  The construction of a model of the gravitational-wave (GW) signal from
generic configurations of spinning-black-hole binaries, through inspiral,
merger and ringdown, is one of the most pressing theoretical problems in the
build-up to the era of GW astronomy. We present the first such model in the
frequency domain, "PhenomP", which captures the basic phenomenology of the
seven-dimensional parameter space of binary configurations with only three key
physical parameters. Two of these (the binary's mass ratio and an effective
total spin parallel to the orbital angular momentum, which determines the
inspiral rate) define an underlying non-precessing-binary model. The
non-precessing-binary waveforms are then "twisted up" with approximate
expressions for the precessional motion, which require only one additional
physical parameter, an effective precession spin, $\chi_p$. All other
parameters (total mass, sky location, orientation and polarisation, and initial
phase) can be specified trivially. The model is constructed in the frequency
domain, which will be essential for efficient GW searches and source
measurements. We have tested the model's fidelity for GW applications by
comparison against hybrid post-Newtonian-numerical-relativity waveforms at a
variety of configurations --although we did not use these numerical simulations
in the construction of the model. Our model can be used to develop GW searches,
to study the implications for astrophysical measurements, and as a simple
conceptual framework to form the basis of generic-binary waveform modelling in
the advanced-detector era.
