Modeling the stiffness of the string

The stretching of the frequencies of the partials can be calculated as:

$$f_{n}=n f_{0}\sqrt{1+Bn^{2}}$$

where $B= \frac{\pi^3 E d^4}{64 l^2 T}$ =inharmonicity factor,
$f_{0}$ =fundamental frequency of the string.

E=Young modulus of elasticity, d=diameter.

Physical constants of a Dominant violin string, from Pickering

String	E (N/m)	d(m)	l (m)	T	B
E	15.7	0.000307	0.565	72.56	5.1627e-15
A	7.470	0.000676	0.59	56.25	6.5418e-14
D	6.4	0.000795	0.567	43.72	1.5707e-12
G	6.035	0.000803	0.567	44.57	1.4963e-12

Physical constants of a gut violin string, from Schelleng.

String	B
E	1.5598e-05
A	4.8527e-05
D	2.4841e-04
G	1.3e-3