Sustain ?

[Bertram Henze]

I guess what I am saying is that we seem to be forcing physics to fit our idea...

Yes, that's an old popular approach

[fscotte]

this is one of the finest discussions of mandolin mechanics I have read in many years of reading this forum. Thanks to all.

I have a question- Can Q, mass, and stiffness be independently measured on existing instruments?

Don't think so. If you find a way, please let me know.

[CarlM]

Can Q, mass, and stiffness be independently measured on existing instruments?
Don't think so. If you find a way, please let me know.

Mass and stiffness should be able to be measured, Q probably has to be derived. They cannot be controlled independently but should be measurable.

Make the top too stiff and light with carbon fibre lattice bracing and the mandolin will sound very loud and obnoxious.

Canadian luthier Mario Proulx told a friend of mine that he could make a guitar as loud as a banjo but it would sound like a banjo.

Regarding consistency of Loar graduations, we all need to realize that in the 1920s measuring was not as sophisticated as now. Micrometers and dial indicators were expensive and less common even in the machine shops. Even metal working shops used techniques referred to as "file and fit" to build tooling and equipment. Tooling up for WWII brought the big change where shops became more rigorous working to dimension and machine tools and measuring tools improved by a quantum leap. I would be surprised if 1920s Gibson used the types of dial gauges even home builders use today. They probably used calipers and rulers.

What evidence is there to suggest that a smoothly transitioned graduation is any better than one that is rough carved? The plate will move based on its overall mass and stiffness. It does not seem to matter if it is a bit thicker here or a bit thinner there. Any extra thickness simply adds to the stiffness and vice versa.

There are a couple of conceptual models that suggest to me that smoother transitions should be better. One is from a load bearing structural perspective. Design of arches and domes is well established. I have done a fair amount of computerized stress analysis models on hollow containers where we would incorporated arches or domes to add stiffness. Those abrupt changes always create stress concentrations and points for failure. Things like ribs (like the tone bar braces) can add a lot of stiffness while keeping mass down but there is a hinge and stress concentration at the transition. It is a tradeoff whether the added mass or stress concentration causes a greater problem. The vibration loads and unloads the plates like a series of static loads. The same modes that define acoustic vibration also define buckling and collapse. This has been well studied since the 1940s and 1950s and is far from new science.

The other model that may apply is looking at a recurved archery bow. The shape of the bow is like a cross section through the plates. The motion of the bow unrolls the recurve and the rest of the bow as it is drawn and released. The video below shows the movement of the limbs and vibration on release. If a bow is built with irregularities, flat spots or hinges in the curve it will break at those points. Adrian Minarovic may have some further insight on this as he has built bows.

These views may give some further insight on the motion of the plates.

[Phil Goodson]

There has been lots of discussion about "sustain" and what determines it. My concept of 'sustain' is something like, "it makes noise for a long time" after energy is applied (string is picked).

But if you were trying to learn how to change the sustain of any instrument, how would you measure that, so that you could objectively compare two instruments.
Is there a definition like (decibels at time 1 minus decibels at time 2) divided by (time 2 minus time 1) or some such way to express what is being talked about? Or is this just too mystic to look at scientifically?

[fscotte]

Mass and stiffness should be able to be measured, Q probably has to be derived. They cannot be controlled independently but should be measurable.


Canadian luthier Mario Proulx told a friend of mine that he could make a guitar as loud as a banjo but it would sound like a banjo.

Regarding consistency of Loar graduations, we all need to realize that in the 1920s measuring was not as sophisticated as now. Micrometers and dial indicators were expensive and less common even in the machine shops. Even metal working shops used techniques referred to as "file and fit" to build tooling and equipment. Tooling up for WWII brought the big change where shops became more rigorous working to dimension and machine tools and measuring tools improved by a quantum leap. I would be surprised if 1920s Gibson used the types of dial gauges even home builders use today. They probably used calipers and rulers.



There are a couple of conceptual models that suggest to me that smoother transitions should be better. One is from a load bearing structural perspective. Design of arches and domes is well established. I have done a fair amount of computerized stress analysis models on hollow containers where we would incorporated arches or domes to add stiffness. Those abrupt changes always create stress concentrations and points for failure. Things like ribs (like the tone bar braces) can add a lot of stiffness while keeping mass down but there is a hinge and stress concentration at the transition. It is a tradeoff whether the added mass or stress concentration causes a greater problem. The vibration loads and unloads the plates like a series of static loads. The same modes that define acoustic vibration also define buckling and collapse. This has been well studied since the 1940s and 1950s and is far from new science.

