String Theory For Guitarists, Part 1
The First in a Multi Part Series About How Strings Vibrate
Few topics are as hotly discussed on the internet as what component of a guitar is most important. In that argument, I would posit that the string is the most important part. Play a guitar without a pickup, or without finish or tonewood, and you will still get something very guitar-like. Play a guitar without strings, and you end up looking like one of these guys. So the question becomes, if the string is so vital, do you understand enough how it works?
​
A string seems like such a simple thing. A piece of wire, fastened at both ends, vibrating away. While the general concept is true, there is actually a ton of science behind it. My goal with this multipart series is to start simple and work our way through the science of strings with a focus on how it applies to guitars.
​
String Materials
​
"A string without a material is not a string at all." I'm pretty sure some Chinese proverb says that or something. If not, I get to own the phrase! Perhaps no property is as basic to a guitar string as the material it is made out of. There are a variety of materials used, from nylon plastic for a classical guitar, to bronze/steel combinations for acoustics, to nickel and/or steel for electric guitars.
​
A key property for electric guitar string materials is that it must be ferromagnetic. That means it needs to be able to interfere with a magnetic field, like the one produced by a pickup. The physical measure used for ferromagnetism is called magnetic permeability, which is the measure of how easily a magnetic field will be formed in a material, which makes it then interfere with that field when in motion. The specific ferromagnetic properties of the string material, along with its construction, determine exactly what kind of signal you get out. Steel and nickel, for example, have a similar magnetic permeability while stainless steel can have a permeability up to 10 times higher. A string made all of stainless steel will produce a larger disturbance in the (electromagnetic) force. A string made all of nickel or carbon steel will produce a smaller disturbance, and may therefore be perceived as "quieter". Below are the magnetic permeabilities of some common string materials.
​
Carbon (Plain) Steel: ~100
Nickel: ~100
Nickel Steel Alloys: ~100-400
Stainless Steel: 1000-1800
Relative Magnetic Permeability of Some Common String Materials*
Another important property is stiffness. The stiffness determines how much it will vibrate like an ideal string and how much it will vibrate like a bar. You might say "what's the difference?", but the difference between vibrations of a string vs. a bar are quite stark. The stiffness is related to the property known as Young's Modulus of Elasticity, or simply modulus of elasticity. Below are the moduli of elasticity of our common string materials. A higher modulus of elasticity means the material is more stiff.
Carbon (Plain) Steel: 29.0
Nickel: 29.0
Nickel Steel Alloys: 27.8
Stainless Steel: 27.6
Modulus of Elasticity for Common String Materials**
The final property we are going to discuss is the material's resistance to corrosion. Corrosion is when the string material interacts with the air, sweat, humidity, etc. and creates a very thin layer of a different substance on the surface of the string. Plain steel is rather susceptible to this, particularly grades with a high carbon content. Nickel, on the other hand, is highly resistant to corrosion. For this reason, many strings use steel on the inside and a nickel alloy wrapped around the outside, resulting in good ferromagnetic strength, the right amount of stiffness, and good resistance to corrosion.
String Construction
​
Once the materials for a string are selected, the string needs to be made. In order for a string to vibrate like an ideal string, the material stiffness needs to not be too high. Too high, and it will act more like a bar or a rod. So for smaller strings, a plain steel wire is sufficient.
​
Once we start getting to larger strings, however, we need to rethink our approach. So how do we keep stiffness down while making it possible to get lower pitch? That is where wrapped strings come in to play. A wrapped string consists of a core, or inner section, and a wrap which is wrapped around the core for the length of the string. Most modern strings will use a steel core that has a hexagonal cross section. This provides some of the ferromagnetism as well as a shape that has corners that will "grip" the wrap so that it doesn't slide around. The photo below shows a magnified .046" wound low E string, showing the hexagonal core and the round wrap.
Magnified Image of a .046" Wound Low E String Showing Hexagonal Core and Round Wrap
The outer wrap is what really separates the boys from the men in the string world. The wrap material, size, and treatment are considered trade secrets because this is where the character of the string is really brought to light. Some strings use a nickel allow wrap, some use various formulations of steel. Ernie Ball Cobalt's, for example, use a steel alloy with a small amount of cobalt, which is extremely strong, to create its signature sound.
​
As wound strings get bigger, both the core and the wrap increase in diameter. Once strings get really large, however (such as bass strings), the core is then wrapped by a small diameter wrap, followed by a second wrapping of a larger diameter wrap. Balancing the materials and cross sections is both an art and a science. This is why you see roughly a gazillion different string brands and formulations, each claiming to have the ultimate in (insert characteristic of choice here).
An Ideal Vibrating String
​
In the sections above, we have mentioned that we want our real world strings to vibrate like an ideal string. We've probably all seen the figure of what a vibrating string looks like. In the figure below, we show what is called the natural mode. It can also be called the resonant mode, or one of a host of other terms, but natural mode is most common in the scientific community, so we will go with that. The reason that we want a real string to vibrate as similarly to an ideal string as possible is that the math is really easy. The figure is what an ideal string looks like when excited by its natural frequency.
​
So what do we know about ideal strings? Well, we know exactly how to calculate out frequencies, for a start. If you are curious how to do so, there is a great calculator found here. Also, the harmonics are perfect multiples of the natural frequency. Getting away from an ideal string means that the harmonics are no longer perfect multiples. This means harmonics will get slightly detuned from where they "should" be, and we perceive that as not being quite as musical. Additionally, we can start to investigate what effects some other characteristics have. However, that, my friends, is a story for...
​
String Theory for Guitarists, Part 2