Many people are taught some scales:
Major
Natural Minor
Harmonic Minor
Melodic Minor

This is probably the most horrific thing you can learn/be taught because it utterly destroys the way minor mode music works.

Firstly, let me explain the word "mode" here: In CPP "classical" music, composers didn't write "in a scale", they wrote "in a key" - in fact, they wrote "in a key, in X mode of that key". So it's actually far more informative to think of keys for classical music, not as C Major, or C minor, but "Key of C, minor mode" or "key of C, Major mode" - so the word "mode" in this case means "version" rather than Ionian, Dorian, etc.

Furthermore, let me reiterate - composers didn't write "in scales". That's something people do today - "use the Dorian Mode to write a piece" - it's kind of unfortunate because it brings up the common question:

Which Minor Scale is this piece written in?
or
When I'm writing in minor, which scale do I use, Natural, Harmonic, or Melodic?

The problem with such questions is that they show that people truly don't understand how minor keys work. Now I want to be clear here - there are people who do write a piece specifically using Harmonic Minor, and even in Jazz, there are modes of Harmonic minor sets. In some ways, these represent a misunderstanding of the past, but are so commonplace they've become accepted. But in other ways, they're also part of the style so they're excused. But in the PAST, this is how minor mode pieces work:

First, forget everything you know about Natural, Harmonic, and Melodic. They don't exist.

A minor mode piece uses 7 notes (pitch names) regularly. These are the 7 notes that agree with the key signature, and alterations of two of those notes. The two possible alterations are scale degrees 6 and 7, which can appear as raised versions in addition to their "key signature" versions. So, the notes commonly appearing in A minor are:

A B C D E F F# G G# (A)

Now, that brings up the question of when and how to use scale degrees 6 and 7, and which of the two versions you can use.

Put simply, altering a note makes it want to continue in the direction of its alteration. Raising 6 makes it "want to go" to 7, and raising 7 makes it "want to go" to 8 (or 1, the Tonic).

Here's the issue: Composer liked the sound of a penultimate (second-to-last) chord containing a note that's a half-step below the tonic. This is the "Leading Tone". Even in modal music, before the CPP era, composers were altering the 7th scale degree in any mode to make it a half-step (LT) rather than whole step (Subtonic) below the tonic. So, once Major/minor tonality was stabilized, Major keys had a LT, but minor keys did not. Furthermore, the minor key in its "key signature" form has a strong tendency to be heard as its relative major - that is, minor wants to drift towards major. In order to prevent that drift (and because they already used it and liked it), the LT is introduced. This introduction destroys any feeling of drifting towards the relative major, and makes it sound like the Tonic is the Tonic!

But this creates a problem: It makes the distance between scale degree 6 and scale degree 7 an Augmented 2nd, rather than a whole step. This is a difficult interval so sing, and sometimes, to play in tune. Furthermore, it sounds a bit "foreign" (and other cultures did make use of this interval, so especially so) since the other tones of the scale are either half or whole steps.

So to fix this, scale degree 6 is raised as well.

So simply put, raised 6 is used to lead to raised 7, which is used to lead to the Tonic. So upward passages go: E F# G# A, rather than E F G# A, or E F G A (by the way, the latter two are not impossible, just atypical).

Descending passages on the other hand go:
A G F E, rather than A G# F E or A G F# E, etc.

Scale degree 6 in its "key sig" version pulls down to 5, and in it's raised version, up to raised 7. Scale degree 7 in its "key sig" version pulls down to 6 (unraised 6), and it's raised version up to 8/1.

I should mention as an aside here, if you mix raised and lowereds, for example:
E F# G A
You have what was heard as a modal version (this is the upper four notes of Dorian) and was avoided when trying to make the music sound "minor" rather than like older, modal music. So typically, either both are raised, or both are lowered. Passages like A G F# G# A are certainly possible though - to avoid the augmented 2nd.

But suppose you don't have a melody or part that has both? Suppose all you have is E to F, or A to G, which do you use?

Many people are taught these possible chords in minor:
I ii^o (ii) III III+ iv IV v V VI VII vii^o

But this again is misleading. These are not the chords used in minor mode pieces - in other words, just because you can use Melodic Minor and Harmonic minor to build chords, doesn't mean you should - after, those scales don't really "exist".

