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  String Gauges for Alternate Tunings
1. Introduction
The "standard tuning" of a guitar (EADGBE, from low to high) is a highly versatile tuning, and conveniently accommodates everything from hard rock and heavy metal to baroque or classical music. However, many guitarists also use so called alternate tunings, of which countless versions exist. Because guitars and most string sets are designed for standard tuning, alternate tunings may bring some complications and sometimes risks, such as a degradation in sound or intonation, low volume, bad playability, or even damage to the guitar. This article explains the ins and outs of alternate tunings, and gives solutions to prevent potential problems.
(A detailed mathematical description of both solid and wound guitar strings can be read here.)
2. Alternate tunings
Alternate tunings make it possible to play tonal combinations on a guitar that no mortal man could ever play in standard tuning. Moreover, the unexpected things that happen (because you are used to standard tuning) can be very inspiring. The number of alternate tunings is only limited by our creativity. Some popular alternate tunings are:
DADGBE (also called Dropped D tuning)
DGDGBD (also called open G tuning)
CGDGCD (also called Orkney tuning)
DADGAD
DADEAD
EADEAE
CGDGAD
...but many more exist. You create alternate tunings simply by adjusting the string force of each appropriate string. Higher force for a higher pitch, lower force for a lower pitch. However, guitars and most string sets are designed for standard tuning, so if we change to alternate tunings, several things must be kept in mind.
1. When you tune a string lower, there will be a loss of tone and volume. Sometimes the string will start to buzz against the frets, because the lower force will also increase the vibrational amplitude (the lateral motion in the middle of the string after you pick it). At lower force, the string will also be more sensitive to the force in your left hand (i.e. the fretting pressure) and sideways string bending, which may degrade your intonation.
2. Alternate tunings may have some strings at normal force, some at higher force, and some at lower force. This may create an unevenness of tone and feel.
3. When you tune a string higher, the string force increases. If overall string force gets too high, your neck may need readjustment, or the playability of the guitar will suffer. You also risk breaking strings, or even worse, cause damage to the guitar!
For all of the reasons above, an unwritten rule is to not to tune a string higher than 1½ steps, or lower than 2 steps from its standard pitch. If you want to push it further, it is recommended to substitute the 'extreme' strings with different gauges: thicker if they are tuned down, thinner if they are tuned up. If you often play in one specific alternate tuning, it may even be a good idea to create your own dedicated, custom string set. After all, loose strings can be purchased at many musical stores and everywhere on the Internet.
The question that immediately arises is: Fine, but what gauge of strings do I need then? For those of you with little patience, the answers are in the table below.
Recommended guitar string gauges for various tunings.
S= standard tuning, G = open G, D = DADGAD, O = Orkney.
Those of you who want to know how I got to these numbers are invited to read the rest of this article, and descend with me into the dark and cold dungeons of theoretical physics. It's a place where you can learn a lot... :-)
3. Physics of the Vibrating String
The behavior of vibrating strings has been under the attention of scientists and other smart guys since thousands of years. So we are going to skip all the theory and present the result that they have come up with in the end. Here it is (don't get intimidated):
 This fundamental formula predicts the tone a string will produce, once you know the tension, the string length, the diameter and the weight of the material it is made of. Those of you who did not like physics in high school, stay with me! It's going to be fun.
Let's have a closer look, and explain the symbols.
 The f stands for the string vibration frequency. This is the number of times the string moves left and right, after you pick it, during a time interval of one second. For example, the A string on a guitar has a (fundamental) frequency of 110 Hz, pronounce: "Hertz" (has nothing to do with rental cars). Consequently, after you pick it, it will produce exactly 110 oscillations per second, provided the guitar is tuned correctly, of course. The m stands for the specific mass of the string. This is the weight (in kg) of one cubic meter of string material. For steel, this in the order of 8000 kg. The p is the famous number pi, equal to 3,1415... The T stands for the pulling force of the string. This force will act on the bridge and on the tuner in the headstock. Typically, this force amounts to some 100 to 150 N (pronounce: Newton), which corresponds to approximately 10-15 kg (some 20-30 lbs). The L stands for the string length (in meters). A typical steel string guitar has a string length of 25½ inch, or approximately 0.65 m. The D is the string diameter (in meters). Most of the time, string diameters are given in inches. For example, a '012' string has a diameter of 0.012 inch, which is a little more than 0.3 mm (0.0003048 m). Strictly speaking, this formula is only valid for unwound strings. In practice however, it will give adequate results if used for wound strings too (the discrepancy is typically limited to some 10%). So we will use this formula now to understand some fundamental properties of guitar strings, things that all guitarists experience every time they play, or change strings.
4. String Tension versus Weight
In the formula given earlier, you see that the square root of the string tension T is divided by the square root of the (specific) string mass m. This means that if you change a string for another one, fabricated with, say, two times heavier material, the string tension must also be made two times larger in order to get the same note. Conclusion:
Now you will understand why nylon strings have lower tension than steel strings. It's because nylon weighs less than steel. In fact, nylon weighs so much less than steel, that if you would take an unwound nylon string as thick as an unwound steel string, the string tension would be very, very low, and the string would be completely unplayable. That is why unwound nylon strings are made so thick . This increases the weight, which allows for a higher tension.
The wound strings of a nylon string guitar have windings made of metal alloys (bronze etc.) so here the difference in mass, and hence in string diameter, is less in comparison with a steel string guitar. But because the core of the string is made of nylon fibers in stead of steel, the string is usually lighter and consequently has a lower tension than a wound steel string (which has a steel core).
