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This is a small question with an unfortunately large answer. Firstly, the natural minor is in fact one of the Modes taken from the benchmark Major scale, itself a mode originally called the Ionian. Always remember, EVERYTHING in Music Theory uses the major scale as a reference.

If you play the white notes of the keyboard from C to C you will hear the major scale/ionian mode. If you then move to the sixth note of said major scale (A) and then play from A to A, you will here the Aeolian mode, more commonly known as the natural minor. This relationship of the major scale and its relative minor as it is known, is fully transferable from key to key, ie the notes of G major if played from its 6th note (E) will provide you with the relative key of E natural minor.

This next bit is a bit tricky to describe without musical examples but I'll give it a try.

One of the most important factors of the major scale is the semitone movement between its 7th note and its octave which gives the scale a pleasing conclusion, a device which is commonly used at the end of a musical phrase or statement. Known as a perfect cadence, when harmonised this musical device is, in fact the fundamental musical movement in Western harmonically driven music. It can be described in the key of C major as the chords G(7) to C. If you listen to any Mozart or Beethoven you will commonly hear this chord movement at the end of a section or movement. It's know as a cadenza (from the word Cadence)

The problem with the natural minor scale is, it does not have this semitone interval between its 7th and octave. In the case of A natural minor (relative to C major) The scale progresses thus, A B C D E F G A. The notes of G and A have a tone between them and so does not sound as definitely final as the sound produced at the end of a major scale.

So, at some point in history, I know not when nor by whom, the decision was taken to raise this seventh note by a semitone to give the end of the scale a similar sound to the end of the major scale. Thus the harmonic minor was born.

It is known as the harmonic minor because when harmonised this alteration in the scale notes produces a definite sounding perfect cadence rather than the rather less definite and flattersounding cadence produced by the unaltered natural minor scale. The difference being the preferable (at that time) sound of the chord of E Major to A minor at the phrase end as opposed to the duller and less final sound of the chord of E minor to A minor. Of course nowadays, composers are totally free to choose whichever sound they prefer thus breaking convention.

The inherent problem with the harmonic minor is, since we've moved the seventh note towards the octave, it naturally has to move further away from the 6th. this produces a Leap within the scale of a minor 3rd, a hump if you like, which, again conventionaly, at the time was considered ungainly and a bit difficult for singers to get their voices around.

So, again the decision was taken to alter the scale a further time, this time pushing the 6th note up by a semitone to smooth out the gap and make it easier to sing melodies, hence the melodic minor.

Chances are, depending upon circumstances, a piece of music which is in a minor key will use all 3 types of minor, the choice of which type to use at any paticular time being dependant upon the effect to be created.

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