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The one problem I have with the Melodic Minor is that I just don't know how and where to use it. From my comprehension, it is the Minor scale when descending and when ascending it has a maj6 and maj7. I don't know how I can use this scale harmonically or melodically. I have done a lot of experimentation with this scale, but I just cannot figure out how to use it.

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You have the ascending and descending backwards. The major intervals are used when ascending, to provide an upward tendency. (a different Caleb here, BTW!) – Caleb Hines Sep 20 '14 at 2:40
There's already a good answer to this here:… – Caleb Hines Sep 20 '14 at 3:42
One funny thing you can do with it is to take a simple minor chord progression and change it, so the chords of melodic minor are used. This turns a folk song into something interesting without sounding too weird. – Martin Drautzburg Sep 20 '14 at 9:06
@CalebHines Ah, right. I asked this late at night. Thanks for pointing that out. – Caleb Sep 20 '14 at 13:37
Yeah, although it's not particularly hard to arrange an arrival at the relative major instead. The standard deceptive cadence isn't all that hard either, particularly to the first inversion - ♯7 will fall to 3 (mostly over V), you'll get a nice falling 5th or rising 4th in the bass, and you'll also get a barely separated cross-relation between ♯6 and ♮6, but I tend to consider that a feature, not a bug. ;) – Patrx2 Jan 7 '15 at 19:15

The basic idea of the melodic minor scale is to be able to traverse the minor scale by step while having the option to take advantage of the leading tone while avoiding the augmented 2nd interval. It may seem random when you use melodic and when you use natural minor scale degrees, but there is a very simple test: Are you going to the tonic or are you leaving the tonic?

I'll give a few common examples of how you would decide whether you used the raised 6th and 7th or the natural ones in a melody.

Example 1 - i chord

The first example is when a i chord is used. Let's just say we're in the key of A minor. If you wanted to start on an A and wanted to use a lower neighboring tone then you would use G# instead of G.

Ex 1

If you wanted to start on an A and wanted to use a double passing tone to go to the dominant then you would use G instead of G# and F instead of F#.

Ex 2

Example 2 - V chord

Another common example is when you use a V chord. V typically goes to i so most likely you will use the raised 6th and 7th. We're still in A minor and ff you wanted to start on an E and wanted to use a double passing tone to go to the tonic then you would use F# instead of F and G# instead of G.

Ex 3

Example 3 - iv and VI chords

You do have to be careful with the underlying harmony. Sometime this rule is broken if the underlying harmony uses the natural minor's natural 6th or 7th. For example if you are using iv you would typically use the natural minor scale because the iv chord contains the natural 6th.

Ex 4

If you are using VI you would typically use the natural minor scale because the VI chord contains the natural 6th.

Ex 5

Harmony wise pay attention to the melody and be consistent. If the melody uses the raised 6th and 7th use them and if the melody uses the natural 6th and 7th then use them. If neither are used in the melody then you can use both, however I would lean more towards the natural minor because it makes the progression sound more like minor then major. It in the end is up to you, but keep in mind the feel of your song.

In conclusion, pay attention to where the melody and progression are going. If it's to the tonic and the chord does not contain the 6th or 7th of natural minor then you most likely will use the raised 6th and 7th. If you are going away from the tonic use the natural 6th and 7th.

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I like your point about going toward the tonic. A lot of the time melodies aren't simple ascending or descending lines, but can jump and change direction. A jump to the raised seventh will tend to pull toward the tonic; a jump to the natural seventh won't. Both tonic-raised7-tonic and tonic-nat7-tonic are useful melodic figures, the former suggesting an inability to escape the tonic, and the latter suggesting a full escape and return. – supercat Feb 10 '15 at 19:49

Just to distill my answer from CalebHines link (and put things in a sassy manner); simply put, you're over-thinking it my friend!

Where to use the Melodic Minor Scale

  • In a melody
  • In a minor mode

How to use the Melodic Minor Scale

  • Tones are raised when ascending to provide tendency to "tonic"
  • Tones are lowered when descending to avoid augmented interval

Stylistic use of the Melodic Minor Scale

  • I don't know, do what ever you want; it's your music.
  • Look at how other composers have used it in the past. I'm not going to suggest anything as its use throughout history is too pervasive.
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