The Harmonic Major scale is a simple alteration of the major scale. The sixth degree is lowered and this creates an augmented second between the sixth and seventh degrees. In contrast to the Harmonic Minor scale it is a major type scale with a major third between the first and third degrees. Written out as an alteration of the major scale using numbers (1 2 3 4 5 6 7)  the steps are 1, 2, 3, 4, 5, b6, 7. Viewed as two four-note tetrachords and compared to modes in the major/minor system, the lower tetrachord is major (Ionian) and the upper tetrachord is harmonic minor.

Starting from the note C the scale is:

C  D  E  F  G  Ab  B

The harmony in triads is

C Maj   D dim   E min    F min   G maj   Ab aug    B dim

As sevenths

C Maj7   D min7b5  (D dim7)   E min7    F min/maj7  (F dim7)   G7   AbMaj7#5 (Ab dim 7)    B dim 7

I particularly like the fully extended seven note arpeggios which can be created using this scale.

C  E  G  B  D  F  Ab

D  F  Ab  C  E  G  B

E  G  B  D  F  Ab  C

F  Ab  C  E  G  B  D

G  B  D  F  Ab  C  E

Ab  C  E  G  B  D  F

B  D  F  Ab  C  E  G