A piezoelectric material is one that generates a voltage in response to a mechanical strain (and vice versa). The most useful piezoelectric materials display a transition region in their composition phase diagrams, known as a morphotropic phase boundary, where the crystal structure changes abruptly and the electromechanical properties are maximal. As a result, modern piezoelectric materials for technological applications are usually complex, engineered, solid solutions, which complicates their manufacture as well as introducing complexity in the study of the microscopic origins of their properties. Here we show that even a pure compound, in this case lead titanate, can display a morphotropic phase boundary under pressure. The results are consistent with first-principles theoretical predictions, but show a richer phase diagram than anticipated; moreover, the predicted electromechanical coupling at the transition is larger than any known. Our results show that the high electromechanical coupling in solid solutions with lead titanate is due to tuning of the high-pressure morphotropic phase boundary in pure lead titanate to ambient pressure. We also find that complex microstructures or compositions are not necessary to obtain strong piezoelectricity. This opens the door to the possible discovery of high-performance, pure-compound electromechanical materials, which could greatly decrease costs and expand the utility of piezoelectric materials.