Loudness vs.string tension

[Marty Kasprzyk]

Has anybody ever measured the dB increase in loudness going from "light" to "medium" to "heavy" tension strings?

I'm trying to mathematically determine how much but I doubt I'm doing it right.  For example a Tomastic Infeld Dominant "light" tension E string has a tension of 16.5 lb and a "heavy" string has a tension of 20.1lb. Their ratio is 20.1/16.5= 1.213. Assume the bowing force through the bridge on to the violin's top is the same ratio and the resulting sound pressure (loudness?) follows then the 10x log of 1.213 is 10*0.084 or only 0.84 dB increase.

So going from a "light" to "heavy" tension E string gives only a 0.84dB loudness increase which doesn't seem like very much at all.   What does actual testing of these strings show?  Where am I going wrong?

[martin swan]

I don't suppose a theoretical increase in loudness relates to what actually happens to  a specific violin subjected to greater or lesser tension/downbearing.

Also, might bowing force automatically adjust to differences in string tension?

And to cap it all, changes in dB are not the same as changes in perceived loudness.

[Michael Darnton]

My experience is that it's a myth that more string tension gives more volume. Of course as Martin said it depends on your starting point, but also the tone quality changes and that can change perception without changing dB.

[Aston4]

2 hours ago, Marty Kasprzyk said:

Has anybody ever measured the dB increase in loudness going from "light" to "medium" to "heavy" tension strings?

I'm trying to mathematically determine how much but I doubt I'm doing it right.  For example a Tomastic Infeld Dominant "light" tension E string has a tension of 16.5 lb and a "heavy" string has a tension of 20.1lb. Their ratio is 20.1/16.5= 1.213. Assume the bowing force through the bridge on to the violin's top is the same ratio and the resulting sound pressure (loudness?) follows then the 10x log of 1.213 is 10*0.084 or only 0.84 dB increase.

So going from a "light" to "heavy" tension E string gives only a 0.84dB loudness increase which doesn't seem like very much at all.   What does actual testing of these strings show?  Where am I going wrong?

 

My amateur theory at this point in my journey, backed up with a great deal of experimentation:

Heavy tension on the top of the violin has potential to dampen the movement of the plate, so as much potential to dampen the volume as to increase it.  Different pieces of wood will have different ideal pressure preferred on them where the balance between the energy of the string transmitted, and that kinetic string energy converted to sound energy by the top and bridge and body is optimum.  Higher tension string  may produce higher kinetic energy of string, only to be lost in the excess (damping) pressure on the top.

Maybe this idea is why Thomastik tried drilling a hole through the top plate for the soundpost to connect directly to bridge: to take tension off the top, to limit damping.

Violin at it's optimum setup point for tone, or loudness, are often exclusive.  The very loud violins with also great tone, simultaneously, are more rare.  I have plenty of sweet sounding violins that are quiet.  If I adjust them for maximum (objectively measured) loudness, some portion of sweetness is lost.  I have one that is both nuts loud and nuts sweet and will never part with it.  

 

Idea: drill a hole on underside of top plate, but only partially, maybe 2/3 of the way through, that the soundpost slots into.  This removes some damping from the lower thickness of the wood of the top plate.  Maybe does nothing.  Maybe makes crack.  But maybe does something great.  Who knows.  I do not have the skill yet to try something like this.

[ctanzio]

50 minutes ago, Aston4 said:

Heavy tension on the top of the violin has potential to dampen the movement of the plate, so as much potential to dampen the volume as to increase it.

 

Only a small percentage of the increased string tension actually makes it onto the plate as increased bridge pressure.

A static increase in bridge pressure on the plate has no effect on damping properties. The plate will continue to vibrate with the same amplitude but about a slightly displaced plane.

The formula

dB = 10 log(T2/T1)

is theoretically accurate as a measure of vibrating energy difference between the two strings. How this translates into loudness in the violin would be a bit more complicated.

But one can estimate how much more energy the heavier string is theoretically pumping into the bridge given the same amplitude of vibration of both strings.

Energy Ratio = 10^(dB/10)

 

If the dB is 0.84, then

Eheavy/Elight = 10^(0.84/10) = 1.21

So the higher tension string is vibrating with 21% more energy.

 

[Aston4]

13 minutes ago, ctanzio said:

Only a small percentage of the increased string tension actually makes it onto the plate as increased bridge pressure.

A static increase in bridge pressure on the plate has no effect on damping properties. The plate will continue to vibrate with the same amplitude but about a slightly displaced plane.

