  Recently, a tetraquark mixing framework has been proposed for light mesons
and applied more or less successfully to the isovector resonances, $a_0(980),
a_0(1450)$, as well as to the isodoublet resonances, $K^*_0(800), K^*_0(1430)$.
In this work, we present a more extensive view on the mixing framework and
extend this to the isoscalar resonances, $f_0 (500)$, $f_0(980)$, $f_0 (1370)$,
$f_0(1500)$. Tetraquarks in this framework can have two spin configurations
containing either spin-0 diquark or spin-1 diquark and each configuration forms
a nonet in flavor space. The two spin configurations are found to mix strongly
through the color-spin interactions. Their mixtures, which diagonalize the
hyperfine masses, can generate the physical resonances constituting the two
nonets, which, in fact, coincide roughly with the experimental observation. We
identify that $f_0 (500)$, $f_0(980)$ are the isoscalar members in the light
nonet, and $f_0 (1370)$, $f_0(1500)$ are the similar members in the heavy
nonet. This means that the spin configuration mixing, as it relates the
corresponding members in the two nonets, can generate $f_0 (500), f_0 (1370)$
among the members in light mass, and $f_0(980), f_0(1500)$ in heavy mass. The
complication arises because the isoscalar members of each nonet are subject to
an additional flavor mixing known as OZI rule so that $f_0 (500), f_0 (980)$,
and similarly $f_0 (1370), f_0 (1500)$, are the mixture of two isoscalar
members belonging to an octet and a singlet in SU$_f$(3). The tetraquark mixing
framework including the flavor mixing is tested for the isoscalar resonances in
terms of the mass splitting and the fall-apart decay modes.
