My understanding of the various modes is that, relative to the base note’s natural major key:
- Ionian is the same as natural major;
- Dorian flats the third and seventh;
- Phrygian flats the second, third, sixth, and seventh;
- Lydian sharps the fourth;
- Mixolydian flats the seventh;
- Aeolian flats the third, sixth, and seventh (natural minor);
- Locrian flats all but the prime and fourth.
I also understand that there’s a concept of a Harmonic minor, in which the minor seventh is sharped (or, in other words, only the third and sixth are flatted). I further understand that there’s a concept of a Harmonic major, in which the sixth - and only the sixth - is flatted.
Can these be applied to other modes, besides Aeolian and Ionian, respectively?
Regarding Harmonic minor: Since this obviously would only apply to keys in which the seventh is already flatted, this means that, in addition to Aeolian, only a Harmonic Dorian (flat third), Phrygian (second, third, and sixth), and Locrian (flat second, third, fifth, and sixth) would be possible. I don’t count Harmonic Mixolydian here, since that’s just the same as Ionian.
However, when you consider that the purpose of a Harmonic minor is to enable the dominant chord to be a major chord, rather than minor, then this picture changes a bit, since a major dominant requires that the fifth, seventh, and second all be not flatted. Therefore: the Phrygian mode requires sharping its second as well, making it into normal Harmonic minor. If Harmonic Locrian requires its fifth being sharpened, then it will devolve into normal Harmonic minor as well, and if not, then its fifth is already major. So either way, no new modes there.
That leaves Harmonic Dorian. This would entail flatting the third and nothing else. Is this actually a mode used? If not, is there a reason why not?
Regarding Harmonic major: Following the same logic as above, only modes with a sixth not flatted can have it flatted; excluding Ionian, this leaves Dorian, Lydian, and Mixolydian. Dorian wouldn’t work, since flatting the sixth just gives a normal Aeolian scale. Lydian could technically work, but having a sharp fourth and flat sixth not only feels weird but also sounds horrendous. And then there’s Mixolydian, which would have a flat sixth and seventh.
Narrowing it down further based on a normal Harmonic major yielding a minor fourth chord, Lydian would be impossible without flatting the sharped fourth, but a theoretical Harmonic Mixolydian would work just fine. As with the Harmonic Dorian above, is this a mode actually used, and if not, why?