The truth of the matter is that chords that contain 6 or 7 adjust those notes depending on their function. For example, I've already mentioned that the LT is there so it will go to the Tonic. Thus chords containing the leading tone have a Dominant Function. But we only change "natural" 7 to raised 7 in the two dominant chords:
v becomes V, and VII becomes vii^o (or in am, em becomes EM, and GM becomes G#^o).

On a III chord (CEG in am), scale degree 7 is not typically (in fact, really, never, or so rare as to be considered never) raised to make III+.

Now, don't get in a tizzy - theory textbooks always mention this chord. Then they fail to give any examples of it. That's because classical composers didn't use III+ - the reason they put it is just to show everyone the four possible triad forms - M, m, o and + - if they didn't give this example, which can be "made" from the "harmonic minor scale" then they'd have no + chord to show (FYI, V+ is the one augmented triad typically encountered).

Likewise, A C E G# is not a chord found in CPP works. It's the Tonic chord, you don't need to add the LT to it - the LT wants to go to the tonic - but you're already on the tonic - see the problem. Furthermore, 7ths in CPP music alwasy (like without fail) resolve DOWN - putting a note you've altered to make it lead up, that's the 7th of the chord, is totally counter to the purpose of using either of those things - besides, it's astylistic.

So basically, you use raised 7 on Dominant Harmonies (V and vii^o), especially when they lead to the Tonic. See, in other words, you use raised 7 to change a HARMONY. In other words, scale degree 7 is altered for HARMONIC reasons - get it? It's not a "harmonic minor scale" - the harmonic minor scale is merely a memory device to remind you that scale degree 7 in minor is usually altered for harmonic reasons.

But you don't use raised 7 on III or i7 because those are not Dominant chords.

scale degree 6 is altered when you're going to a chord containing altered 7. So there's no need to make iio into ii to lead to III. And you don't change III to III+ so that you can change iio to ii. Chords that use raised 6 are IV (instead of iv) so you get IV-V, or IV-viio. VI is also adjusted, but virtually never as a triad, and usually as a 7th chord - it changes VIM7 (like FACE n am) to #vi%7 (sharp-six-half-diminished=7, or F# A C E in am). It also goes to V or viio (and actually will go to viio in root position which is one of the few times viio is used in root position).

But (and again, even though theory texts often point out you "can"), iio is not made into ii in minor, nor is VII made into VII#7 (G B D F# in am) or vii%7 (G# B D F# in am) - again it's kind of pointless to add raised 6 to a chord to make it go to something with raised 7 when viio7 already contains raised 7!

Now, just to be clear, you do this for melodic reasons - to avoid an +2nd. Did you catch that? Melodic reasons. Chords using raised 6 do so for Melodic reasons. Sound familiar? Again, a melodic minor "scale" is just there to remind you how raised 6 is typically encountered - in a melodic context.

Now, can you go from iv-v? Sure. Can you go from iv-V? Sure. One uses the concept of "natural notes" to lead down (F-E in am) and the other uses something similar (F-E) but with the added reason of changing 7 for harmonic purposes! So we say the former "comes from" melodic minor and the latter "comes from" harmonic minor.

But truth be told, Harmonic Minor and Melodic Minor actually come from the music, not the other way around!

By the way, the whole "use raised 6 and 7 going up, and "natural" 6 and 7 going down" is also a bit of a myth:

Many pieces do in fact do this:
i - v6 - iv6 - V has a bass line that, in am, goes a g f e. And:
V - IV6 - V6 - i has a bass line that, in am, goes E F# G# A.

And take a look at the melody of Bach's Bouree in Em:
E F# G F# E D# E F# B C# D# E Dn Cn B, etc. There are "harmonic", "melodic", and "natural" uses all within the same phrase. It should be obvious Bach was not "using the Harmonic Minor Scale" or "Using the Melodic Minor Scale" to write this piece - he was "writing in the minor mode, which entails using scale degrees 6 and 7 in unraised or raised forms depending on the situation".

Furthermore, you can find examples where harmonies and melodies do not follow these "rules" of these scales.

So I hope this sheds a bit of light (in as brief an overview as this is and can be) on how classical composers treated minor key music and what those scales really mean.

The scales are OK for practicing fingering patterns, and for learning which scale degrees are being altered, but beyond that, they're merely memory devices for the "9 note scale" actually implemented in minor key music in the CPP era.

fine.