  The popular log-linear relation between supermassive black hole mass, M_bh,
and the dynamical mass of the host spheroid, M_sph, is shown to require a
significant correction. Core galaxies, typically with M_bh > 2x10^8 M_Sun and
thought to be formed in dry merger events, are shown to be well described by a
linear relation for which the median black hole mass is 0.36% - roughly double
the old value of constancy. Of greater significance is that M_bh ~ (M_sph)^2
among the (non-pseudobulge) lower-mass systems: specifically, log[M_bh/M_Sun] =
(1.92+/-0.38)log[M_sph/7x10^{10}M_Sun] + (8.38+/-0.17). `Classical' spheroids
hosting a 10^6 M_Sun black hole will have M_bh/M_sph ~ 0.025%. These new
relations (i) bring consistency to the relation M_bh ~ sigma^5 and the fact
that L ~ sigma^x with exponent x equal to 5 and 2 for bright (M_B < -20.5 mag)
and faint spheroids, respectively, (ii) mimic the non-(log-linear) behavior in
the M_bh-(Sersic n) diagram, (iii) necessitate the existence of a previously
over-looked M_bh ~ L^{2.5} relation for Sersic (i.e.\ not core-Sersic)
galaxies, and (iv) resolve past conflicts (in mass prediction) with the
M_bh-sigma relation at the low-mass end. Furthermore, the bent nature of the
M_bh-M_sph relation for `classical' spheroids will have a host of important
implications that relate to (i) galaxy/black hole formation theories, (ii)
searches for the fundamental black hole scaling relation, (iii) black hole mass
predictions in other galaxies, (iv) alleged pseudobulge detections, (v)
estimates of the black hole mass function and mass density based on luminosity
functions, (vi) predictions for space-based gravitational wave detections,
(vii) connections with nuclear star cluster scaling relations, (viii)
evolutionary studies over different cosmic epochs, (ix) comparisons and
calibrations matching inactive black hole masses with low-mass AGN data, and
more.
