A string’s gauge (thickness) is directly related to its tension. The thicker the string, the more tension it will exert on the instrument, all other things being equal.
Tension is calculated through three things:
- Pitch of the string
- Length of the string
- Mass of the string
On a bowed psaltery that we’ve already built, we can’t change the pitch, (unless we want a terrible sounding instrument!) or the length, so the only way to change the amount of tension on the string is by manipulating its mass.
Why would we want to change the amount of tension on a string? Well, one useful measurement is called the tension-to-length ratio. This measures how many pounds of tension is on the string per inch. But in the real world, what it actually measures is how tight or loose the string feels.
If the T/L ratio is low, (as is usually the case on the lowest – and longest – strings), the strings will feel very loose. Likewise, if the T/L ratio is high, (common on the shortest strings), the strings will feel very stiff and rigid. A change in this ratio will also change the properties of how the string sounds; it will still be in tune, but it will sound different. Maybe stiff, or maybe weak or thin, or a number of other things. (I will readily admit that I don’t fully understand all of the subtleties of music strings in this area.)
We vary the thicknesses of the strings in order to even out the ratio of the tension and to normalize some of the strings’ tonal qualities. If the shortest and the longest strings both have the same (thin) gauge of wire and the same amount of tension, that means that the lowest string will feel much looser than the shortest string. Even though the overall tension on both strings is the same, there will be very little downward pressure on the longest string. It won’t make strong contact with the bridge, and its vibrations won’t drive the soundboard and reach the rest of the instrument as well as the shorter strings.
To compensate for this, we can gradually increase the string gauges so that the longest string will at least have a decent amount of tension spread across the string. Similarly, we can also reduce the gauge of the shortest strings so they don’t feel quite so tight.
A lot of times, we cannot perfectly even out all of the tension and get a balanced tension-to-length ratio, but we can usually avoid any extremes on each end of the psaltery. This helps keep the tone sound even and more consistent as you progress down the strings.
Now, on our sample psaltery, I would normally vary the string gauge from .010″ to .014″ across the entire instrument, but I have instead chosen to use a middle gauge: .012″ diameter as a good in between wire for the sake of simplicity. This prevents too large of an extreme from occurring at either end of the psaltery. Since this is only a 2-octave psaltery, there is not that much of a spread of lengths between the strings anyway. The biggest diversity occurs when the strings get both very long and very short.
Now, to help clear up a few misconceptions about string gauge:
Thicker string gauges are not used to stretch the range of pitches lower, and thinner string gauges are not used to stretch an instrument’s range higher. String gauge has very little, if anything, to do with the available range of an instrument.
An exception to this is over-wound strings—common on other stringed instruments—which is a whole different animal. I’ll focus only on solid music wire in this discussion. But briefly, an over-wound string has a layer of outer winding that is meant to artificially inflate the mass of the string, (one of the three variables listed on the previous page that can influence a string’s tension). But the winding doesn’t really contribute to the string’s strength, thereby allowing it to sound at a lower frequency while maintaining the same amount of tension.
But underneath the outer windings, these strings have the very same gauges and sizes of music wire as those that are commonly used in construction of bowed psalteries. The core wires are the very same, and adhere to the very same universal principles as regular music wire; its just that wound strings are much more complex, using any number of materials (bronze, copper, steel, etc.) for the windings.
But getting back to the discussion at hand: making a plain steel string thicker doesn’t allow it go any higher or lower than it normally could. This may seem counter- intuitive, but try to follow:
If you make a string thicker, it is much stronger and will break at a higher tension. But, this increase in strength is offset exactly by an increase in mass, which is self-defeating. The string is still made of the exact same material, just more of it. In a nutshell, a thicker string is strong and can handle more tension, but it will also take that much more tension to bring that thicker string up to the same note.
On the flipside, making a string thinner doesn’t make it any weaker – at a given pitch – than a thicker string. Remember, on a psaltery the pitch and length of the string are both fixed! A thinner wire has a lower breaking point, but the wire also will require a proportionately equal reduction in tension to be tuned to the same note as a thicker wire made of the same material.
One minor exception to this is steel music wire – because of the way it is made – which has a slightly higher tensile strength at thinner gauges. This increase is mostly negligible within the small variances of diameters used in psalteries, but pound for pound, the strongest wire is actually the thinnest!
(πr2 × Tensile Strength = Breaking Point)
Here’s a real world example taken from an actual psaltery:
The string E6 (1318 Hz) on a psaltery is exactly 7 inches long. It is strung with a .010″ diameter string. Assuming a tensile strength of 387,000 PSI for this steel string, this means that the breaking point of the wire itself is about 30.39 pounds. Since it is tuned to 1318 Hz, there is about 19.6 pounds of tension on this string. At the current setup, this string is at about 64.5% of its breaking point. (And its T/L ratio is 2.8 pounds/inch, which is good.)
Now, let’s see what happens when we put a heavier string on and keep it tuned to the same pitch. (I’m sure someone, somewhere, is saying to themselves: it’s got to make a difference!) We’ll go up to a .014″ steel string, since it is the same material, the tensile strength is still at 387,000 PSI; the string therefore has a breaking point of nearly double what our thinner wire had – a whopping 59.57 pounds for the breaking point! Now, accordingly, it is also that much thicker too, and yes, I’m sorry, but it will take a full 38.4 pounds to bring this hefty string up to the frequency of E6 (1318 Hz.) With the current setup, this bigger, tougher, stronger string is at about – well, surprise, surprise! – we’re still stuck at 64.5% of the string’s breaking point! (And the T/L ratio has been raised to around 5.5 pounds/inch, which is rather high.)
And here’s another kicker: that thicker .014″ wire – which was assumed to have an equal tensile strength of 387,000 PSI (on average) – is actually a tad bit weaker due to how steel music wire is manufactured. It’s more like 369,000 PSI (average) tensile strength, so the breaking point is really closer to 56.9 pounds. So in reality, the 38.4 pounds of pressure we needed to bring it up to pitch was stressing the string at close to 67.5% of its limit, not 64.5%.
Basically, string gauges are used to control tension and the T/L ratio, not an instrument’s range. When dealing with steel music wire, the vibrating length of the string is what determines its range.
Great article, thanks!
Considering two examples at the end of the article, there are:
1. And its T/L ratio is 2.8 pounds/inch, which is good.
2. And the T/L ratio has been raised to around 5.5 pounds/inch, which is rather high.
So, what is the “normal” range for T/L ratio?
According to the Smithsonian Physical Tables the smaller the diameter(the smaller the extruded grainsize) the higher the tensile strength. On my tenor banjo the tension is 23.9# for 440Hz and 23″ scale which equals 305,000psi and then you bang on it with a pick increasing its tension. A .012″ diameter “A” string is under the same tension. The formula is the force is equal to the frequency times diameter times length/20.7 quanity squared.. Hope this helps.