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When Naming The Notes in Modes...

Ab Phrygian would be the third mode in the key of Fb Major......

Like Dogbertday said, think E Major as the parent key with G# Phrygian as the third mode.

I would actually say it is enharmonic to the third mode of "Fb Major". I tend to think that Ab Phrygian is it's own scale that doesn't necessarily have to be subject to the Major scale.

I probably would avoid using "Fb" though unless it were theoretically relevant. It is more practical to refer to it as E most of the time, in my opinion.

That said you can call the notes pineapple, banana, cherry, pickle, grape, pork sandwich, if you like, it's the intervals between them that dictate the tonal relationships of the notes, not the way you name them according to a sense of key.
 
Ahh i used parent scale the wrong way. This makes sense, playing it before trying to say the notes as I played it was really annoying. Bbb just doesn't sound right, nor does it fit well into rhythms

Bbb is enharmonic to A and Bbb is quite a valid name under certain circumstances. I don't see how the name of a note has a single thing to do with rhythms though.
 
A G# in the key of E Major will always be a G# no matter what mode it is part of.

By the way the key of Fb doesn't exist . There are only 3 keys that have enharmonics scales : B (Cb),F# (Gb) and C# (Db).


SB

I don't agree. Fb, Gb, Ab, Bbb, Cb, Db, Eb. It exisits alright, I just typed it. Just because it doesn't appear on the circle of 5ths diagram doesn't mean it can't theoretically exist
 
I don't agree. Fb, Gb, Ab, Bbb, Cb, Db, Eb. It exisits alright, I just typed it. Just because it doesn't appear on the circle of 5ths diagram doesn't mean it can't theoretically exist

Well the theoritical reason for not to use it is because you will have double alterations in the key signature. By doing so you are just going in circle with a lot of alterations for nothing when you can have the same pitches written in a more clear and easiest way. But I know that in classical music when no tempered instrument are involved you can make B major music sounds brighter then Cb major but personally I never experimented that myself. I would not like to have to play fretless in Cb instead of B in an orchestra LOL.

SB