The formula

dB = 10 log(T2/T1)

is theoretically accurate as a measure of vibrating energy difference between the two strings. How this translates into loudness in the violin would be a bit more complicated.

But one can estimate how much more energy the heavier string is theoretically pumping into the bridge given the same amplitude of vibration of both strings.

Energy Ratio = 10^(dB/10)

 

If the dB is 0.84, then

Eheavy/Elight = 10^(0.84/10) = 1.21

So the higher tension string is vibrating with 21% more energy.

 

That's why I'm an amateur.  

[Violinnut]

4 hours ago, Aston4 said:

 

My amateur theory at this point in my journey, backed up with a great deal of experimentation:

Heavy tension on the top of the violin has potential to dampen the movement of the plate, so as much potential to dampen the volume as to increase it.  Different pieces of wood will have different ideal pressure preferred on them where the balance between the energy of the string transmitted, and that kinetic string energy converted to sound energy by the top and bridge and body is optimum.  Higher tension string  may produce higher kinetic energy of string, only to be lost in the excess (damping) pressure on the top.

Maybe this idea is why Thomastik tried drilling a hole through the top plate for the soundpost to connect directly to bridge: to take tension off the top, to limit damping.

Violin at it's optimum setup point for tone, or loudness, are often exclusive.  The very loud violins with also great tone, simultaneously, are more rare.  I have plenty of sweet sounding violins that are quiet.  If I adjust them for maximum (objectively measured) loudness, some portion of sweetness is lost.  I have one that is both nuts loud and nuts sweet and will never part with it.  

 

Idea: drill a hole on underside of top plate, but only partially, maybe 2/3 of the way through, that the soundpost slots into.  This removes some damping from the lower thickness of the wood of the top plate.  Maybe does nothing.  Maybe makes crack.  But maybe does something great.  Who knows.  I do not have the skill yet to try something like this.

Would not more tension also diminish the overtones, hence loud under one‘s ear but not in the concert hall???

[David Burgess]

A higher tensions string, at the same length and pitch, will have more mass. I would expect this to put more energy into the violin.
However, it seems that too much energy going into a violin can overdrive it, making it "choke". Can't be played aggressively. The loudness tops out early, and the sound goes downhill (maybe even reduces in apparent loudness) and fails to maintain normal "slip-stick" action if it's pushed beyond that early peak. This reduces the breadth of the sound palette and loudness available to the player.

(In my experience and opinion)

[baroquecello]

I don't think a higher tension means a louder tone per se, however, thicker strings for several reasons encourage players that are not used to thinner strings to play with a heavier bow hand, and that does make an instrument louder. At least that is my observation on cellos. 

It does matter how big a difference in tension we are talking about. The difference between thomastik Rondo and Dominant is so huge that yes, dominant is much less loud on most instruments. But here again, that doesn't necessarily translate to less projection. Brinton Smith recently made a video comparing several strings and on his cello, in the hall, Dominant was the best projecting string. He was surprised because under the ear, it was not the case. 

[Anders Buen]

13 hours ago, Marty Kasprzyk said:

Has anybody ever measured the dB increase in loudness going from "light" to "medium" to "heavy" tension strings?

I'm trying to mathematically determine how much but I doubt I'm doing it right.  For example a Tomastic Infeld Dominant "light" tension E string has a tension of 16.5 lb and a "heavy" string has a tension of 20.1lb. Their ratio is 20.1/16.5= 1.213. Assume the bowing force through the bridge on to the violin's top is the same ratio and the resulting sound pressure (loudness?) follows then the 10x log of 1.213 is 10*0.084 or only 0.84 dB increase.

So going from a "light" to "heavy" tension E string gives only a 0.84dB loudness increase which doesn't seem like very much at all.   What does actual testing of these strings show?  Where am I going wrong?

There is some information on this in one of the volumes of Erik V Janssons «Acoustics for Violin- and Guitar makers». He uses string impedance, but relates it to loudness, tension, and material properties, I guess mass per length string material.I think also Stoppani have made a string calculator, as he produces gut strings for different early and late instruments.

[Marty Kasprzyk]

Hi Anders,  

Thanks for the Janssons reference (https://www.speech.kth.se/music/acviguit4/part4.pdf) .  His example 4.8 b says:

"b) if the weight is increased 10% but the tuning is kept equal the string tension must be increased 10% and the specific vibration sensitivity is lowered 20 % (the sound level increases 2 dB)"

 

An increase of 10% tension is similar to going from "light" tension to "medium" tension violin strings or going from "medium" to "heavy" tension for my Dominant violin E string example I mentioned earlier.

