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Question about string mass/diameter


PhilipKT
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I love it when a student asks a question I cannot answer because it sets me on a search and increases my own awareness.

This morning, I was talking to an inquisitive student about strings and mentioned that frequently the A string sounds thin and brassy. He asked me,”why is the A string thinner than the other strings? Why don’t they all have the same diameter? Then the A string won’t sound too bright and thin.”

I stuttered for a few seconds and then said,”I have no idea.”

Im sure it has to do with tension and mass. I assume that a thicker string tuned to the same Pitch would sound flabby and unresponsive, and less mass is required to get the same response at a higher pitch.

But that’s just a guess.

Input from the crowd would be welcome!

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There's a string design issue involved - the fundamental frequency and string length determine the ratio of string tension to string mass.  For a given material the mass can be controlled by changing the string diameter, but thinner strings are weaker.  Other than that, string 'sound' is a much more complicated issue and 'flabby', 'unresponsive', etc are rather poorly defined terms.  The statement that 'frequently the A string sounds thin and brassy' sounds more like a belief than an observation - maybe among cheap and poorly set-up violins played by low-tier students?

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4 hours ago, PhilipKT said:

...I assume that a thicker string tuned to the same Pitch would sound flabby and unresponsive...

You can easily test this hypothesis by tuning a D string down to A and playing it.  Then do the same with a G string.

But string design is complicated.  It's not just the thickness of the string.  If you make a thicker string of the same material, you will increase the mass per unit length, which will necessitate a higher tension if you want the same vibrating frequency (note).  If you make the thicker string from a lighter material to keep the mass per unit length constant, you introduce the variable of a different material.  And thicker strings are generally less flexible, so they vibrate differently.  (The purpose of windings is to increase string mass without decreasing flexibility.)  And the bow will exert more torsion on a thicker string.

It's complicated.

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3 hours ago, Brad Dorsey said:

You can easily test this hypothesis by tuning a D string down to A and playing it.  Then do the same with a G string.

But string design is complicated.  It's not just the thickness of the string.  If you make a thicker string of the same material, you will increase the mass per unit length, which will necessitate a higher tension if you want the same vibrating frequency (note).  If you make the thicker string from a lighter material to keep the mass per unit length constant, you introduce the variable of a different material.  And thicker strings are generally less flexible, so they vibrate differently.  (The purpose of windings is to increase string mass without decreasing flexibility.)  And the bow will exert more torsion on a thicker string.

It's complicated.

OK so with a given material, a given length and a desired pitch, the optimum mass, and therefore the diameter, would be different from note to note?

If I understand that correctly, (with the caveat that there’s more detail to it than that)we could use a thicker A string if we use a different material? And if that is true, theoretically We can have good sounding strings of equal thickness?

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3 hours ago, Dr. Mark said:

There's a string design issue involved - the fundamental frequency and string length determine the ratio of string tension to string mass.  For a given material the mass can be controlled by changing the string diameter, but thinner strings are weaker.  Other than that, string 'sound' is a much more complicated issue and 'flabby', 'unresponsive', etc are rather poorly defined terms.  The statement that 'frequently the A string sounds thin and brassy' sounds more like a belief than an observation - maybe among cheap and poorly set-up violins played by low-tier students?

I’m just now seeing this comment, I apologize. I appreciate your comment about the ratio of tension to mass, I should’ve thought of that myself And I think that might be the answer to my question.


When cellists speak about the A String sounding thin, or bright-in a negative sense- or piercing, for instance, There is an understanding among cellists as to what we are referencing, And we try to avoid that, and get the “bright” without the “shrill”

 

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Philipp, I'll try to make it understandable. This is however not a scientific explanation, as I lack the background for such an explanation.

Assuming a uniform string material (say bare gut) and a stable pitch, (like with bowing) there are three main important parametres that can be manipulated: tension, diametre and string length. One can manipulate these three parametres to get to the desired pitch, but (like with bowing: speed, weight and contact point) altering one will inescapably require you to alter the others, and any change will affect the sound produced. Keeping the same pitch: Increasing diametre (thicker string) will lead to a higher tension (if the string length remains the same) or will require a shorter string length (if the tension is to remain the same). On the cello, unlike on a piano, for instance, the string length is the same for all four strings. This means that, given a uniform material for all strings, only the diametre and the tension are the factors that can be manipulated. However, a string needs a certain amount of tension in order to be playable with a bow and produce good sound. I've read that for steel strings, they sound best if they are strung at a tension that is almost their breaking point. This is the reason that one should not tune metal strings too sharp. The main parametre left that can be manipulated is the diametre. If I therefore want a lower pitch, at roughly the same tension, then I need a thicker string, so that it will vibrate at a lower frequency, as more material will lead to a lower frequency (I'm assuming this has to do with inertia/kinetic energy).

Here is where modern string makers start tweaking with different materials. They use heavier materials for the lower strings (for instance on cellos: tungsten winding for lower strings vs aluminium winding for a strings), so that the weight increases more relatively to the diametre than it would using a uniform material. When compared to the higher strings, in other words, the lower strings can be made thinner than they would need to be if they were made from the same material as the higher strings. Bare gut g and c strings are massive. A drawback of thick strings, apart from for the left hand, is that they respond slower to the bow, so there is also that reason to make sure the lower strings are as thin as possible. What you can also observe in practically all string sets, is that the lower strings progressively produce less tension at their desired pitch compared to higher strings, which is another reason why lower strings are not as thick as they "should" be.

In cello string making, thinner seems to be regarded as better, even for the a string. I've never understood this, as I'm a thicker string guy myself, playing on gut, but that is how it is. Nowadays it should not be that hard to make a thicker a string, using a light and strong synthetic core material, and an aluminium winding, for instance. But I don't think any modern string brand has this as an ideal. Instead they focus on trying to limit the string diametre of the lower strings, without losing too much tension. Maybe @Bohdan Warchal wants to try this out once? I'd love an a string as thick as a d string (or even thicker, if you ask me).

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There is another critical parameter which is elasticity. You can imagine that a solid rod would not function as a string at all because it has virtually no elasticity. Whereas  a rubber string would have too much elasticity to produce much sound. Therefore the thick lower strings need to have enough elasticity to respond easily but not too much to produce a strong sound.

 

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Many years ago I was in a band that required tuning my guitar lower than normal, on the low E string two whole steps. The strings were really flabby and difficult to play so my solution was to get larger diameter strings and that worked to increase their tension and make them more playable. It also required significant adjustments to the guitar including enlarging the string grooves in the nut, adjusting the saddle heights and intonation, adjusting the tension of the truss rod in the neck, etc. Is it necessary on a violin to make significant setup adjustments when changing string diameters or tensions? It could be that these things needed adjustment simply to account for the lower pitch as well I guess.

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It’s important that the string grooves on both the nut and bridge are going to be appropriate, if changing string diameters, tensions etc.

I regularly see things where people tried different types/brands of string, and just put them on without thinking anything might need to be adjusted. The end result is often a string becoming shredded by the nut or bridge, as it wedges and becomes pulled apart, rather than sliding over them.

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