  The position of the peak of the matter power spectrum, the so-called turnover
scale, is set by the horizon size at the epoch of matter-radiation equality. It
can easily be predicted in terms of the physics of the Universe in the
relativistic era, and so can be used as a standard ruler, independent of other
features present in the matter power spectrum, such as baryon acoustic
oscillations (BAO). We use the distribution of quasars measured by the extended
Baryon Oscillation Spectroscopic Survey (eBOSS) to determine the turnover scale
in a model-independent fashion statistically. We avoid modelling the BAO by
down-weighting affected scales in the covariance matrix using the mode
deprojection technique. We measure the wavenumber of the peak to be
$k_\mathrm{TO} = \left( 17.6^{+1.9}_{-1.8} \right) \times
10^{-3}h/\mathrm{Mpc}$, corresponding to a dilation scale of $
D_\mathrm{V}(z_\mathrm{eff} = 1.48) =
\left({36.2^{+4.1}_{-4.4}}\right)r_\mathrm{H}$. This is not competitive with
current BAO distance measures in terms of determining the expansion history but
does provide a useful cross-check. We combine this measurement with
low-redshift distance measurements from type-Ia supernova data from Pantheon
and BAO data from eBOSS to make a sound-horizon free estimate of the
Hubble-Lema\^itre parameter and find it to be $H_0=\left({74.7\pm 9.6}\right) \
\mathrm{km/s/Mpc}$ with Pantheon, and $H_0=\left({72.9^{+10.0}_{-8.6}}\right) \
\mathrm{km/s/Mpc}$ with eBOSS BAO. We make predictions for the measurement of
the turnover scale by the Dark Energy Spectroscopic Instrument (DESI) survey,
the Maunakea Spectroscopic Explorer (MSE) and MegaMapper, which will make more
precise and accurate distance determinations.
