  Quantifying mechanical disorder in solids, either disordered crystals or
glassy solids, and understanding its range of variability are of prime
importance, e.g.~for discovering structure-properties relations. The bounds on
the degree of mechanical fluctuations in disordered solids and how those depend
on solids formation history remain unknown. Here, we study a broadly applicable
quantifier of mesoscopic mechanical disorder $\chi$, defined via the
dimensionless fluctuations of the shear modulus, over a wide variety of
disordered computer solids and upon varying different control parameters.
$\chi$ is intimately related to basic properties of disordered solids, such as
elastic constants and plastic deformability, and can be experimentally
extracted by wave-attenuation measurements. We find that a large variety of
self-organized glassy solids, where disorder is an emergent property, appear to
satisfy a generic lower bound on $\chi$. On the other hand, we show that $\chi$
is unbounded from above, and may diverge in systems driven towards the critical
unjamming point. These results highlight basic properties of disordered solids
and set the ground for systematically quantifying mechanical disorder across
different systems.
