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For example: what's known as the Mixolydian mode is really just the major scale with one small adjustment -- the 7 is one semitone flat (b7); The Lydian mode is really just the major scale with a different small adjustment -- the 4 is one semitone sharp (#4). The three minor modes all have one thing in common -- the 3 is one semitone flat (b3) and they differ among themselves by other small adjustments that all refer back to the major scale. So if you really know the major scale, you can easily understand and figure out the others by knowing what adjustments to make to it.
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C Major Scale.
C D E F G A B C
Is also, the Ionian Mode. That is the first Mode. C to C no sharps no flats.
So if we list them all :-
C D E F G A B C - Major Scale - Ionian
D E F G A B C D - Dorian Mode
E F G A B C D E - Phrygian
F G A B C D E F - Lydian
G A B C D E F G - Mixolydian
A B C D E F G A - Aeolian Mode
B C D E F G A B - Locrian
There are no sharps, and no flats anywhere in any of those modes.
Now what I think is confusing the issue, is that you are talking about starting a mode from C.
For instance.
If I wanted to play the Lydian Mode in C, which isn't the same as above, I have to keep the same step pattern.
F t G t A t B s C t D t E s F
C t D t E t F# s G t A t B s C
Now I have the sharpened 4th
This continues on in the way you have explained....7th flattened for the Mixolydian and such.
As long as you follow the step pattern of the Mode when it originates from the Scale of C Major (ie moving up one note at a time as I explained earlier) then you can find the Mode for any Key reasonably quickly.