Melodic Minor Scale

Melodic minor raises both the sixth and seventh degrees of natural minor when ascending, then reverts to natural minor descending (in classical practice). The reasoning: harmonic minor's augmented second between ♭6 and raised 7 is difficult to sing in an ascending line, so raising the 6th too creates smooth stepwise motion. In jazz, only the ascending form is used in both directions — because its seven modes are among the most harmonically rich in all of music theory.

Construction

Classical form:
A melodic minor ascending:  A  B  C  D  E  F#  G#  A
A melodic minor descending: A  G  F  E  D  C   B   A   (= natural minor)

Jazz form (used in both directions):
A  B  C  D  E  F#  G#  A

Formula: 1  2  ♭3  4  5  6   7
= major scale with only the 3rd lowered
= "major scale with a minor 3rd"

Melodic Minor in Common Keys

Key	Notes	Compared to major (same root)
A melodic minor	A B C D E F# G#	A major with C♮ (♭3) instead of C#
D melodic minor	D E F G A B C#	D major with F♮ (♭3) instead of F#
G melodic minor	G A B♭ C D E F#	G major with B♭ (♭3) instead of B
C melodic minor	C D E♭ F G A B	C major with E♭ (♭3) instead of E
F melodic minor	F G A♭ B♭ C D E	F major with A♭ (♭3) instead of A
B♭ melodic minor	B♭ C D♭ E♭ F G A	B♭ major with D♭ (♭3) instead of D

The Seven Modes of Melodic Minor

The modes of jazz melodic minor are among the most important scales in modern jazz harmony. Each has a specific harmonic application:

Mode	Common name	Formula vs major	Used over
1st	Jazz melodic minor / Jazz minor	♭3	Im(maj7), m6 chords
2nd	Dorian ♭2 / Phrygian ♮6	♭2, ♭3, ♭7	Sus♭9 chords, dark minor
3rd	Lydian augmented (Lydian #5)	#4, #5	maj7#5 chords
4th	Lydian dominant	#4, ♭7	7#11 chords, tritone sub dominants
5th	Mixolydian ♭6 / Hindu	♭6, ♭7	7♭13 chords
6th	Locrian ♮2 / Half-diminished	♭2... no: ♮2, ♭3, ♭5, ♭6, ♭7	m7♭5 (half-diminished) chords
7th	Altered / Super Locrian	♭2, ♭3, ♭4(=3), ♭5, ♭6, ♭7	7alt chords — all altered extensions

The Most Important Modes

Mode 4 (Lydian Dominant): 1 2 3 #4 5 6 ♭7
  = Mixolydian with raised 4th
  Best over 7#11 chords, tritone sub dominants, non-resolving dominants
  Example: C Lydian dominant (= G melodic minor from C) over C7#11

Mode 7 (Altered / Super Locrian): 1 ♭2 ♭3 3 ♭5 ♭6 ♭7
  = all extensions altered
  Best over 7alt chords resolving to tonic
  Example: G altered (= A♭ melodic minor from G) over G7alt→Cmaj7

Mode 6 (Locrian ♮2): 1 2 ♭3 4 ♭5 ♭6 ♭7
  = Locrian with natural 2nd
  Better than regular Locrian over m7♭5 — avoids the harshest tension
  Example: B Locrian ♮2 (= D melodic minor from B) over Bm7♭5

Sound Over Im(maj7)

The primary use of the 1st mode (jazz melodic minor itself) is over a minor chord with a major seventh — the Im(maj7) chord. In A minor, this is Am(maj7) = A C E G#. The raised seventh (G#) against the minor third (C) creates a distinctive, slightly searching quality — neither fully settled (like Dorian) nor completely tense (like harmonic minor). It's the bossa nova sound, the film noir sound, the introspective sound:

"What is this thing called love" — Im opening uses melodic minor colour
Bossa nova minor chords (ImM7) — melodic minor defines the sound
"Corcovado" (Jobim) — the floating, unresolved minor quality

References

Levine — The Jazz Theory Book
Bergonzi — Inside Improvisation Series, Vol. 5 (Melodic Structures)
jazzguitar.be — Melodic Minor Scale ↗