Arto's String Calculator, version 2.2. Don't forget ENABLE JavaScript and Java! (v. 2.2 in 14.9.04) (v. 2.1 in 24.4.03), original version 1996)

The Note Properties:

Name	Octave	Tuning
c c sharp d e flat e f f sharp g g sharp a b flat b	C'' - B'' C' - B' C - B c - b c' - b' c'' - b'' c''' - b''' c'''' - b'''' c''''' - b'''''	a' = 415,3 Hz 440 Hz

This produces the frequency: Hz

Then you must set the string properties: the vibrating length of the string in millimeters and the density of the string material in Kg/m³. The latter may be the tricky part, if the string maker didn't provide that data. See 'Help on selecting the string material density'.

After setting these parameters you can start making the calculations. There are two basic ways:

1. You can give the string diameter and see, what would be the corresponding string tension. This is useful for example, when you want to know "Can I use this string for that course?"
2. You can give the desired string tension and check, what string diameter you need to achieve it. This is useful, for example, if you already know that some string feels good, and you want to find out, what diameter to use to get the same tension for some other course.

Of course you can make also other kind of calculations. Some examples:

• You have a string and you want to know, where it can be used. Just set the diameter and change the note. Or change the string length.
• You just want to know the frequence of a note. The calculator always shows the frequency of selected note. Do not edit the frequency field.
• ...

I made this calculator lute instruments in mind, but of course it can be used to calculate string tensions and diameters for whatsoever stringed instrument: harpsichord, harp, viola da gamba, guitar, ..., even grand piano. It is, anyhow, very important to understand that it can calculate only plain string calculations! Thus wound strings, catlines, and such, are excluded.

The allowed ranges of input values are:

note	C''(415) to b'''''(440)
frequency	15.4 - 7902.0 Hz
string length	10 - 4000 mm
string density	500 - 15000 Kg/m³
input diameter	0.01 - 20.0 mm
input tension	0.01 - 100 Kg

Absurd results are allowed, see the advice on selecting tension and diameter.

Back to the calculator

When a string would become too thick to sound well, densier material can help. That is why loaded (densified) gut can be good for lute bass strings. On the other hand, dense material - for example "carbon" (high density hydrocarbon polymer?) - may be too thin for the top string.

If you select denser and thinner string, the sound can be clearer and 'sharper' than a less dense (and thus thicker) alternative.

Some example densities (If you click one of the 'radio buttons', that value is set to the Density field of the calculator! Of course you can also edit the field):

1000 Kg/m³, nylon
1276 Kg/m³, gut
1791 Kg/m³, "carbon" (high density hydrocarbon polymer?)
7800 Kg/m³, iron
8600 Kg/m³, brass

Densified (loaded) gut weights more than gut, but less than "carbon" (high density hydrocarbon polymer?).

If you don't know the density, but you have the string, you may measure its diameter, length and weight, and then use this "sub-calculator" (it is a Java-applet):

Your browser doesn't support Java!

At the moment, you have to copy the calculated value to the Density field of the main calculator! (Perhaps some day it will go there automatically.:-)

Back to the calculator

But the matter is quite complicated: For top strings I use more (for example my archlute's 67 cm top g has 4.0 Kg, but that is quite much). If the instrument has single strings the tension can be more than with double courses. The octave doubles should have less tension than their counterparts. It might be good idea to lessen the tension slightly towards bass. When there is difference of length between neighbouring courses (lutes with bass extension), the lowest short basses could have more tension than the highest long basses, to lessen the difference of sound quality. Etc., etc...

Experimenting is the only way of finding well sounding tensions for each lute and string material. And the sound of all courses should be balanced ...

About harpsichords, harps, violas, modern guitars, grand pianos, ..., I do not say anything. (If somebody wants to tell me some clues, I'll be happy to add them here)

You can produce also crazy tensions with the Calculator , but remember that no string or instrument will stand 50 Kg's tension per string (well, perhaps grand piano :-). I have not tried 5 Kg's or more in my lutes, and nobody will do that with my lutes!

Also very small tensions can be calculated, but I think 1 Kg is too little for a lute string.

In my opinion a reasonable range for lute string tensions is something between 1.7 Kg and 4.9 Kg.

Back to the calculator

If I am selecting the top string to a lute whatsoever (well not the theorbo), and if I use nylon, my first thought is 0.45 mm. This has worked quite well.

You can also calculate crazy diameters with the Calculator , but nobody is selling such strings to you. Think for example a string with diameter of 5 mm: what could you do with that? Well, perhaps hang out your laundry ... A gut string of diameter 0.1 mm couldn't stand any reasonable tension...

The only way of finding well sounding string diameters is by making experiments. All depends on the lute and the string material chosen.

About diameters of metal strings for harpsichords, Irish harps or grand pianos I do not say anything. (If somebody wants to tell me some clues, I'll be happy to add them here)

Back to the calculator