To realize a high-accuracy optical clock, the 2S1/2 ↔ 2F7/2 electric octupole (E3) transition in 171Yb+ is well-suited. The same ion also features an electric quadrupole (E2) transition. Because the two transitions have a large differential sensitivity to the fine structure constant α, tight limits on its possible variations can be obtained by comparing their frequencies at various positions in spacetime. These limits can then be used to constrain models predicting such variations. In particular, the couplings of so-called ultralight bosonic dark matter (m << 1 eV/c^2) to standard model particles would lead to coherent oscillations of constants, with an oscillation frequency corresponding to the Compton frequency of the dark matter mass. We conduct a broadband dark-matter search by comparing the frequency of the E3 transition to that of the E2 transition, and to that of the 1S0 ↔ 3P0 transition in 87Sr. We find no indication for significant oscillations in our experimental data, and improve existing bounds on the scalar coupling of ultralight dark matter to photons for dark-matter masses of about 1E−24 to 1E−17 eV/c^2. As recently shown, couplings to quarks and gluons can also be investigated with our optical frequency ratio measurements by considering the effect an oscillating nuclear charge radius would have on electronic transitions. Alternatively, an optical frequency can be compared to a microwave clock based on a hyperfine transition, such as a Cs fountain clock.