You can consider it as a part of the Dorian mode, second mode of the major scale.
Indeed, the Dorian mode is spelled 1 - 2 - b3 - 4 - 5 - 6 - b7, by leaving out the fourth (4) and the minor seventh (b7) you get the 5 notes of the Dorian pentatonic scale.
D Dorian mode
D
E
F
G
A
B
C
Formula
1
2
b3
4
5
6
b7
D Dorian pentatonic scale
D
E
F
x
A
B
x
One Octave Shapes
Here are four guitar diagrams showing how to play the Dorian pentatonic scale (Kumoi scale) within the space of one octave.
Two Octave Shapes
The following shapes show how to play the Kumoï scale within two octaves.
5 Positions
Here are five positions for the Dorian pentatonic scale spanning the whole guitar neck.
Notice that each shape starts from a different degree of the scale.
Difference With Kumoï Scale?
The Dorian pentatonic and the Kumoï scales are simply the same.
The name is different according to the country and the style of music.
Difference With Hirajoshi Scale
The only difference between these two scales is that the Hirajoshi scale has a b6 whereas the Kumoi has a natural 6.
Thus giving the interval pattern 1 - 2 - b3 - 5 - b6 for the Irajoshi scale and 1 - 2 - b3 - 5 - 6 for the Kumoï scale.
Confusions and Differences
It seems there are many confusions about the construction of the Dorian pentatonic scale.
Some books and teachers give three other formulas :
1 - 2 - b3 - 5 - b7, also known as Pygmy scale, an African scale from Rwanda.
In any event, they all derive from the Dorian mode and works well over minor chords, it is up to you to choose the one you prefer, depending on the harmonic context.
Dorian pentatonic scale (Kumoï)
1
2
b3
5
6
Dorian pentatonic scale (2)
1
2
4
5
6
Dorian pentatonic scale (Degree II of the major pentatonic scale)
1
2
4
5
b7
Dorian pentatonic scale (Pygmy scale)
1
2
b3
5
b7
Here are four guitar neck diagrams to make the difference between these Dorian pentatonic scales.
Dorian Pentatonic Lick Over a Major II-V-I
This simple lick below shows how the Dorian pentatonic scale can be applied to the ii chord of a basic II-V-I progression.
You can notice that this II-V-I jazz line is built only with pentatonic scales.
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