2 bB total is a lot!   And a total spread of 4dB its much more than the 0.84 db that I had calculated so my 10log(20.1lb/16.5lb)=0.84dB must be incorrect.

Unfortunately Janssons did not show the equations that he used for his vibration sensitivity and dB calculations.

 

[Michael Darnton]

Jansson probably didn't also know or consider what Aston was implying: whether the change in string weight was moving any specific non-theoretical violin into optimum from some location in the plus or minus range or was it taking an optimized violin and moving it into worse performance. It's easy to understand why any specific real instrument may not perform as the theory suggests, or even may go in the opposite direction.

So if his theories are simple theory they may give a theoretical answer but be little or no help or consequence in making real world decisions. And they'd only be functional working rules in conjunction with some concrete way to first determine a specific violin's level of optimization AND the direction needed towards optimization. Without that it's all interesting, but basically useless as a tool for accomplishing real world results.

David touched on another issue, that for various reasons different weight strings have different tonal profiles. There are a lot of different ways to accomplish that goal. Heavy gauge Super-Sensitives may be the same tension as some Dominant set, but they won't sound the same.  I think that I have mentioned here previously that I ran into Aaron Rosen in Korea and he said that he was using light gauge Dominants on the road in weird weather because they gave him the type of gut-like sound he wanted without gut's instability, and at no loss of volume. He was competing against a full orchestra in that rehearsal and doing just fine. Was he past optimization for normal strings and were the lighter strings moving him backwards into it, for a better result? We don't know, but we might guess that a theoretical recommendation for heavier strings for more output could have been detrimental, whereas his own choice was appropriate, solidly based on his own long experience and expertise.

The real world is an interesting place, for those of us who habitually live there.

[Anders Buen]

3 hours ago, Marty Kasprzyk said:

Hi Anders,  

Thanks for the Janssons reference (https://www.speech.kth.se/music/acviguit4/part4.pdf) .  His example 4.8 b says:

"b) if the weight is increased 10% but the tuning is kept equal the string tension must be increased 10% and the specific vibration sensitivity is lowered 20 % (the sound level increases 2 dB)"

 

An increase of 10% tension is similar to going from "light" tension to "medium" tension violin strings or going from "medium" to "heavy" tension for my Dominant violin E string example I mentioned earlier.

2 bB total is a lot!   And a total spread of 4dB its much more than the 0.84 db that I had calculated so my 10log(20.1lb/16.5lb)=0.84dB must be incorrect.

Unfortunately Janssons did not show the equations that he used for his vibration sensitivity and dB calculations.

 

Hardanger fiddles use lighter gauge strings, and they are shorter by about 2cm or so. However the tuning is usually higher than for a violin. The A string can be tuned to B, C C# or in seldom cases D, a transpose. The G string is also usually a half or whole note higher, but this can vary due to scordatura.

I have measured about 100 instruments in the same room, the same procedure and the same mic source distance, on eyeballing, distributed over about 10 years.

The Hardangerfiddles are about 3 dB less loud than the violins in average. It is an audible difference. 10 dB difference is experienced as a doubling or halving of the subjective sound level. 5 dB is clearly noticeable, and steps of 5 dB is used in noise mapping and as steps between sound classes for buildings.

I think the major difference between violin and Hardanger fiddle sound, if the same playing tecnique is used, is in the strings and the bridge. I think the same may hold for Baroque versus classic violins.

Edited March 28 by Anders Buen
Spelling errors corrected

[Marty Kasprzyk]

1 hour ago, Anders Buen said:

Hardanger fiddles use lighter gauge strings, and they are shorter by about 2cm or so. However the tuning is usually higher than for a violin. The A string can be tuned to B, C C# or in seldom cases D, a transpose. The G string is also usually a half or whole note higher, but this can vary due to scordatura.

I have measured about 100 instruments in the same room, the same procedure and the same mic source distance, on eyeballing, distributed over about 10 years.

The Hardangerfiddles are about 3 dB less loud than the violins in average. It is an audible difference. 10 dB difference is experienced as a doubling or halving of the subjective sound level. 5 dB is clearly noticeable, and steps of 5 dB is used in noise mapping and as steps between sound classes for buildings.

I think the major difference between violin and Hardanger fiddle sound, if the same playing tecnique is used, is in the strings and the bridge. I think the same may hold for Baroque versus classic violins.

