  The spectrum of three-diagonal self-adjoint $p$-periodic Jacobi matrix with
positive off-diagonal elements $a_n$ an real diagonal elements $b_n$ consist of
intervals separated by $p-1$ gaps $\gamma_i$, where some of the gaps can be
degenerated. The following estimate is true $$
  \sum_{i=1}^{p-1}|\gamma_i|\geq\max(\max(4(a_1...a_p)^{\frac1p},2\max
a_n)-4\min a_n,\max b_n-\min b_n). $$ We show that for any $p\in\mathbb{N}$
there are Jacobi matrices of minimal period $p$ for which the spectral estimate
is sharp. The estimate is sharp for both: strongly and weakly oscillated $a_n$,
$b_n$. Moreover, it improves some recent spectral estimates.
