The nucleus $^{49}\mathrm{Sc}$, having a single ${f}_{7/2}$ proton outside doubly magic $^{48}\mathrm{Ca}$ ($Z=20$, $N=28$), is one of the very few isotopes which makes possible testing of the fundamental theory of nuclear magnetism. The magnetic moment has been measured by online $\ensuremath{\beta}$ NMR of nuclei oriented at milli-Kelvin temperatures to be $(+)5.616(25)\text{ }\text{ }{\ensuremath{\mu}}_{N}$. The result is discussed in terms of a detailed theory of the structure of the magnetic moment operator, showing excellent agreement with calculated departure from the ${f}_{7/2}$ Schmidt limit extreme single-particle value. The measurement completes the sequence of moments of Sc isotopes with even numbers of ${f}_{7/2}$ neutrons: the first such isotopic chain between two major shells for which a full set of moment measurements exists. The result further completes the isotonic sequence of ground-state moments of nuclei with an odd number of ${f}_{7/2}$ protons coupled to a closed subshell of ${f}_{7/2}$ neutrons. Comparison with a recent shell-model calculation of the latter sequence is made.