Synthetic speech quality is now close to parity with human speech for isolated read speech utterances. There has therefore been a resurgence of interest in using speech synthesis for speech science research. However, many speech synthesis models lack control over prosody. The few models that are controllable do not use interpretable control values or controls that relate to prosodic theory. We present a model that enables control, by conditioning on a hierarchical Legendre polynomial representation of F0 at the phrase and word levels. The polynomial coefficients are data-driven but linguistically-motivated and have been used in previous studies of pitch accents and phrase contours. The coefficients are interpretable in their characterisation of the F0 contour because they describe mean F0, slope, and convexity. We demonstrate sufficient control of F0 to produce speech that is intonationally similar to a reference sample. Objective and subjective evaluations are used to compare our Legendre-conditioned model to a baseline, to a model conditioned on categorical prosodic features, and to an oracle model conditioned on ground-truth F0. Our model has lower F0 prediction error and higher correlation with ground-truth. Future work aims to apply these features to conversational speech, by learning Legendre coefficients from large speech corpora.