The difference between Accidental and Contingent

Accidental as an adjective:

Not essential; incidental, secondary.

Accidental as an adjective (philosophy):

Nonessential to something's inherent nature (especially in Aristotelian thought).

Accidental as an adjective (music):

Adjusted by one or two semitones, in temporary departure from the key signature.

Accidental as an adjective:

Occurring sometimes, by chance; occasional.

Accidental as an adjective:

Happening by chance, or unexpectedly; taking place not according to the usual course of things; by accident, unintentional.

Accidental as an adjective (geometry):

Being a double point with two distinct tangent planes in 4-dimensional projective space.

Accidental as a noun:

A property which is not essential; a nonessential; anything happening accidentally.

Accidental as a noun (painting, pluralonly):

Those fortuitous effects produced by luminous rays falling on certain objects so that some parts stand forth in abnormal brightness and other parts are cast into a deep shadow.

Accidental as a noun (music):

A sharp, flat, or natural, occurring not at the commencement of a piece of music as the signature, but before a particular note.

Contingent as a noun:

An event which may or may not happen; that which is unforeseen, undetermined, or dependent on something future; a contingency.

Contingent as a noun:

That which falls to one in a division or apportionment among a number; a suitable share; proportion.

Contingent as a noun (military):

A quota of troops.

Contingent as an adjective:

Possible or liable, but not certain to occur; incidental; casual.

Contingent as an adjective:

(with upon or on) Dependent on something that is undetermined or unknown.

Contingent as an adjective:

Dependent on something that may or may not occur.

Contingent as an adjective:

Not logically necessarily true or false.

Contingent as an adjective:

Temporary