 

Janssons' 4.8c example said a 5% increase in string length gives a 0.5 dB increase so maybe your Hardanger's  6% decrease in string length from a violin gives only a 0.6 dB decrease in loudness. Perhaps other construction differences give most of the 3 dB difference.

Have you tried putting a regular violin bridge on a Hardanger  and use standard EADG violin strings to see if its short string length was causing the difference in dB or if the difference was due to other things in a Hardangerfiddle's construction?

[Marty Kasprzyk]

9 minutes ago, Marty Kasprzyk said:

 

Janssons' 4.8c example said a 5% increase in string length gives a 0.5 dB increase so maybe your Hardanger's  6% decrease in string length from a violin gives only a 0.6 dB decrease in loudness. Perhaps other construction differences give most of the 3 dB difference.

Have you tried putting a regular violin bridge on a Hardanger  and use standard EADG violin strings to see if its short string length was causing the difference in dB or if the difference was due to other things in a Hardangerfiddle's construction?

That reminds me of our late US senator Everett Dirkson's quote:

"A billion here, a billion there, and pretty soon you're talking about real money."

my version is   "A dB here, a dB there, and pretty soon you're talking about real money."

I just had a professional viola player compare one of my violas with his.  His was was about 3dB louder but his cost about $30,000 more which is $10,000/dB.  So even a little dB increase is really important.

Everett Dirksen

[Greg Sigworth]

This is an interesting problem with many factors. Energy is introduced by the bow on the string; more pressure of the bow on the string results in greater vibration of the string (increase of energy). There must be a formulae for the energy of a vibrating string and would include string weight per length, tension and amplitude of vibration. As this is controlled by the one using the bow if you want more volume play with more downward force and increase bow speed, and other factors too. There may be a string which has an optimal weight/tension ratio that makes this easy to do and control, and different players may prefer different strings. Just having tighter strings which weight more may or may not help the player. Energy goes into the string, then into the bridge and some back into the other stopped string location, then into the island between the F holes, then to the violin corpus with all that vibration (greatly simplified) and finally into the air as sound energy. What makes this energy transfer so that the great sound is made at the hands of the great virtuoso? A louder violin may not be a better sounding violin.

[Aston4]

4 hours ago, Greg Sigworth said:

This is an interesting problem with many factors. Energy is introduced by the bow on the string; more pressure of the bow on the string results in greater vibration of the string (increase of energy). There must be a formulae for the energy of a vibrating string and would include string weight per length, tension and amplitude of vibration. As this is controlled by the one using the bow if you want more volume play with more downward force and increase bow speed, and other factors too. There may be a string which has an optimal weight/tension ratio that makes this easy to do and control, and different players may prefer different strings. Just having tighter strings which weight more may or may not help the player. Energy goes into the string, then into the bridge and some back into the other stopped string location, then into the island between the F holes, then to the violin corpus with all that vibration (greatly simplified) and finally into the air as sound energy. What makes this energy transfer so that the great sound is made at the hands of the great virtuoso? A louder violin may not be a better sounding violin.

I've done quite a bit of physics here and there, but don't recall ever seeing such an equasion specifically relating all those things at once to a string under tension.  Could maybe play with some spring/pendulum stuff... maybe I'll mess around with it in a few days if I'm in the mood.  I'd be surprised if the big makers like Pirastro haven't applied a ton of physics/math to it.  Plenty of smart math/physics/engineering types ins Deutschland readily on tap.  Then again maybe they just play around with different fishing lines and wire wrapping machines to see what happens 

[Violinnut]

On 3/28/2024 at 3:09 AM, Michael Darnton said:

My experience is that it's a myth that more string tension gives more volume. Of course as Martin said it depends on your starting point, but also the tone quality changes and that can change perception without changing dB.

I just changed my e string. The one at first was very strong one (.28) I put a lighter one that had less pressure and it actually helped the tone, I can not say that it was not as loud, but it sure helped the D and A string. It now sounds much better.

By the way, would more pressure also not destroy some of the upper harmonics. 

[Anders Buen]

The bow string dynamics is complicated. One of my mentors, the late Knut Güettler, had bow string simulation and physics as his main field. Jim Woodhouse have also been deep into this. I do not have a full overview of it, but the playability is one of the factors involved. It is related to the bridge admittance, high response makes it more difficult to make the Helmholz motion of the string go. The extreme example is the wolf note. But the effects are active in the normal range too.

I think the heavier strings are somewhat more difficult to get into action than light strings. The damping of the string, the interior damping factor, if it is higher, the bowed string will be easier to start and it affects the spectrum somewhat. I believe it becomes a bit brighter. 

