Minor In Possesion

If you go here you can see the scales laid out against each other

Can someone spell out the differences between these, and if any are just alternate namings of others:

Natural Minor
Harmonic Minor
Melodic Minor

I've never seen Natural and Harmonic mentioned in the same breath, are they the same?

I know melodic is the one that's different descending than ascending, how is it different?

The natural minor (aka pure minor) is the Aeolian mode. For example, A natural minor is spelled: A B C D E F G A. When you build diatonic triads on the notes of the scale, notice that the 5th, E, is a minor chord. In order to function as a Dominant, it would have to be a major triad (E G# B; 7ths and other extensions are optional). So, how do we achieve the strong dominant-tonic (V-i) resolution?

We raise the 7th degree of the scale (G) to G#, artificially creating a leading tone. This note is the major 3rd of the E chord, thus yielding the major chord on V, and the G# exists in A minor to lead smoothly to the A (if a line is descending, not harmonized by the Dominant chord or reasonable facsimile, or going somewhere other than the A, the flat 7th degree, G, is usually used). This is the harmonic minor scale; it is called 'harmonic' minor because of the V harmony it allows. In A, the harmonic minor is spelled: A B C D E F G# A. In the good old days of vocal church music, the interval from the 6th to the raised 7th (an augmented second) was difficult to sing, and was considered unmelodic. So, how do we make it easy to sing and more 'melodic' to the ear?

Simple--we raise the 6th degree of the harmonic minor scale (in A minor, that means raise the F to an F#) whenever it precedes the raised 7th degree (G#). The A melodic minor scale is spelled: A B C D E F# G# A. However, because the G# (from the harmonic minor scale) is used as a leading tone and part of the Dominant (V) harmony, and the F# of the melodic minor is used to lead to that raised 7th (G#), the melodic minor's descending form is identical to the natural minor--those raised notes aren't needed.

The 'ascending' and 'descending' forms are not used strictly when ascending or descending; their application depends largely on the melodic and harmonic content at a given point in a piece of music. Often, the ascending form will be used in a descending line, and vice-versa, but you probably don't want to worry about that yet. :P

There is also the so-called 'jazz minor' scale, which is nothing more than the ascending form of the melodic minor, used both ascending and descending.

Well the scales themselves are simple enough:

Natural minor:

1-2-b3-4-5-b6-b7-8

Harmonic minor:

1-2-b3-4-5-b6-7-8 (note raised 7th)

Melodic minor:

1-2-b3-4-5-6-7-8 (raised 6th and 7th, natural minor used descending)

As for the reason why, the 7th of harmonic minor was raised in order to have a dom7 V chord instead of a min7 v and thus make the resolution back to the tonic more dramatic and powerful.

The 6th was rasied to form melodic minor in order to avoid the wide gap that was difficult to sing.

I appreciate you guys spelling that out for me. I'll memorize it.