5. String Pitch versus Length
If we consider one single string on a guitar, its weight and its tension are constant (as long as we don't touch the tuners, of course). Consequently, the only thing we can do to produce another note on that string, is to change its length L. This is, of course, the whole principle of playing guitar and that is exactly why we have frets on the fretboard.
If you fret the string at the 12th position, you will reduce the length of the string by a factor of two (because the 12th fret is located exactly at the middle of the string). From the formula, you see that the string will now produce a tone of twice the frequency:
Because a string fretted at the 12 position corresponds to one octave, we also know now that one octave higher corresponds to twice the frequency.
There are more interesting proportions that we can figure out. For example, a string fretted at the 5th fret creates an effective string length equal to 3/4 the length of the open string (take a ruler and check it if you want). The frequency will then be 4/3 (just reverse the numbers) times the frequency of the open string. So, if you fret the A string on the 5th position, the corresponding note, a D, will therefore produce a frequency of 4/3 times 110 Hz (the frequency of the open A, remember?) which makes 147 cycles per second, or 147 Hz.
A string fretted at the 7th fret creates a string length of 2/3 times the length of the open string. The frequency will then be 3/2 times the frequency of the open string. With a little bit of effort (and maybe a ruler), you can derive all the fundamental proportions from music theory.
An interesting rule of thumb is that a half note corresponds to approximately six percent change in frequency:
You can also say:
6. String Pitch versus Tension
At this point we are going to have a look at what happens with alternate tunings. I paste our formula once more in the space below, so that you don't have to scroll up and down all the time.
Before we proceed, we must address the common belief that the thicker strings on a guitar have a higher string tension than the thinner strings. This is not true.
This means that the thick, fat, low E-string pulls with more or less the same force as the tiny little high E-string, or any other string in between. Many people think that the thick bass strings pull much harder, but this is not the case. A guitar with an uneven string tension would be very uncomfortable to play, because you would have to adjust the force in your fingers for every different string you play. Therefore, the strings of a guitar have (nearly) identical tension by design, and the different fundamental frequencies of the open strings are a result of the different diameters only.
For those of you who want to understand this all in more detail, we will simplify our formula somewhat.
We assume that all strings are made of the same material (more or less correct for a steel string guitar), so m is the same for all stringsWe don't consider fretted strings, so L is the same for all stringsWe adjust the tuners so that all strings have identical tension, so T is the same for all strings. Under these assumptions, we can simplify the formula as
f equals a constant number divided by D
or, in other words, the vibration frequency is inversely proportional to the string diameter. So: twice the thickness produces half the frequency (one octave lower), half the thickness produces twice the frequency (one octave higher).
Some manufacturers list the string tension on their packaging. Here is an example for a set of d'Addario EJ16 strings:
As you can see, the string tension is indeed more or less identical for all strings. We also see that the low E string, two octaves lower than the high E string, has a four times (two times two) larger diameter. The deviations are typically by design. For example, the manufacturer may decide to adjust the properties of some strings for a better overall balance in tone, volume or feel. Also, the wound strings are made of various materials with different masses, and the effect of the windings has not been incorporated in our formula. This causes some discrepancy if you compare a wound string with a plain (unwound) string. Nevertheless, the rule of thumb that frequency is inversely proportional to string diameter has good overall validity for strings of the same type (wound or plain).
7. String Tension versus Gauge
We all know that a set of thin strings are easier to play than a set of thick strings. As discussed before, the reduced diameter will increase the pitch, which is compensated with a lower tension. Therefore, they require less force in your left hand. The easy playability comes at the cost of volume: the reduced string mass has less energy when the string vibrates.
If your guitar is hard to play, one option you have is to change to lighter strings. But how much lighter? That would be a nice thing to know before you buy the new strings. In order to answer that question, we will first reshuffle our formula, using the elementary rules of algebra. The result is:
 ...which basically says that the square root of the string tension is proportional to the frequency, proportional to the string length and proportional to the string diameter. This means that a reduction of, say, 6% in string diameter has the same effect on the string tension as a reduction of 6% in frequency (after all, you have to multiply these two in order to get the tension, right?). I take the 6% as an example, because earlier we have seen that a 6% change in frequency corresponds to a half tone.
So, we can also say:
This is an interesting finding, because it allows us to create a table of various string sets, corresponding to the string tension of your original set when you tune down (or up) a half step. This allows us to get a good idea of how our guitar will play with another gauge of strings, simply by tuning the guitar down (or up).
Puzzled? Let me put it this way then. All you need to do is take your original string diameters, and decrease them with 6%. This would give the same string tension as when you tune down a half step. Similarly, increasing the string diameters by 6% would correspond to the string tension of you tune up a half step.
Let's put it all in a table, taking a typical light set (012, 016, 024, 032, 042, 053) as a reference.
So, what this table tells you, is that when you currently have a 012-053 set on your guitar, and you tune down a half step (a half note), the string tension will correspond to a 011-050 set at standard tuning (one column to the right). This will give you a good idea of what you can expect if you change to that lighter gauge.
8. String Diameter for Alternate Tunings
At this point, we can expand the table made in section 6 for more frequencies than just those corresponding to the notes EADGBE, by using our rule of thumb that string diameter times frequency must be constant. In this way, we can produce a table with string diameters for all sorts of open tunings, which will have even string tension.
A smarter approach is to take a popular set of guitar strings as a reference, including any adjustment that was done by design, and interpolate (still using our formula to obtain an even string tension). This method was used to produce the table at the beginning of this article. The reference sets were chosen as follows:
The recommended string diameters are listed below. The dots correspond to several popular tunings (S= standard tuning, G = open G, D = DADGAD, O = Orkney).
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