♭6 ;-) (E-C is minor 6th)

But I think it should be noted from the context of that comment (and the original article) that the names are necessarily ambiguous. So the names E-G-C (or whatever set you choose, how about F#, A#, C#) are pitch positions and don't disambiguate between enharmonic equivalents, eg in isolation we have no reason to prefer F# over Gb. Which is the problem.

You picked a good example because by key signature circle-of-fifths distance from C major, the choices are equidistant.

Gb-Bb-Db can be obtained in the key of Db: Bb, Eb, Ab, Db, Gb. It is that key's subdominant.

F#-A#-C# is in the key of B: F#, C#, G#, D#, A#, and is that key's dominant.

Five sharps or five flats. Same distance from C major.