I like to think of the major and minor scales as both having a tonic, perfect 4th, and perfect 5th. The difference between major and minor is that the major scale has a major 3, major 6 and major 7; whereas the (natural) minor scale has a flat 3, flat 6, and flat 7. I then base all the other scales off these two templates.
The harmonic minor is the natural minor, but with a raised 7th - causing the V chord to be major, and not minor, for a more resolved sounding perfect cadence (V-i).
The melodic minor, is the natural minor but with a raised 6th and 7th. This is to avoid the aug 2nd (3 semitones) between the 6th and 7th scale degrees of the harmonic minor. It is interesting to note that, traditionally, the melodic minor is only ascending, using the natural minor when ascending.
The jazz melodic minor is the melodic minor stated above (raised 6th and 7th) but it is used ascending and descending.
Jazz melodic minor is minor on the bottom with major on top (it differs from regular melodic minor in that it is the same bother ascending and descending). Harmonic minor has that step-and-a-half interval near the top (between the 6th and 7th) that's hard to miss -- very distinctive.
If it weren't for nice people like you, some of us would be still wondering what the elf does C mean...😅
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