The Jazz Minor Scale is the same as the Melodic Minor Scale - I'm calling it this here partly to distinguish it from the regular scale and as well to be certain you don't confuse it with the classical version (which uses the Aeolian mode to descend!).

The Jazz Minor is a Major Scale with a flat 3rd (b3) and it's used over Min/∆7 (minor chords with an added Major 7th) which is a common passing chord in Jazz (check out the second chord in jazz standards Nature Boy or Julian Lennon's pop hit Salt Water). This chord is usually placed between a straight minor and a Minor7 chord and we need that Major 7 scale interval to match the chord tones.

The scale formula for the Jazz Minor is below, it describes the interval distances between each note of the scale. Note the 4 Tones in a row that help give this scale it's unique quality.

	T		S		T		T		T		T		S
1		2		3		4		5		6		7		8

T = Tone [whole step] • S = Semitone [half step]

Comparison With Major Scale

Scales are always compared to the Major Scale to find the intervals used.

	I	II	III	IV	V	VI	VII	I
C Major Scale	C	D	E	F	G	A	B	C
C Jazz Minor	C	D	Eb	F	G	A	B	C
Equation	1	2	b3	4	5	6	7	1

It is derived from the Major scale with a flattened 3rd but can also be thought of as a Natural Minor Scale with a raised 6th and 7th degree.

Chords And Extensions

Because we're thinking modally here we're looking at the individual chords you might use this scale over not the Chords In The Key of the Melodic Minor Scale. Some options are listed below but this one is most commonly used over a min/Maj7.

min/Maj7
min9/Maj7
min11/Maj7 (bit strange)
min13 (Maj7) (also a bit strange)