The other model that may apply is looking at a recurved archery bow. The shape of the bow is like a cross section through the plates. The motion of the bow unrolls the recurve and the rest of the bow as it is drawn and released. The video below shows the movement of the limbs and vibration on release. If a bow is built with irregularities, flat spots or hinges in the curve it will break at those points. Adrian Minarovic may have some further insight on this as he has built bows.

These views may give some further insight on the motion of the plates.

You're definitely talking above my head and I hate to wade too deeply into the science of arches cause then I'll sound a little too dumb for my own good. But I understand the efficiency of an arch in construction, and how weight distribution or stress points can cause issues in its strength and efficiency, but I don't think this is quite the same as in a mandolin plate, where we are talking more about tonal issues and not necessarily strength alone.

Some mando plates are quite thick near the recurve and hardly thicker near the center. And they sound as tonally optimal as any other perfectly contoured mando. That's something I'd like to know why and why and why. Is graduations even needed?

I made reference to the recurve in a bow and a mando plates shape a few long threads ago and was quickly admonished by the smarter heads here.

[fatt-dad]

I think it's time for my favorite lyric, "And all the science, I don't understand. It's just my job 5 days a week!"

Not to take away from builders, that is. . .

Some systems are quite complicated, eh?

f-d

[CarlM]

Some mando plates are quite thick near the recurve and hardly thicker near the center. And they sound as tonally optimal as any other perfectly contoured mando. That's something I'd like to know why and why and why. Is graduations even needed?

I made reference to the recurve in a bow and a mando plates shape a few long threads ago and was quickly admonished by the smarter heads here.

I suspect that you understand as well as anyone.

Part of this issue is defining what a good sound is. Or even getting agreement on it. We talk about "modes" but which modes are stronger, by how much and at what frequencies do they occur? None of that is known to describe what a "good" tone is in scientific terms. The mode shapes are consistent but they will occur at different frequencies, be more or less well defined or spread out and respond differently to driving frequencies (the strings). Some of this is pictured nicely in the Chladni patterns on Peter Coombe's site.

Of course the structural strength aspects are necessary to prevent collapse.

Looking at it in terms of efficiency, the most efficient transmitters are probably the carbon fiber plates that were discussed and those "efficient" systems sound harsh. So maybe the highest efficiency is not completely desirable.

I am curious why the recurve bow analogy is not a good one. I think it could give some insights. I have had some of the "smarter" heads here get on me also in cases where they said things that I know are wrong and they got fairly aggressive about it. At that point I walked away from the discussions. In the structural modeling world there is a saying "All models are wrong. Some give useful information."

[sblock]

Philpool,

Well, your definition of "sustain" as "makes noise for a long time" is as good as any! In fact, that idea can be turned into a "physics" definition without too much trouble, as follows:

Roughly speaking, the acoustic power (sound level) emitted by an instrument when an open string is plucked decays nearly exponentially with time. The characteristic time of this sonic decay is a fairly good measure of the sustain. The so-called "time constant" of the decay is taken to be the time for the signal to decay down to (1/e) = 37% of its initial value. You can also use alternative measures of decay, like the "half-life" (i.e., the time to decay to half the initial value -- this measure is used for radioactivity), or the time taken to fall by 10 dB (decibels), etc., but these are very simply related to the time constant by a multiplicative factor, so it really doesn't matter which one of these equivalent ways you select.

One issue arises because some notes, which are often near resonances, can decay in funny ways, first falling and then rising a bit, as the energy sloshes back and forth between different portions of the resonating instrument before it's either radiated as sound or lost to damping. However, the envelope of the curve for the power emitted still tends to fall off more-or-less exponentially, and you can still use that to estimate the time constant fairly well.

But a more serious issue is that different notes ring out for different times! Bass notes often last longer (but not always). Open strings tend to last longer than fretted ones, and so on. We've all experienced that, I think. So how do you characterize the "sustain" of the instrument using a single numerical value (one number)? Do you just average all the notes? All open strings? Do you agree to take the G-string decay time as the standard, or perhaps the E-string?

Anyway, there is unfortunately no general agreement on a numerical definition of sustain for stringed instruments. But that doesn't mean that one could not provide a given, working definition, and then make some comparisons on that basis.

Sonic decay spectra are NOT hard to measure these days, and nearly anyone with an Android phone or iPhone can do it these days with an app. Or use a computer with a microphone and, say, a program like Audacity or something. You can also measure the initial loudness, too, in decibels, but that is harder because it requires calibration to a formal standard, and not just measuring relative sound levels as they decay away.

