A measurement is presented of the ratio of the inclusive 3-jet cross section to the inclusive 2-jet cross section as a function of the average transverse momentum, $\langle p_{\mathrm{T1,2}}\rangle$ , of the two leading jets in the event. The data sample was collected during 2011 at a proton–proton centre-of-mass energy of 7 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 5.0 fb−1. The strong coupling constant at the scale of the Z boson mass is determined to be α S (M Z)=0.1148±0.0014 (exp.)±0.0018 (PDF)±0.0050(theory), by comparing the ratio in the range $0.42 < \langle p_{\mathrm{T1,2}}\rangle< 1.39~\mathrm{TeV}$ to the predictions of perturbative QCD at next-to-leading order. This is the first determination of α S (M Z) from measurements at momentum scales beyond 0.6 TeV. The predicted ratio depends only indirectly on the evolution of the parton distribution functions of the proton such that this measurement also serves as a test of the evolution of the strong coupling constant. No deviation from the expected behaviour is observed.