Then you have those who wish to complicate life by transposing the modes, keeping the tone and semitone (step and half-step order the same but moving the whole lot up or down by a fixed interval.

I have heard two naming systems used. I do not know which is correct.

One takes the name from the start note - - so they you can have "myxolidian A" which (in this nomenclature) is the myxolidian "scale" starting at A.

Some however name differently, and the logic goes that since all the modes as set out above use all the white notes, all of them must be in C major. So if you move all the notes up a tone, you must have a new set of modes in D, which you can identify by naming just as before, but suffixing the ordinary major key from which the notes come - EG Myxolidian D. In this nomenclature Myxolidian A would have three sharps. However each mode would start on a different note. Ionian A would start 9 semitones up from Ionian C, ie on A but Myxolidian A would then start another 7 semitones up (the interval from C to G) ie on E.

Can anyone justify either system of nomenclature?