  In the Regge phenomenology, the radial spectrum of light mesons is given by a
linear relation $M_n^2=a(n+b)$, where $a$ is a universal slope, the
dimensionless intercept $b$ depends on quantum numbers, and $n$ enumerates the
excited states in radial recurrences. The usual extensions of this relation to
heavy quarkonia in the framework of hadron string models typically lead to
strong nonlinearities which seem to be at variance with the available
experimental data. Introducing a radially static string picture of mesons, we
put forward a linear generalization $(M_n-m_1-m_2)^2=a(n+b)$, where $m_{1,2}$
are quark masses. The vector channel contains enough experimental states to
check this new relation and a good agreement is observed. It is shown that this
generalization leads to a simple estimate of current quark masses from the
radial spectra.
