Best exception for an invalid generic type argument

Question

I\'m currently writing some code for UnconstrainedMelody which has generic methods to do with enums.

Now, I have a static class with a bunch of methods which are

Answer 1

NotSupportedException sounds like it plainly fits, but the documentation clearly states that it should be used for a different purpose. From the MSDN class remarks:

There are methods that are not supported in the base class, with the expectation that these methods will be implemented in the derived classes instead. The derived class might implement only a subset of the methods from the base class, and throw NotSupportedException for the unsupported methods.

Of course, there's a way in which NotSupportedException is obviously good enough, especially given its common-sense meaning. Having said that, I'm not sure if it's just right.

Given the purpose of Unconstrained Melody ...

There are various useful things that can be done with generic methods/classes where there's a type constraint of "T : enum" or "T : delegate" - but unfortunately, those are prohibited in C#.

This utility library works around the prohibitions using ildasm/ilasm ...

... it seems like a new Exception might be in order despite the high burden of proof we justly have to meet before creating custom Exceptions. Something like InvalidTypeParameterException might be useful throughout the library (or maybe not - this is surely an edge case, right?).

Will clients need to be able to distinguish this from BCL Exceptions? When might a client accidentally call this using a vanilla enum? How would you answer the questions posed by the accepted answer to What factors should be taken into consideration when writing a custom exception class?