I study piano and can play a little guitar.
I will tell you how I think of it on piano. Theoretically the concept should be the same on guitar, but personally I have always found the guitar neck confusing compared to the piano keyboard.
I think of the natural minor scale in the same way I think of the harmonic & melodic minor and the major scales: an octave divided into two tetrachords.
A tetrachord is four notes spanning a perfect fourth in a combination of half and whole steps. Before looking at the detail of the tetrachords let's go back to the scales as a division of the octave into two perfect fourths (abbreviated P4.) I will use a tonic of A
for examples. Let's list out the tonic, 4th and 5th of the four scales...
Major [A...D][E...A]
Natural Minor [A...D][E...A]
Melodic Minor [A...D][E...A]
Harmonic Minor [A...D][E...A]
...of course A
to D
and E
to A
are both perfect fourths. I placed those fourths in brackets to delineate the tetrachords. I intentionally haven't yet filled in the inside of the tetrachords, so we can see they are all the same!
Tonally those are the primary scale degrees: the tonic, subdominant, and the dominant. The are the same for all four scales, because those tones are the foundation of the major/minor system.
In terms of pure numbers we have 8 scale tones x 4 scales for 32 total with 4 x 4 primary tones for 16 total. Half of the notes are the same between all four scales!
The specifics of constructing the final scales is filling out the complete tetrachord. There are four types of tetrachord. I will list their names, whole step (W) and halfstep (h) series...
Major W W h
Minor W h W
Phrygian h W W
Harmonic h A2 h (A2 is an augmented 2nd or 3 halfsteps)
Our tetrachords begin on A
and E
and theoretically we could play any of the four tetrachord types on either A
or E
...
Major [A B C# D]
Minor [A B C D]
Phrygian [A Bb C D]
Harmonic [A Bb C# D]
Major [E F# G# A]
Minor [E F# G A]
Phrygian [E F G A]
Harmonic [E F G# A]
...but we won't use all of the possibilities. These are the tetrachord types used for the four scale types...
Major [major ][major ]
Natural Minor [minor ][phrygian]
Melodic Minor [minor ][major ]
Harmonic Minor [minor ][harmonic]
Notice that the major and minor tetrachords are used three times! The phrygian and harmonic tetrachords are only used once each for the top half of the minor scales.
Remember these tetrachords are shapes that can be transposed to different positions of the guitar neck (or piano keyboard.)
Mostly we are using the major and minor tetrachords. And those two only differ by the 3rd degree. The minor scales are generated by simply inflecting the top half of the minor scale with either the phrygian, major, or harmonic tetrachords.
Finally, the spelling of each scale is...
Major [A B C# D][E F# G# A]
Natural Minor [A B C D][E F G A]
Melodic Minor [A B C D][E F# G# A]
Harmonic Minor [A B C D][E F G# A]
The bonus for thinking of scales as tetrachord combinations is you can get many other scales with the same process. The dorian, phrygian, and mixolydian modes, and the exotic scales like the double harmonic and Freygish are constructed with combinations of these tetrachords.
If this seems complicated, just remember: it uses only four tetrachords!