Minor Scale Formula

The Minor (Aeolian Mode) scale is much more difficult as there are 3 different versions of the
minor scale; The Natural, Harmonic and the Melodic Minor scales.

The good news is that you can use the Natural minor scale to build the other two, and there are some other tricks to simplify the process.

Natural Minor:W-H-W-W-H-W-W
It's can be seen in all natural keys by starting on A on a keyboard:
A-B-C-D-E-F-G-A
and that is a good way to visualize it if you use a keyboard for your memory-ization

So building a Natural Minor scale starting on C

1. C (Tonic / Root)
2. D (W)
3. Eb (H)
4. F (W)
5. G (W)
6. Ab (H)
7. Bb (W)
8. C (W Octave Tonic)

The Harmonic Minor is the same as the Natural but has a Raised 7th a (half-step) to Create a Leading tone (half-step) between the 7th and 1st (8th) degree as opposed to the Subtonic (whole-step) that the Natural minor has, the tonal gravitational pull with a Leading tone is much stronger than a Subtonic (notice how in C major, B wants to resolve back to C on your instrument; all notes have pull in relation to one another or the tonic).

C Harmonic Minor (Natural Minor w/ 7th raised a half-step)

1. C (Tonic / Root)
2. D (W)
3. Eb (H)
4. F (W)
5. G (W)
6. Ab (H)
7. B natural (3 half-steps) raised 7th
   
8. C (H Octave Tonic)

You might have noticed that the harmonic Minor is the same as C Major but it has a flatted 3rd & 6th, this is also an acceptable way to build the Harmonic Minor or memorize its pattern (Major scale with a Flatted 3rd & 6th).

The Harmonic creates its own problems having 3 half-steps between the 6th & 7th degrees, this is a difficult interval for singers to sing but it works well for chords (harmonically, hence Harmonic Minor) so we have one more minor scale to learn, the odd one.

The Melodic Minor scale:
The Melodic Minor scale has two versions, ascending and descending.
This seems odd but it has its reasons, the melodic minor scale is built upon the
Natural Minor scale as well, but it has a Raised 7th like the harmonic & and raised 6th.

But when you descend you must revert them to what they used to be.

C Melodic Minor Ascending C (Tonic / Root) D (W) Eb (H) F (W) G (W) A (W) raised 6th B natural (W) raised 7th C (H Octave Tonic)

C Melodic Minor Descending C (Tonic / Root) D (W) Eb (H) F (W) G (W) Ab (H) reverted Bb (W) reverted C (H Octave Tonic)

You can interchange all minor scales for Harmonies (chords etc.) or Melodies or anything else you please.