  Complex-mass (finite-width) $0^{++}$ nonet and decuplet are investigated by
means of exotic commutator method. The hypothesis of vanishing of the exotic
commutators leads to the system of master equations (ME). Solvability
conditions of these equations define relations between the complex masses of
the nonet and decuplet mesons which, in turn, determine relations between the
real masses (mass formulae), as well as between the masses and widths of the
mesons. Mass formulae are independent of the particle widths. The masses of the
nonet and decuplet particles obey simple ordering rules. The nonet mixing angle
and the mixing matrix of the isoscalar states of the decuplet are completely
determined by solution of ME; they are real and do not depend on the widths.
All known scalar mesons with the mass smaller than $2000MeV$ (excluding
$\sigma(600)$) and one with the mass $2200\div2400MeV$ belong to two
multiplets: the nonet $(a_0(980), K_0(1430), f_0(980), f_0(1710))$ and the
decuplet $(a_0(1450), K_0(1950), f_0(1370), f_0(1500), f_0(2200)/f_0(2330))$.
It is shown that the famed anomalies of the $f_0(980)$ and $a_0(980)$ widths
arise from an extra "kinematical" mechanism, suppressing decay, which is not
conditioned by the flavor coupling constant. Therefore, they do not justify
rejecting the $q\bar{q}$ structure of them. A unitary singlet state (glueball)
is included into the higher lying multiplet (decuplet) and is divided among the
$f_0(1370)$ and $f_0(1500)$ mesons. The glueball contents of these particles
are totally determined by the masses of decuplet particles. Mass ordering rules
indicate that the meson $\sigma(600)$ does not mix with the nonet particles.
