Empirism says:
there was mentioned that D aeolian is relative to F major (ionian).
so how this happen? :D. Is there somekind of rule why it is way it is and can I use some of tools to figure out those relatives somehow.
Here's how I understood modes, and maybe it will help you...
diatonic modes are basically constructed simply by playing the notes of the key you are in (like F) but instead of starting to play the scale from the first degree of the scale (F in the case of F) and playing until you reach F again one octave higher, you instead start on a different note of the scale, and play through until you reach that note again one octave higher, so...
In the case of the key of C (for simplicity's sake) if you start at C and play to C again, you are playing Ionian.
If you start at D and play to D again, you are playing Dorian... but you are still using all the same notes as the C major scale.
To continue... if you play from the third note of any major scale and play until you reach that third note again, you are playing Phrygian.
4th note to 4th note - Lydian
5th note to 5th note - Mixolydian
6th note to 6th note - Aeolian
7th note to 7th note - Locrian
In the case of F major, the sixth note in the scale is D. So if you play the notes of the F major scale starting from D and through to D again, you are playing D Aeolian.
That's how D Aeolian relates back to F major.
At least... that's one way it does. The sixth degree of a major scale is also the relative minor of the major scale. Maybe he meant that?
In that sense, every Aeolian scale relates back to the major scale it is based on by virtue of starting at the relative minor position.
In another sense, every diatonic mode "relates" back to the key it is based on by virtue of the fact that the modes are made up of only the notes that are in that major key.
Hope that helps. Lots of people tried to explain modes to me in terms of intervals, and it confused me for a long time.