The difference between Accidental and Incidental

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.

Incidental as an adjective:

Loosely associated; existing as a byproduct, tangent, or accident; being a likely consequence.

Incidental as an adjective:

Occurring by chance

Incidental as an adjective (physics, of radiation):

Entering or approaching, prior to reflection (more frequently incident).

Incidental as a noun:

Minor items, not further defined. Incidental expense.

Incidental as a noun:

Something that is incidental.