  The Galactic neutral hydrogen (HI) sky at high Galactic latitudes is suffused
with linear structure. Particularly prominent in narrow spectral intervals,
these linear HI features are well aligned with the plane-of-sky magnetic field
orientation as measured with optical starlight polarization and polarized
thermal dust emission. We analyze the coherence of the orientation of these
features with respect to line-of-sight velocity, and propose a new metric to
quantify this HI coherence. We show that HI coherence is linearly correlated
with the polarization fraction of 353 GHz dust emission. HI coherence
constitutes a novel method for measuring the degree of magnetic field tangling
along the line of sight in the diffuse interstellar medium. We propose
applications of this property for HI-based models of the polarized dust
emission in diffuse regions, and for studies of frequency decorrelation in the
polarized dust foreground to the cosmic microwave background (CMB).
