The empirical forms of the neutral spectra for velocity variances and covariances were established by the Kansas experiment, and are now widely accepted. When these are plotted as spectral functions kEij(k) on log-log graphs they are seen to have three common features: an asymptote at high wavenumber with a slope of -2/3 when i=j and -4/3 when i=1, j=3; an asymptote at small wavenumbers with a slope of +1; and a simple maximum between these asymptotes. Of these features, the slope of the large-wavenumber asymptote is explained by Kolmogorov's theory for the inertial subrange. The other two, both features of the production range of the spectrum, remain unexplained. This paper shows that the slope of the small-wavenumber asymptote can be deduced from two propositions: that the structure of turbulence in the log layer is self similar under wall scaling and that the turbulence consists of coherent structures that are attached to the ground. Here 'attached' is used in the sense proposed by Townsend. The positions of the spectral peaks are influenced by the shapes of the individual structures and by any clumping of the structures into groups. Empirical evidence is that the individual structures are grouped into ramp-like cohorts of structures. This allows a qualitative account of the peak positions, but quantitative results must await modelling of the whole cohorts of structures that constitute these ramps.