The natural major scale on C has the notes: C, D, E, F, G, A, B. What is the difference between natural major, harmonic major, and melodic major scales. What notes of the natural major are changed in harmonic/melodic major?
The harmonic major scale has a lowered 6th scale degree:
1 2 3 4 5 b6 7
The only difference with the harmonic minor scale is the major third, so harmonic major can be obtained from the harmonic minor scale by raising the third.
Raising the third of the melodic minor scale results in a standard major scale, so that's not the way melodic major can be derived.
The term "melodic major" is actually hardly used, but it usually refers to the 5th mode of the melodic minor scale with scale degrees
1 2 3 4 5 b6 b7
This scale is more commonly (and more understandably) referred to as mixolydian b6.
From what I understand, Harmonic Major flattens the 6th degree of natural major: [C D E F G A♭ B]. Melodic Major flattens the 6th and 7th degree of natural major: [C D E F G A♭ B♭].
As for why: The upper tetrachord of harmonic major is identical to that of harmonic minor. For melodic major, the modified 6th and 7th give the scale its "melodic" moniker. AFAIK, these scales are played identically both ascending and descending.
Another possible reasoning for the name of melodic major is from its identity as a mode of melodic minor (the 5th mode, to be specific).
On ascending, what I'd think of as "melodic major" can only be the same as regular Major (Ionian). Harmonic Major is just Harmonic Minor with a raised 3rd, and Aeolian n6 n7 with a raised 3rd is just Ionian again. But it's still possible to see melodic major as a distinct scale because melodic minor can be considered different when ascending and descending. On the way down, you can just use natural minor again. Raising the 3rd of natural minor gives you Aeolian Dominant, which fits what I'd think of as "melodic" major. You could have C-D-E-F-G-A-B-C (ascending) and C-Bb-Ab-G-F-E-D-C (descending). To me melodic major has kind of a contemplative, melancholy, bittersweet feel, mostly because it has I iv.