It might be very interesting to collect and compare data on multiple makers' mandolins for (1) loudness and (2) sustain under a set of well-defined conditions (e.g., using calibrated microphones, fixed distances to the mic, protocols for plucking the string, and so on). I happen to be very skeptical of claims that certain F-model/A-model archtop mandolins are, simultaneously, both louder and have more sustain than the rest. To me, this seems like snake oil! But I will withhold final judgment until the data come in.

[Phil Goodson]

Thanks sblock for your discussion.
You confirm my feelings that it is very difficult to rationally plan or discuss how to "improve sustain" without some agreement about what sustain precisely means to everyone.

[Ivan Kelsall]

From Fscotte - " What evidence is there to suggest that a smoothly transitioned graduation is any better than one that is rough carved ? ". Well - CarlM got there before me. If a top / back is roughly carved with 'steps' in the carving,they could turn out to be 'break points' as Carl describes. A smooth transition from one thickness to another is what's required - at least i don't know any current builder who doesn't carve like that. Also,any unrequired wood will add extra mass to the top / back & thus change it's potential tone,
Ivan

PS - As a one time archer for 10 years until my club folded,it's interesting to note that Adrian builds bows !!. My own bow was Royal Scot ''Golden Claymore'' built by George Bernie & used with 'Firefly' Al.Alloy arrows - 35lb pull at 24".

[fscotte]

Loars aren't smoothly carved or should I say symmetrically carved. There are some significant variations in thickness if comparing the two sides of a top or back.

A thicker part will add weight but also adds stiffness. A brace does the same thing, and they are asymmetrical. What if we had 6 asymmetrical braces - different areas of extra weight and stiffness? Northfield is working with 5 braces now. Dr Cohen built a mando with 6 asymmetrical braces as well. I think to prove the point that the plates still move in the normal modes as a whole plate. The plate doesnt care about symmetry. Only we do.

[fatt-dad]

Here's Dave Cohen's bracing. It's a touch, "Wacky!"



f-d

[HoGo]

What a discussion! Been away just a few days...
Without reading all the previous looong posts...
My take is simple: You have only limited amount of energy. That is clear. Some of it is going to waste. If we want to incerease loudness we want to maximalize the amount of energy that immediately changes into vibration if we qant sustain we need to make the instrument vibrate at lower amplitude (loudness) but without too much losses. These all are so interconnected that you cannot alter any of them without chenging others. If you carve the top thinner (than optimal) you will likely lose more sustain that you gain in volume. To many folks the mandolin will pretend to be loud but it will be the lack of sustain that will trick your mind into thinking it is louder (only till you compare it to other mandolin that icks it in both departments).
For me main goal is finding where the energy is lost - material has a lot to do with that - you want low damping especially in top which is under load from bridge and also end-to end pressure. The back is IMO less critcal as it is under tension and can vibrate relatively freeely while producing sound.
ANother energy thief is bad coupling between top and back if the plates move one against the other creating large changes in internal volume you'll get lots of radiating sound in the lower registers, the upper frequencies seem to radiate mostly from outside surfaces. I try to adjust back and top separately in the white and you can hear how sound changes...
Sustain can be controlled somewhat by shape of arch IMO. From my observation, if the arch is bulbous (especially behind bridge), the part behind bridge will mostly "pump" air with growl but the sustain is rather short in these mandolins. Also wide and thin (deep) recurve will rob some of the sustain especially when it goes around the top under the fingerboard where leverage of neckblock is concentrated. Mandolins stiffer in that area (think the northfield artist) sustain for longer. When I remove material under extension the sustain shortens a bit but I can gain some attack/response/volume.
But to be honest there are way too many factors that come nto play and these are just from my observations, I may find any of them flawed and other factor being dominant in the future..
Regarding evenness of graduations, I think there's no need for perfect grads to 10ths of mm, but rough is no good, decent smooth is OK. Any large ridges create just mass hanging underneath the plate and cause just more unnecessary damping and loss of energy that can potentially be used for tone or sustain.

[Chris Baird]

Besides damping (heat/friction, and sound radiation), acoustic impedance plays a major role in sustain. As the pressure wave moves between various materials a certain amount of energy will move through, and a certain amount will reflect back. Greater impedance will facilitate sustain. There are a number of factors that contribute to greater or lesser impedance, and aren't very intuitive. For certain frequencies (the higher ones) you can make substantial changes to sustain (and inversely amplitude) by changing the bridge and/or nut material (increasing or decreasing the impedance between the string and nut). Likewise, the impedance of the plates and air dictate how much energy is radiated as sound, and how much bounces back into the instrument and creates the standing modal shapes.