Names, names, names

We humans are supposed to be good at naming things. But we end up with thinking we know something by being able to name it. I just had a look at naming the musical modes. And the names are totally conflicting.

I learned them first from the white notes on the piano - and indeed they are such.

C	Ionian	T_T_S_T_T_T_S	Major scale
D	Dorian	T_S_T_T_T_S_T	Harmonic minor without the leading tone
E	Phrygian	S_T_T_T_S_T_T	.
F	Lydian	T_T_T_S_T_T_S	Think Fauré Lydia, sur tes roses joues. Characteristic augmented fourth
G	Mixolydian	T_T_S_T_T_S_T	.
A	Aeolian	T_S_T_T_S_T_T	.
B	Locrian	S_T_T_S_T_T_T	.

The first 7 in the image below are all agreed - they are the white notes as listed above but all transposed to begin on an e. Then I looked at the Greek modes on wiki and they have some names reversed. Haik-Vantoura introduces the characteristic augmented second in several of her modes. Her names and notes do not correspond to the simple 'white note' derivation.

E.g. Chromatic Hypodorian T_S_T_T_S_A
Chromatic Phrygian S_T_T_S_A_S_T
Lydian with minor sixth S_T_T_S_T_S_A
Chromatic Dorian T_T_S_A_S_T_S

My old image based on her book is here. Ionian she calls Lydian = major, and the default mode of the three books, Psalms, Proverbs and the speeches of Job, essentially Aeolian, she calls Chromatic Dorian.

So there's the resolution - call them what you like. And choose what you like for developing the music. (Article here on wiki seems helpful also, particularly distinguishing the hypo prefix.)

Reconciling the names of traditional modes, Greek modes, and Haïk-Vantoura's modes