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What is Equal Tension?
By Daniel Larson
Well, let’s first define what tension is; simply, it is a pulling force. When it comes to strings, the more you turn the peg on the instrument, the more pulling force you are putting on the string. The tension — or pulling force — is also related to the weight of the string, in that, the heavier the string is, the faster the pulling force is going to increase as you turn the peg. These days, this pulling force is measured with a Newton unit, which is how much force is needed to move one kilogram one meter of distance. However, in the 16th century, they did not yet know the relationship between mass and distance to express force, so they used weight units to describe the tension. Technically, weight is a measure of gravity's effect on an object, but gravity is a constant enough force to be used as a standard of measurement. During experiments in the 16th century, investigators would hang weights from the strings to know precisely how much force was on each string. This concept is still useful today; when you have a string with five kilograms of tension, you can imagine a five-kilogram weight hanging from the end. This tradition is still used as a standard of measurement for tension on strings. We can see that the tension is related to the weight of the string. With gut strings, since it consists of only one material, the only way we can change the weight of the string is to increase or decrease the string's diameter to add or remove mass. The string's gauge is vital because it determines the mass, and therefore the weight of the string, and ultimately, the tension.
When designing a set of strings for any instrument, there are two choices:
All of the strings can have the same tension. This system is referred to as “equal tension.”
The tension varies from string to string. This system is referred to as “graduated-tension,” or “scaled-tension.”
In the graduated tension scheme, the first or highest-pitched string has the most tension, the second string has a little less than the first, the third has a little less than the second, and so forth to the instrument's last string. However, this is not true for contrabass instruments, where the tension tends to increase on the lower strings due to some odd physics concerning those lengths and pitches.
Graduated Tension
Our standard Academie sets of strings represent an example of graduated tension. For example, the gauges and tensions of our medium set on a traditional violin tuned to a-415 would be:
e-1 - 0.56mm (5 Kg tension)
a-2 - 0.76mm (4.2 Kg tension)
D-3 - 1.04mm (3.5 Kg tension)
G-4 - 1.48mm (3.2 Kg tension)
For many years, musicians have acknowledged this scheme as having an even “feel” across the strings, being comfortable and responsive to play. Measuring many strings from the late 19th and early 20th centuries, it is apparent violin string gauges with this scaled system have been standard for at least 100 years. Different manufacturers have various ideas about how the tensions of the strings should relate to each other. Still, this graduated system has been in practice at least for most of the modern era.
Equal Tension
In 1636 Marin Mersenne was one of the first scientists to publish exact information about how strings and instruments should be scaled and proportioned to each other. The exact details are intricate, and there are some inconsistencies in his conclusions, but the general gist is that he recommended that strings be proportioned in size so that they all had the same tension when tuned to pitch. It is possible that this was a theoretical exercise, as he mentioned that some musicians do not adhere to these principles, indicating that some practiced a graduated-tension system. He gave no details.
Throughout history, equal tension has been supported and criticized, but it is a legitimate performance practice that may give you the tone you are looking for. The most noticeable feature of the equal tension setup is that the bottom strings are tighter, which will provide more power to most instruments. Additionally, most players feel an evenness across the strings while playing, which is pleasing. Some adjustments in playing may be needed, For instance, the bow may need to move away from the bridge to find a sweet spot, and bow speed and pressure may need to be modified. However, most musicians make subtle adjustments naturally, without much thought.
The advantages of equal tension are:
More power on the bottom and middle of the instrument.
A more even feel across the strings.
Even tone across the instruments.
A balanced pressure on the bridge and front plate.
More balanced tonal projection.
Figuring Equal Tension Gauges
One of the most interesting characteristics about the relationship of one string gauge to another in the equal tension system is how the strings' weights follow the same proportions as the musical intervals. As you know, musical intervals can be expressed as fractions:
Perfect Fifth = 3/2 = 1.5
Perfect Fourth = 4/3 = 1.33333
Major Third = 5/4 = 1.25
Let’s say you have a violin to string and you want your e-1 string to be 0.60mm. To find the matching tension for the a-2, you can simply multiply 0.60 with 1.5 to get a gauge of 0.90mm. That can be multiplied by 1.5 to get a 1.35mm d-3, and subsequently 2.02mm for the G-4. These specifications would allow the violin to have the same tension on each string at any pitch, as long as the intervals between them are fifths.
We can calculate strings of viols and lutes in the same manner. Let’s consider a bass viol with a d-1 gauge of 0.74mm. That can be multiplied by 1.33333 to get a gauge of 0.99mm. That gauge can be multiplied by 1.33333 to get 1.31mm for the e-3. Here in the process, the interval changes to a major third, so 1.25 needs to be the multiplier to obtain the gauge of 1.65mm for the C-4 string. Then, back to the 1.33333 major fourth to calculate 2.20mm for the G-5 string. Finally, the D-6 can be estimated at 2.94mm. The process will build up some errors as numbers and gauges are rounded up or down, but with this multiplying technique, you can get close to perfectly equal proportions.
Alternately, you can go to our string calculators and choose the page for your instrument. Experiment with different values for the first string until you find the gauge that you want for that position. Then, use that value for all of the other strings.
Types of Equal Tension Strings
Our store has sections devoted to standard equal tension sets for violin, viola, cello, bass viol, tenor viol, and treble viol. The lower strings are available in these catalogs as plain gut Pistoy and Gimped construction or as gut-wrapped with either silver or silver-plated copper wires. For those who play other instruments or want non-standard gauges, we have choices of all the different types of strings that we make in almost all useful gauges in our Custom Gauge catalog.
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Hand-made in the USA by Gamut Music, Inc., a leader in the revival of early music strings and instruments. Gut strings are not intended to be used with fine tuners or string adjusters, and those devices should be removed before installing the gut string on the instrument.
All Gamut Academie strings (pure gut and gut/metal-wound) are made with beef serosa unless they specifically say "Sheep Gut." All pure gut Tricolore violin and viola strings are made with sheep gut; gut/metal-wound Tricolore and all Red Diamond strings are made with beef serosa.
Gamut gut string gauges are approximate (≈) diameter. Meaning, that while a ≈0.60mm string is polished in the workshop to a diameter of 0.60mm, changes in ambient humidity, temperature, shipping, and storage conditions can cause to string to expand or contract slightly.
Gimped gut strings and custom gauged equal tension strings are gauged with the equivalent-gauge (=) system. This means that the gauge listed, such as =1.50mm, indicates that the string is approximately equal in weight to a plain gut string of that diameter. Of course, because the wire is much heavier than gut, the string will be much thinner than a plain gut string.
More information about Gamut gut strings, string types, gauges, and string tensions can be found on our FAQ/Articles page. Not finding an answer to your question? Please contact us directly: support@gamutmusic.com.