luthery/physics question: sympathetic resonance and sustain

[RJVB]

I've been trying to wrap my head around a little problem and hope to get some more food for thought here (or a probably definitive answer from someone like Alan Carruth!).

It's about about a piece I'm working on (on the Cabaret) that ends with two long 3-note chords of harmonics on the top 3 strings: 12th fret followed by the 5th fret. The last one has a fermata.

For the 1st chord I don't really bother about sympathetic resonance esp. since the 6th string is already sounding and that 1st harmonic is loud enough (and lasts only 2 beats).

The 2nd one is much more delicate. There you really hear the lower strings. It took me a while to realise that they're probably also getting a "kick" through the bridge: I play these chords fingerstyle, loud and barely arpeggiated.

For now I'm anchoring my thumb between the D and A strings before playing the final chord which prevents those 2 from sounding and also seems to reduce the transfer of my attack to the low E. It still vibrates of course. Musically that's OK because there's an E in the chord (albeit 4 octaves higher).

The question is if this (partly) sympathetic vibration steals vibration energy from the (very) high E that's supposed to be heard for a while and if I thus would do better to mute all 3 lower strings.

I've tried to determine this by ear but it's hard enough to play this chord the same way consistently without having to use the thumb to mute the lowest 3 strings.

[ProfChris]

Think about it in terms of energy transfer.

The plucked string transfers energy to the bridge and soundboard. The bridge/soundboard movement transfers energy to the air = sound.

The bridge/soundboard movement also transfers some energy to the other strings, producing sympathetic resonances. If you could stop that energy transfer, then more energy would go into the soundboard, probably increasing sustain.

This raises two questions:

1. Does damping the other strings prevent some energy transfer? I don't know, but I suspect the answer is a little.

2. Is that enough energy to extend sustain enough to be heard? Again I don't know, though I suspect not.

The way to find answers would be to record the note, with and without damping, and compare the waveforms. Audacity will do this nicely. You'd want a series of each notes, and average them. If the peaks are taller for one than the other, that's louder. If the length of the waveform is longer, that's more sustain.

A better way from a performance perspective might be to do the same to friends who have good ears, and ask them which way of playing the note sounds best. Overtones might be more pleasing, in which case you'd want to keep them.

[Robin, Wales]

I think that it is very complex and incredibly variable guitar to guitar. It is easy to paint the picture that the top of a guitar vibrates up and down and that moves air and creates sound. But I would have to say that my experience with fretted zithers and mountain dulcimers makes me think a little wider.

For example: I have owned many old dulcimers and zithers designed for table playing. They normally have 3 x wooden feet. These instruments sound weak when played on my lap, or held in the air. But on my thick solid wood kitchen table or on a big oak table in the local pub they can fill the room with sound - more bass, more top, more sustain.

I can't tell you in terms of physics what's going on. But if does make me think that getting vibrations (from both ends of the strings) right throughout a guitar (top back, sides, neck, bracing etc) is quite important. I'm sure that we have all had that experience of picking up two guitars of the same model and finding one is more alive than the other. I wonder if that is because everything is just more "engaged" in one of the guitars.

So you could think about your question in terms of what is allowing vibrations to flow, and what is filtering them, and what is suppressing them.

My archtop is definitely very different to my flattop in terms of timbre (sustain, bass, punch ect) - but both are equally as loud, yet the archtop top is "shifting" less air.

It is definitely complicated!

[RJVB]

Originally Posted by ProfChris

Think about it in terms of energy transfer.

That's exactly what I've been doing, and I've come up with more or less the same questions you raise.

I've also been thinking about recording and comparing, but that's where the trouble getting a consistent attack of the chord and consistent damping of the strings comes in.

Originally Posted by Robin, Wales

For example: I have owned many old dulcimers and zithers designed for table playing. They normally have 3 x wooden feet. These instruments sound weak when played on my lap, or held in the air. But on my thick solid wood kitchen table or on a big oak table in the local pub they can fill the room with sound - more bass, more top, more sustain.

That's not exactly the same situation. What you're dealing with there is transmitting vibrations to something that will act as a soundboard. I remember seeing speaker drivers designed to use a table in much the same manner (20 or more years ago).
Do you have the impression the table transfers energy back into your instrument?

In the case at hand we have an "onboard" soundboard that definitely has a 2-way interaction going on with the strings. I have little doubt that the total sustain is longer if I do allow the low strings to be set into motion by my attack, but I'm convinced that's not "true" sympathetic resonance but more akin if not equal to the effect you get when you tap the bridge. Preventing that and then removing my finger could easily give more sustain too in terms of overall sound production, but in this case they'll be under rather than overtones and so the question is whether we're hearing what's written (answer: probably not).

My archtop is definitely very different to my flattop in terms of timbre (sustain, bass, punch ect) - but both are equally as loud, yet the archtop top is "shifting" less air.

