In my knowledge, a distant key is any key that is not enharmonic, parallel, relative, or closely related to the original key. However, some people claim that distant keys are simply keys that are not closely related or relative, which would mean parallel and enharmonic keys are distant. What is exactly the standard definition of a distant key?
Good question! I think it is some how like old, elder and oldest ... distant, more distant, quite distant, most distant. No distant key at all is only the same key.
I assume the related keys are close keys or next (nearest) distant keys.
I would count to them the relatinship of a perfect fifth. (Difference 1 sign as # or b)
The relative keys have the same signs but differ by the added chromatic leading tones.
The parallel keys difference is 3 signs. Cm
Now we could discuss the variants and their relationship of thirds and consider also relationships between the parallel keys of the fifth-related keys and the variants and parallel keys of C.
Resume: The distance is depedending of the common tones, common thirds and - with other words - the signs as # and b.
So the distant keys will be defined by the amount of different signs and the relatinshp of thirds. The So in C you will exclude F, G, am, dm, em or (define as nearest “related”.
Next relatinship will be found in the parallel keys:
http://learnmusictheory.net/PDFs/pdffiles/03-03-TypesOfKeyRelationships.pdf I habe found this quotation: