Giant steps key centres

There is a famous tune called "Giant Steps" by John Coltrane.
Someone like me has been practicing it regularly for 30 years and never played it live. Harmonically strangely complex and simple at the same time.
Haunting.
 
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John Coltrane's "Giant steps" key centres.
You only need to think of the three key centres, although the "melody" notes are transposed "with respect to" the home key, F major.



Explanation - Note how JC only uses the 5th, 3rd and 2nd notes of the major scale, here shown in the home key of F.
But they are transposed to the underlying three key centres. Transpose all notes over orange [Db] up by TWO major thirds ,and transpose all notes over Blue [A] up by ONE major third - you will find the "Giant Steps" original melody.
[adjust octaves]
-A-
 
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