harmonic major modes

We've already discussed the Harmonic Major mode, but I want to cover its modes just because they're so cool.

The Harmonic Major is basically an Ionian b6. All the other modes will fall into this pattern (i.e. a familiar mode name plus one alteration).

ionian b6	1	2	3	4	5	b6	7	1	2	3	4	5	b6	7
dorian b5		1	2	b3	4	b5	6	b7
phrygian b4			1	b2	b3	b4	5	b6	b7
lydian b3				1	2	b3	#4	5	6	7
mixolydian b2					1	b2	3	4	5	6	b7
aeolian b1						b1	2	b3	4	5	b6	b7
locrian bb7							1	b2	b3	b4	b5	b6	bb7

The Locrian bb7 might seem weird. Since we've only added one alteration why is there a double flat??? The reason is that the 7 in the Locrian is already a b7, so if you slap on another flat you get the bb7.

Also, as detailed elsewhere, the b1 isn't so useful practically. If we re-analyze the aeolian b1 we'll see that it's construction is thus:

1 #2 3 #4 #5 6 7

The #4 is a hallmark of the Lydian mode. And we've already encountered the Lydian #5 -- Lydian Augmented -- in the melodic minor modes (it's mode 3). So this can easily be named
Lydian Augmented #2.