Ottawa's guitar repair shop

String Gauges

Talkin’ About Strings

Often in discussion with my customers they ask me about string gauges and what are the best strings on the market. Opinions vary, of course, on which manufacturer produces the best strings. But let me approach this subject with you in a generic way. There is a lot of physics involved, and I go over that later in the article, but here are some key points to remember when choosing your string sets:

• Not all strings are created equal. There are only a handful of string brands I recommend because of their quality and reliability: D'Addario, Elixir, Ernie Ball and GHS. For bass strings, the same three are still on the list, plus Smith and LaBella. Lower quality strings have inconsistent vibration patterns, which cause buzzing, and have inconsistent windings and cores, which cause poor intonation. Avoid hand made strings; they are never precise enough to intonate correctly.

• Choice of string gauges affects: action, output, harmonics, intonation, sustain, and picking speed.

• Choosing the proper string gauge for your instrument’s scale length, tuning, picking style and musical genre is a significant factor in your sound. Ensure you have the correct string gauge for your needs.

• What style of music do you play? Blues, light rock, jazz, metal, folk, bluegrass, flamenco…require different gauges for different stages. For electric guitars, most players use a set of 10-46 or 11-49.

• Heavier gauge strings actually produce a bigger sound and more neck tension (see section on Hooke’s Law and how physics explains this phenomenon). In Short, the bigger the strings, the smaller the amplitude for a same attack, and therefore, lower action is achievable. Hooke’s Law: The Physics of Guitar Strings This law will help you understand how string tension and setup go together. In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or Hookean materials. Hooke's law in simple terms says that strain is directly proportional to stress.

Mathematically, Hooke's law states that



x is the displacement of the spring's end from its equilibrium position (a distance, in SI units: meters);
F is the restoring force exerted by the spring on that end (in SI units: N or kg·m·s-2); and
k is a constant called the rate or spring constant (in SI units: N·m-1 or kg·s-2).

Now, lets use this to prove that heavy gauge strings have a smaller amplitude than a light gauge string when plucked with the same force. For this example, we are going to compare Nickel strings.

A string under tension behaves as a simple spring (stretching it
along its length should be equivalent to stretching it by plucking).
Given the diameter, initial length and Young's Modulus of nickel, the
spring constant of each guage of string can be calculated (k = EA/L).
Young's Modulus (E) of nickel is 200GPa. A (the cross-section area) is
equal to pi*r2.

Converted from inches to millimeters, the A value for each string is:
A1 = (3.14159)(0.254mm/2)2 = 0.051mm2
A2 = (3.14159)(0.2794mm/2)2 = 0.061mm2

The spring constants of each guage of string work out as follows:

k1 (of the 0.010" string) = ((200GPa)(0.051mm2))/647.7mm = 0.015748031
k2 (of the 0.011" string) = ((200GPa)(0.061mm2))/647.7mm = 0.018835880

Hooke's Law states that the force of a spring is equal to the distance
it is stretched times its spring constant (F = kx).

Since we tune the string, and then apply a constant force to pluck it,
we can say that the total force on the string is equal to the spring
constant times the total distance stretched (the string stretches some
when tuned, as you know). In math, that looks like:

(F0 + Fp) = k(x0 + xp)
*F0 is the force applied by tuning to E, Fp is the force of the pluck,
x0 is the stretch caused by tuning to E and xp is the stretch caused
by the pluck. x0 is, out of necessity, directly correlated to the
amplitude of the standing wave in the string (I think this makes

Multiply thtough to get: F0 + Fp = kx0 + kxp
but we know that F0 = kx0 so: F0 + Fp = F0 + kxp
F0 cancels and it's simply: Fp = kxp

Isolate xp: xp = Fp/k

Now we can compare the xp of each string:

xp1 = Fp/0.015748031
xp2 = Fp/0.018835880

Fp is constant for each string (That is the even force used to pluck the string), so we can easily see that xp1 > xp2.
Since the smaller diameter string stretches more under the same force,
the amplitude of its standing wave will be greater.

- Action: You can have a lower action on a guitar, for a same tuning, when using heavier gauge strings. Because of the greater tention in the string, it will occupy less space when vibrating (amplitude) if it was picked with the same force as the lighter string. I will prove this by using Hooke's law later in the artice

- Output: Since a heavier string gauge has more tension, it has more stored energy (Hooke's law F=K.x). This greater energy is directly translated into greater output in an acounstic guitar. In an electric guitar, the output is increased because the thicker strings incur a stronger variation in the magnetic field of the pickups.

- Artificial Harmonics: One of the best ways to explain an artificial harmonic is to quote the Wikipedia article:

"To produce an artificial harmonic, a stringed instrument player holds down a note on the neck with the non-dominant hand, thereby shortening the vibrational length of the string, uses a finger to lightly touch a point on the string that is an integer divisor of its vibrational length, and plucks or bows the side of the string that is closer to the bridge. This technique is used to produce harmonic tones that are otherwise inaccessible on the instrument. To guitar players, one variety of this technique is known as a pinch harmonic.

This technique, like natural harmonics, works by canceling out the fundamental tone and one or more partial tones by deadening their modes of vibration."

Producing an artificial harmonic is a sinch on heavier strings (like a 0.52 tuned to E) because of the increased tension and stored energy. Just try it. If you're currently able to do a pinch harmonic on your lower string, try down tuning it a step and half and try again. Not so easy anymore, is it?

Intonation: Intonation in guitars and basses is what refer to as the instrument being in tune along the length of all its strings. This being said, all strings have elestic properties. They stretch when brought up to pitch, but their vibration also stretches them. The best was to demonstrate stretching through vibration is by doing the following exercise: Tune your low E string down to D. Only pluck it lightly and use your tuner. Once you've reached D, keep your tuner plugged in and pluck that string with a lot more force. What did the needle of your tuner do? It went sharp didn't it?

Because of the low tension in the string, there is more available elesticity. And the mass of the string vibrating from one side to the other taps into that elesticity and stretches the string, increasing its pitch and making it sharp.

So, the increased tension in heavier gauge strings helps work against this phenomenon (even though it is physicaly impossible to eliminate it). A string with low tension will also bend between the frets when your finger presses it down, also increasing it's pitch. Heavier gauge strings, therefore, will reduce the variation in pitch when picking the string and when you are fretting it.

- Sustain: In practice, this point is easy to prove. if you use two identical Gibson Les Paul's as an example, and one is setup with 10-46 strings and the other with 11-52's, the one with the heavy strings will have more sustain. But why? Back to Hooke's law. Because the heavier strings have more stored energy (F) they have more energy available for release, i.e. sustain.

- Picking speed: Picking on heavier strings takes some getting used to when you've been on light strings for a while. But since the strings don't move around as much, skipping from one string to the next is swifter and easyier to control.