Funny you say that. The piece in question is Eddie Lang's arrangement of Rachmaninoff's Prelude Op. 3 #2, so in terms of authenticity I should be playing it on my archtop. The entire question is moot there. Not only is the sustain of the 3 top strings much longer than the nylgut top strings on my Cabaret, there's also very little of that initial transfer of my attack. Logical: the archtop is probably at least 6mm thick under the bridge whereas my Cabaret's top is almost see-through thin everywhere, and the tension of the steel strings is a lot higher. (One of the 1st things I always do on a new nylon-string flat-top is to make tiny notches at the rear of the saddle so strings don't slide over it when I dig in.)

But FWIW, my archtop is punchier than the classical but the classical is a lot louder (except in those very high registers or when I really start whacking it with a heavy pick).

[Robin, Wales]

I built this double fretboard zither with sympathetic drones between the fretboards. If I get the drones tuned to match the two fretboards (one in D and one in G) then they seem to add a reverb and sustain to whatever I am playing on the fretboards. If they are not in tune then that is lost. Some food for thought?

[RJVB]

Originally Posted by Robin, Wales

If I get the drones tuned to match the two fretboards (one in D and one in G) then they seem to add a reverb and sustain to whatever I am playing on the fretboards. If they are not in tune then that is lost. Some food for thought?

Reverb - undoubtedly. Sustain - yes, if you consider that sympathetic resonance is going to be (mostly) in frequencies that can be thought of as supportive for the notes you're playing. On violin it's an accepted technique to improve the sound of certain "ungrateful" notes (C and F come to mind) or to add some amount of vibrato to an open string by fingering the same note an octave below or even above.

Something I did consider but not yet mention is that the vibration in an unplayed lower string could also act as an energy reservoir.

The question remains whether this gives a desirable outcome, and I have my doubts about that. If a piece ends on a long low open E you're probably happy with the additional colour that the high E is going to give. Having a long high E replaced gradually by the low E seems a lot less welcome.

[Alan Carruth]

RJVB wrote:
"I've been trying to wrap my head around a little problem and hope to get some more food for thought here (or a probably definitive answer from someone like Alan Carruth!)."

Ouch!

There are no 'little' problems in guitar acoustics.

I just spent about 20 minutes typing out what would have been a nice beginning to an answer that may even have been somewhat close to correct. I'm going to have to think about a better approach.

Jansson, in his 'Acoustics for Violin and Guitar Makers', 4th edition, talks about sustain as being the length of time a signal remains audible. There are several ways to get it, but the two basic ones are what you could call 'banjo' sustain, and 'Les Paul' sustain.

On a banjo there is not much difference in impedance between the string and the bridge, or between the soundboard and the air. Energy is transferred very quickly and effectively from the string to the air. The sound level rises fast, and falls off fast, but the top is so effective at making sound that the level can stay audible for a fairly long time because not much is lost in translation.

On a Les Paul the impedance of the bridge is so high that the energy can't get out of the string quickly, and even if it could, the body is not very effective at converting it into sound. By itself it makes a sound that is barely audible for a very long time. However, when placed on something like a table, that is marginally better at putting out sound, the string energy can be metered slowly enough to last a long time, but fast enough to be audible. That's the situation with those zithers.

The problem here is that any 'acoustic' guitar that's worthy of the title is going to be much more complex than those models. You're likely to see both sorts of sustain at one pitch or another, and maybe even at the same pitch from, say, different strings. And your guitar may (will, most likely) be very different from mine in that respect.

All you can do is look at the ways in which energy can 'leak' out of the string at the given pitch, how the guitar will convert that into sound, and any 'flywheels' there might be along the way that could store some of it, to feed it back as 'sustain' later.

I'd better stop for now.

[RJVB]

Originally Posted by Alan Carruth

There are no 'little' problems in guitar acoustics.

Sure, but I had this colleague once who ended up brainwashing me that "everything is relative" (in a Russian accent), so often did he repeat that slogan

I just spent about 20 minutes typing out what would have been a nice beginning to an answer that may even have been somewhat close to correct. I'm going to have to think about a better approach.

Lol, thanks for trying anyway! I don't know how much you left of that answer, because I didn't see or missed anything new that you hadn't already taught me Unless the actual answer can be resumed as "it depends", from

The problem here is that any 'acoustic' guitar that's worthy of the title is going to be much more complex than those models. You're likely to see both sorts of sustain at one pitch or another, and maybe even at the same pitch from, say, different strings. And your guitar may (will, most likely) be very different from mine in that respect.

All you can do is look at the ways in which energy can 'leak' out of the string at the given pitch, how the guitar will convert that into sound, and any 'flywheels' there might be along the way that could store some of it, to feed it back as 'sustain' later.

The guitar is the Eastman implementation of Buscarino's interpretation of (apparently) a Hauser I with lattice bracing (wood), a carved (maple) back and an oval soundhole. Should be simple, no?
As I hinted above, the (spruce) top is so thin that it doesn't even block normal classroom/office lighting (but not so much it sounds like a banjo).