[sciurius]

The main difference is that @ehre is transposing keys, while we are transposing intervals.

When transposing intervals, the result of D one interval down is ambiguous, it can be Db or C#.

Using the transposition rules for keys, the result of D when transposing from F to E is non-ambiguous: C#.

The result of D transposing from C# to C, also one interval down, would then be Db.

We would need to apply enharmonic equivalents, otherwise Ab transposing from C# to C would become Abb. In the real of well-tempered tunings we call this G,