest. Obviously, if you increase tension enough to push a string past its elastic limit, there will be problems, but much lower tensions generally cause proportionally larger frictional damping and further deviation from the "ideal" string model. Of course, real strings aren't exactly "ideal" anyway. But as the tension goes down, the string stiffness becomes, proportionally, more prominent. An "ideal" string has zero stiffness.

On your second point: the fundamental note sounded - with string tension and string mass/length fixed and the string plucked in the normal way - is determined purely by the "effective" length of string. That "effective" length of the string is, more or less, the distance between where the bar makes contact and where the string first hits the changer. The fundamental vibration mode has that half-wavelength. With an "ideal" string, the modes of oscillation are integer multiples of that fundamental frequency.

The best site I know online is the Professor Steven Errede's course website at the University of Illinois Champaign/Urbana for Physics 498PM - The Physics of Music and Musical Sound. There are tons of lecture notes, theoretical models, and experimental results on various instruments, including standard guitar. No pedal steels, unfortunately - one student did build a lap steel, but I didn't see any real analysis. The website is here:

http://online.physics.uiuc.edu/courses/phys498pom/

In particular - if you look at the Fall, 2000 projects - student Steven Treharne investigated the free-decay transient time constant (what some of you are calling sustain) on the open strings of a 6-string guitar. Lots of amplitude decay graphs to look at for fundamental and second-harmonics for plucked open guitar strings. IMO, anybody who wants to study the effect of various pedal steel parameters on the free-decay transient time constant would be well-served to start with this kind of stuff.

[Bruce Atkinson]

Interesting stuff at the U of I site, Dave.

Unfortunately, much of the physics is far beyond me.

After reading through this thread and its discussion and the thread on 'tone' a couple weeks ago, I'm rapidly coming to the conclusion of "whatever sounds good" is the the 'right' tone and 'right' amount of sustain. Every player can buy/build/play to suit whatever their personal tastes say is 'right'. While every player would like to have to tone and 'sound' of the well-known players, some already gone from this world, one player may sound OK to me, but be 'the BEST' to you, and only mediocre to someone else.

While I would personally like to play at the skill level of someone who has played steel for 30-40 years, with less than 6 months under my belt, I doubt I'll ever sound even half as good as someone currently playing in a band somewhere. But hey, even ignoring my wrong-strings, wrong-pedals, wrong-whatever playing, I'm not trying to please an audience. I only have an audience of one...two if you count my dog that simply leaves the room when I start to play.

This has been a most informative and thoughtful thread on sustain...or continued resonance. Many thanks to all who have participated!

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[Bruce Atkinson]

Interesting stuff at the U of I site, Dave.

Unfortunately, much of the physics is far beyond me.

After reading through this thread and its discussion and the thread on 'tone' a couple weeks ago, I'm rapidly coming to the conclusion of "whatever sounds good" is the the 'right' tone and 'right' amount of sustain. Every player can buy/build/play to suit whatever their personal tastes say is 'right'. While every player would like to have to tone and 'sound' of the well-known players, some already gone from this world, one player may sound OK to me, but be 'the BEST' to you, and only mediocre to someone else.

While I would personally like to play at the skill level of someone who has played steel for 30-40 years, with less than 6 months under my belt, I doubt I'll ever sound even half as good as someone currently playing in a band somewhere. But hey, even ignoring my wrong-strings, wrong-pedals, wrong-whatever playing, I'm not trying to please an audience. I only have an audience of one...two if you count my dog that simply leaves the room when I start to play.

This has been a most informative and thoughtful thread on sustain...or continued resonance. Many thanks to all who have participated!

[Bruce Atkinson]

Interesting stuff at the U of I site, Dave.

Unfortunately, much of the physics is far beyond me.

After reading through this thread and its discussion and the thread on 'tone' a couple weeks ago, I'm rapidly coming to the conclusion of "whatever sounds good" is the the 'right' tone and 'right' amount of sustain. Every player can buy/build/play to suit whatever their personal tastes say is 'right'. While every player would like to have to tone and 'sound' of the well-known players, some already gone from this world, one player may sound OK to me, but be 'the BEST' to you, and only mediocre to someone else.

While I would personally like to play at the skill level of someone who has played steel for 30-40 years, with less than 6 months under my belt, I doubt I'll ever sound even half as good as someone currently playing in a band somewhere. But hey, even ignoring my wrong-strings, wrong-pedals, wrong-whatever playing, I'm not trying to please an audience. I only have an audience of one...two if you count my dog that simply leaves the room when I start to play.

This has been a most informative and thoughtful thread on sustain...or continued resonance. Many thanks to all who have participated!

[Clete Ritta]

Ed,
Very informative posts! Thanks.
I studied acoustics, circuit logic and audio engineering back in the early 80s. Ive forgotten much of the scientific terminology since then (Im a working musician), but youve refreshed much of that very concisely.

...Just to complicate things...the non string vibrations are in several modes = along the element (body etc), across the element, Z axis of the element, and several modes of each of these directions. These can be solved via Finite Element Analysis programs (FEA).

When I read this, I remembered the word "node". It reminded me of standing waves, etc. I thought of nodes as those tonal dead spots that Jim Sliff experinced on a particular P bass around B (60hz?), or as an instruments resonant pitch perhaps. Is a "node" a dead spot? The word used in quote (i added italics) above was "mode". Is this the same as a node in this context?

(hmmm, just looked up Normal mode, but it's still a little fuzzy as it concerns PSG here. I barely passed college physics!

[John Billings]

Naw man! This is a node;

"any of various fungal diseases of trees characterized by the formation of an excrescence, knob, or gnarl."

[ed packard]

Clete...in vibrational analysis, mode tends to mean in this way, or in that way, as in horizontal or vertical etc.

Node in string vibration generally means a zero point as in at the nut or bridge. Some texts have used nodes and nulls wherein the null is the zero, and the node is what could be called the loop.

John B...a very knotty problem indeed! many wood bodied PSGs would therefore have the possibility of many nodes = Gnarly.

Just to have some experimental fun with the subject, clamp the contact mike that comes with the Peterson tuner on the body or ? of your PSG, pluck a string and see the fundamental on the tuner. Notice how long it lasts....now repeat this on all strings and compare. Move the mike and repeat.

If you have the software, do this but feed the FSA and see the spectrum of your "losses".