Hierarchical models for the coupling between two recorded signals. A spectral model of ONE series needs no new likelihood, because a periodogram ordinate is exponential about the spectral density; two series is different, since the cross-spectrum is complex and the pair's periodogram at each frequency is complex Wishart. This package supplies that likelihood, parameterized so that coherence and phase are distributional parameters with their own linear predictors, which is what makes a random effect on coherence or a smooth in coherence over frequency an ordinary 'frmtmb' formula. The parameterization cannot leave the positive definite cone, because a logit link on coherence IS the constraint, and the complement it needs is computed on the log scale from the linear predictor so that the guarantee survives in floating point rather than only on paper. The reason to want it: coherence estimated from few segments is biased upward by about the reciprocal of the segment count, the bias does not shrink when subject coherences are averaged, and concatenating subjects instead cancels the cross terms whenever phase varies between them. Both failures are measured in the vignette against a known truth.