Arto's String Calculator, version 2.2.

(3 Oct 2007) Now there is also a Mobile Phone Version of this calculator! (Corrected version is 1.4 If you took the earlier version, please replace it by 1.4 or later.)

The Note Properties:
Name Octave Tuning
a' =
This produces the frequency: Hz

The String Properties:
Length: mm Density of the material: Kg/m
Give this Calculate The Result
Diameter: mm
Tension: Kg

Do you need help on selecting the
Density Tension Diameter

Using Arto's String Calculator

The calculator functions only with browsers that know JavaScript-language (for ex. Netscape Navigator 2.0 or more)! Don't forget ENABLE JavaScript!

When using the calculator, you must first select the note: its name and the octave. There is also the choice between two tunings, the 'modern': a'=440 Hz, and 'baroque': a'=415 Hz. (Here we actually use 415.3 Hz instead, because equal temperament was used for the frequences. The difference is not significant.)

Then you must set the string properties: the vibrating length of the string in millimeters and the density of the string material in Kg/m. 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:

There is more information of tension and diameter in 'Help on selecting the string tension' and 'Help on selecting the string diameter'

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/m
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.

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Help on selecting the string material density

The main principle of selecting string density is: The denser the string material, the thinner the string needed for the same note.

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:

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

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Help on selecting the string tension

My first thought for a lute string tension is about 3 Kg.

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.

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Help on selecting the string diameter

The diameter of nylon, gut and "carbon" (high density hydrocarbon polymer?) strings for lutes normally varies from about 0.3 mm to 1.4 mm. Already these extremes may have unwanted properties and are seldom used: very thin string may sound 'picky', and also break easily, very thick may be quite dull.

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)

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Copyright Arto Wikla, 1996
Version 2.0, 15.5.1997

My other pages: Music page / Homepage
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