I understand that octane is really a measure of the resistance to self
ignition in the pressure/temperature map. High temperatures or high
pressures will cause self ignition (actually this is detonation), but
octane gives us a way to measure the combinations of pressure and
temperature that also causes self ignition. It isn't measured directly
but instead octane is measured as an equivalent fuel mixture based
evaluation using an extra rugged variable compression ratio lab engine
under various conditions.

As the piston approaches TDC, the pressures and temperatures in the
cylinder rise due to adiabatic compression. If the
pressure-temperature combination ever reaches the limit supposedly
defined in the above map, the whole air-fuel charge detonates
violently. The ignition is not controlled by the magneto anymore as
the whole charge expolodes at once. With detonation, the turbulence
inside the cylinder is so violent that the combustion boundary layer
next to the cylinder head is scrubbed away, causing the cylinder head
to receive even more heat - which quickly leads to a runaway situation.

I doubt octane has anything to do with the rate of flame propagation
except that if detonation should occur, there really isn't a flame
front.

Pinging is different. With it there is charge ignition from
non-sparkplug sources that are usually the glowing (or at least extra
hot) embers inside the combustion chamber. These multiple ignition
sources cause the pressures to rise more rapidly than simply the spark
ignition, and things could deteriorate into detonation if it persists
long enough. With pinging there is still a flame front, although it is
from more sources so the pressures will rise more quickly.

It has taken a long time for me to understand the difference between
detonation and pinging. Detonation quickly wrecks engines and grossly
feeds on itself.