The neutron-rich 39S nucleus has been studied using binary grazing reactions produced by the interaction of a 215-MeV beam of 36S ions with a thin 208Pb target. The magnetic spectrometer, PRISMA, and the γ-ray array, CLARA, were used in the measurements. Gamma-ray transitions of the following energies were observed: 339, 398, 466, 705, 1517, 1656, and 1724 keV. Five of the observed transitions have been tentatively assigned to the decay of excited states with spins up to (11/2−). The results of a state-of-the-art shell-model calculation of the level scheme of 39S using the SDPF-U effective interaction are also presented. The systematic behavior of the excitation energy of the first
11/2− states in the odd-A isotopes of sulfur and argon is discussed in relation to the excitation energy of the first excited 2+ states of the adjacent even-A isotopes. The states of 39S that have the components in their wave functions corresponding to three neutrons in the 1f7/2 orbital outside the N=20 core have also been discussed within the context of the 0 ℏω shell-model calculations presented here.