RAVI

Since I am in India right now ... Our great Ravi Shankar passed away last year, an era which disappears.
  I attended one of his concerts in the 70s, I remember fondly his courage in trying to explain what is Classical Indian Music to a public of junkies ...

  In his wonderful book "My Music My Life", partly autobiographical, and especially devoted to Sitar, his instrument, there is, without comment, an image of an ancient harp or harp-zither from India, apparently from the nineteenth century or the early twentieth :

  The reproduction is not great, but you can still see how it looks, a bit like the Burmese harp, which is probably of Indian origin. It is a harp without pillar (what might suggest a pillar is the shadow of the neck...), like many Oriental and African harps.
  On the neck, there is a series of bridge pins, and the strings are wound around wooden pegs, very ornate, and arranged on top.
  On the body, a bridge, and probably a tailpiece below.
  What is curious, but anything is possible in India, is that this instrument seems to have disappeared...?
Dimensions? Tessitura? Gut strings or metal? One element could be useful, the spacing between strings, but deduct all other dimensions from there...
  I did some research with the Hindi name given by Ravi Shankar, "mandal Viladi nada" but nothing ... the term "mandal" (circle) indicates all kinds of circular objects, but no harp...
  Does anyone has already seen (and heard!) this device somewhere, or knows a bit more about this?

CALCULATING THE TENSION OF A STRING: THE TAYLOR EQUATION

A simple enough way to implement the famous "equation of Brook Taylor" (English mathematician and musician of the seventeenth century) :

- Measure one, or better several strings of the considered diameter ;
- Weigh them with the most accurate balance as possible: the greater the length of string, and the most precise will be the weighing, of course.
- Determine the MASS PER LENGTH UNIT (m) by dividing the value weighed in kilograms by the length in meters.

The equation reads:

 Where:
f is the frequency in Hertz of the pitch,
k denotes the harmonic wanted (here equal to 1),
L is the length of the string,
F is the tension of the string we are looking for,
m is the mass per length unit that we have calculated.

We raise it to the square to eliminate the root, we make some permutations to rewrite the equation in a more convenient form :

                              

Consider an example: Let a nylon Tynex string tuned A4, 440 Hz, 0.4 m (40cm) long.
We take a string 1mm in diameter, which measures initially 1.33 m long and weighs 1g or 0,001 kg (be careful not to tangle with the zeros!).
The mass per length unit is m = 0.001 / 1.33 = 0.00081 Kilo /meter.

We can now replace the terms of our equation by numeral values:

F = 0.00081 X 440 X440 X 4 X 0.4 X 0.4 = 100.36 N

N  for "Newton" which is the unit of measurement of the tension. To obtain this value in kg we must divide by the coefficient 9.81. This gives us: F = 100.36 / 9.81 = 10.23 kg (At the sea level..).

If a string of the same length but 0.9 mm in diameter is placed, a tension of 8.71 kg is obtained, it may be a little dull... For a string of 1.25 mm in diameter, on the other hand, we get 17.17 kg of tension, almost double! Rude for the fingers and the soundboard ...

One note: as the tension is proportional to the square of the length, one can see why, especially in the trebble range, a difference of one or two centimeters can be problematic: the strings break in rehearsal ... and as this same tension is also proportional to the square of the frequency, the solution is, of course, often, to tune the pitch lower ...

These explanations are all my master's of science and friend Yann Baol Le Noalleg, poet, mathematician, physicist and distinguished Breton speaker...