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We present a determination of the ratio of kaon and pion leptonic decayconstants in isosymmetric QCD (isoQCD), $f_K / f_\pi$, making use of the gaugeensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f= 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, includingconfigurations close to the physical point for all dynamical flavors. Thesimulations are carried out at three values of the lattice spacing ranging from$\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm.The scale is set by the PDG value of the pion decay constant, $f_\pi^{isoQCD} =130.4~(2)$ MeV, at the isoQCD pion point, $M_\pi^{isoQCD} = 135.0~(2)$ MeV,obtaining for the gradient-flow (GF) scales the values $w_0 = 0.17383~(63)$ fm,$\sqrt{t_0} = 0.14436~(61)$ fm and $t_0 / w_0 = 0.11969~(62)$ fm. The data areanalyzed within the framework of SU(2) Chiral Perturbation Theory (ChPT)without resorting to the use of renormalized quark masses. At the isoQCD kaonpoint $M_K^{isoQCD} = 494.2~(4)$ MeV we get $(f_K / f_\pi)^{isoQCD} =1.1995~(44)$, where the error includes both statistical and systematicuncertainties. Implications for the Cabibbo-Kobayashi-Maskawa (CKM) matrixelement $|V_{us}|$ and for the first-row CKM unitarity are discussed.

Ratio of kaon and pion leptonic decay constants with $N_f = 2 + 1 + 1$ Wilson-clover twisted-mass fermions