INDIAN MUSIC FORUM ARCHIVES: Sitar Forum: string tension on indian instruments

I am an amateur lute and guitar player
interested in indian classical music and
instruments.

I am looking for informations on string
tension on indian string instruments,
mainly for sitar, sarod, tanpura.

For instant, on a sitar the string tension
of the playing strings can't be to high
because pulling the string to the side
even further increases the tension
extremely (?)

Does anybody have informations on this?
Alternativley: What are typical combinations
of string length, diameter and material on
those instruments?

Greetings,
Stefan

peace,

Remco

Thank you both for your replies.

Remco, I agree, that the string tension
depends on a lot of factors, as you
mentioned. I was just especially curious
about the meend technique. As a physicist,
I like to calculate things and I
found that if a sitar player pulls a string
to increase the tone by one fifths this
will more than double the string tension!
So I asumed initial string tension must be
lower than on the instruments I play
(guitar,lute), otherwise I can only pity
the poor sitar player's hand. (I have read
somewhere, that sitar player's can play a
fifths on one fret, perhaps this is wrong)

K.K., thanks a lot for your two links. They
are indeed good sources for information
on strings!

Greetings,
Stefan

thank you for your clarification on
meend on the sitar. I was not sure
about these large intervals, because
to me it seemed to be too demanding
for the left hand fingers.

Greetings,
Stefan

Question for you. You mention that you found that the stress doubles for every fifth that's bent. How would that be determined if you don't know the original tensional stress? Just curious. . .

yes, string length and gauge are
surely very important for the
string's stability. I think the
crucial points here are the points
were the string is fixed at the
bridge and the nut. On a long
string instrument the side movement
of the string while pulling
is smaller compared to the string
length than on a short string
instrument. Thus the stress on
the fixing points is not so strong
and the string will last.

However, I still wonder about the
player's hands. I think it must
be a painfull experience to learn
playing the sitar in the beginning.

The calculation of the string tension
is as follows. The square of the
frequency of a string is proportional
to the string tension:

freq^2 = c*tension.

c is a constant that depends on the
string length, diameter and density.

If you use this equation for two
frequencies freq1,freq2 and the
corresponding tensions tension1,tension2
and divide the two equations this gives:

(freq2/freq1)^2 = tension2/tension1

The frequency of a fifths is 1.5 times
higher than that of the groundnote. Thus
in this case:

tension2/tension1 = 1.5^2 = 2.25
= more than doubled

For an octave on surbahar the
frequency is even twice as high, so
the tension2 is 2^2=4 times higher than
the initial tension1!

Greetings,
Stefan

---

Stefan (Jun 17, 2002 07:58 a.m.):
Hi Remco and K.K.

Thank you both for your replies.

Remco, I agree, that the string tension
depends on a lot of factors, as you
mentioned. I was just especially curious
about the meend technique. As a physicist,
I like to calculate things and I
found that if a sitar player pulls a string
to increase the tone by one fifths this
will more than double the string tension!
So I asumed initial string tension must be
lower than on the instruments I play
(guitar,lute), otherwise I can only pity
the poor sitar player's hand. (I have read
somewhere, that sitar player's can play a
fifths on one fret, perhaps this is wrong)

K.K., thanks a lot for your two links. They
are indeed good sources for information
on strings!

Greetings,
Stefan

---

E = MC2

Energy is equal to M (mizrab stroke force) x C (cuss words from cut on finger) x 2 (number of beers consumed in a rapid fashion).

Your very welcome. . .know what I mean, know what I mean?

Russ: I omitted the constant c because
it was not important for the above
calculations, but since you are going
to do your own calculations, here is
the complete formula:

freq^2=tension/(4*string_length^2*density)

string_length from bridge to nut. Density
is mass per volume of the string material.

The string tension is measured in any unit
of kind "force per area". I am familiar with
the metric system, so I would use
newtons/millimeter^2. psi should work too.
However, I don't how the "pounds" in psi
is defined (it should be a force unit) and
how it relates to the mass units. In any
case all units on the right side of the
equation must cancel out to give
Hertz^2=(1/s)^2, the unit of the left side.
You can use unit converter, to find relations
between different units, for instance:
http://www.pmel.org/unitconv.htm

I finally found the time to go trough the
recommended links, so can give an example.
According to the sitar tuning chart at
http://www.silverbushmusic.com/sitartuning.html
the highest playing string is tuned to Ma,
which corresponds to western f,
freq = 175 Hz
diameter = 0.012 inch = 0.3048 mm
I assume a string lenght of 0.9 m.
This might me completly wrong, I have never
seen a sitar close enough.
density = 7800 kg/m^3 (steel)

With these values I calculate

tension =4* (175 Hz)^2*(0.9m)^2*7800kg/m^3
= 773955000 Newton/m^2

Thus the force on the string would be
tension * area:

force = 773955000 Newton/m^3 * 3.14159 * (0.0003048 / 2)^2 m^2
= 56

10 Newton roughly correspond to the weight of 1 kg.

Thus, if the values I used a right, and you do
a 5 step meend (thus you double the tension), this is as if you were pulling on a string that is streched by more than a
10 kg weigth. Ouch!

Good luck with your calculations,
greetings,
Stefan

P.S.: sorry for this lengthy post

Jerry- Don't worry, this is just a sideline! Physics is not my bag either, although it is in my background. We are here for the music. But keep in mind that J.S. Bach used mathematical relationships between numbers to develop tempered tuning, the backbone of all western music. And hey, the Greeks do make a terrific gyro!

Stefan- Like Jerry said, wow! You've already got me scratching my head. But two things came to mind reading your results. First, I wouldn't use standard grade steel density for this one. I would use the body-centered crystalline, high temperature, high pressure, and high-carbon polymorph known in the materials trade as martinsite (type of cryowire, see the Silverbush description of this). Should yield significantly higher density. Secondly and more musically related, the force needed to play a clean note (or bend the note) increases as you move up the scale to the next higher note. Since I believe the frequencies (notes) are not fundamental integers of each other, the stress would increase by a log function. Therefore, it would be an upslope curve if you graphed frequency vs force, the curve being the constant of proportionality. A great deal more force is requied to pull a 5 note meend at the high C fret than is required at middle C. Don't need math to tell me that one as my fingers would do the talking (owwww)!

I also apologise for this long thread, but at least my bobbin is empty now. Sure wish the font size would quit doubling with each new paragraph. That's annoying!