I will have to look this up in order to understand it better. Güettler and Woodhouse would not use string brands in their literature. However, Fan Tao at DAddario have a good insight into this, even the competitors strings. And may comment on this while the recordings of the Zoom meetings are stopped. There is a recorded presentation by him on YouTube from such a VSA Violin Acoustics Talk a few months ago.

[LCF]

8 hours ago, Marty Kasprzyk said:

That reminds me of our late US senator Everett Dirkson's quote:

"A billion here, a billion there, and pretty soon you're talking about real money."

my version is   "A dB here, a dB there, and pretty soon you're talking about real money."

I just had a professional viola player compare one of my violas with his.  His was was about 3dB louder but his cost about $30,000 more which is $10,000/dB.  So even a little dB increase is really important.

Everett Dirksen

Well 3 dB is twice as loud.

 

Politicians treat our money as if it was logarithmic such that $1000 is barely any more than $100. It is hardly detectable.   Give them just a mm and they'll take a cm, then a meter, 100 meters, a kilometer and so ad infinitum and  next year it will be ten times worse.

[LCF]

16 hours ago, Marty Kasprzyk said:

Hi Anders,  

Thanks for the Janssons reference (https://www.speech.kth.se/music/acviguit4/part4.pdf) .  His example 4.8 b says:

"b) if the weight is increased 10% but the tuning is kept equal the string tension must be increased 10% and the specific vibration sensitivity is lowered 20 % (the sound level increases 2 dB)"

 

An increase of 10% tension is similar to going from "light" tension to "medium" tension violin strings or going from "medium" to "heavy" tension for my Dominant violin E string example I mentioned earlier.

2 bB total is a lot!   And a total spread of 4dB its much more than the 0.84 db that I had calculated so my 10log(20.1lb/16.5lb)=0.84dB must be incorrect.

Unfortunately Janssons did not show the equations that he used for his vibration sensitivity and dB calculations.

 

Marty he has expressed two important  string formulae in friendly percentage terms, the first being the standard Taylor(Mersenne) formula relating F, T, L and M which I won't attempt to format completely here but eg where F  is proportional to 1/(2*L) via Taylor, Jansson has stated percentage change in F is proportional to - the percentage change in L, which is a very neat way to describe it.

 

Similarly his specific vibration sensitivity is just the characteristic admittance of a string under tension:

Yo = 1/sqrt(T*M)

Again, he expresses this in relative percentage terms.

 

What I like is fig 4.3 which shows the mobility plot with string harmonic peaks relative to the specific vibration sensitivity, logarithmically, but also shows the sharp anti-resonance peaks in between them. These are the impedance peaks. Perhaps it is an interesting thing to contemplate what could possibly happen there?

[martin swan]

Just to say again, loudness on a theoretical model has nothing to do with what will happen on a violin, loudness and perceived loudness are not the same, and audibility is not always related to loudness.

So to say that heavier tension strings are going to make a violin "louder" is a nonsense. And to attempt to calculate by what proportion - that's counting angels on the head of a pin.

[LCF]

32 minutes ago, martin swan said:

Just to say again, loudness on a theoretical model has nothing to do with what will happen on a violin, loudness and perceived loudness are not the same, and audibility is not always related to loudness.

So to say that heavier tension strings are going to make a violin "louder" is a nonsense. And to attempt to calculate by what proportion - that's counting angels on the head of a pin.

I think this is made more complex by the fact that various string manufacturers approach higher tension stringing in different ways. If there was a universal simple way of increasing the tension of a given string the theory might have more rational consequences however you can increase the core diameter or increase the wrapping weight or wrapping diameter or the  wrapping smoothness, or fool around with various interlayers in a myriad of ways, or do some of all of these things so there is no easy way to predict specific outcomes. The core physics is undeniable but violins are ornerey and bowing makes everything insanely complicated.

[Marty Kasprzyk]

When I put a new string on and turn the pegs to bring it up to pitch it starts with a low pitch and low loudness note and as I turn the peg the notes get higher in pitch and louder as the string tension increases.

Am I the only one who notices this loudness increase or is this just my ears and brain not working again.

 

 

[LCF]

3 minutes ago, Marty Kasprzyk said:

When I put a new string on and turn the pegs to bring it up to pitch it starts with a low pitch and low loudness note and as I turn the peg the notes get higher in pitch and louder as the string tension increases.

Am I the only one who notices this loudness increase or is this just my ears and brain not working again.

 

And the amount of vibration also decreases as it gets tighter, louder, sharper