har. min., melodic min, aeolian mode. are used when?

The harmonic minor was introduced in order to provide stronger chord progressions than the natural or pure minor could produce, hence the name harmonic minor.

Let's say you're writing a song in the key of A minor and each verse ends with two chords Em7 - Am (chord v7 - chord i). That's not a very decisive ending, but it's the best you can get using only notes from the natural minor scale. So you use the harmonic minor at that point instead and, as it contains the note G# instead of G, your Em7 (notes E G B D) will become E7 (E G# B D.)

E7 - Am is a much stronger progression because G# is only a semitone away from the key note A and leads strongly to it (hence the name leading tone).

Now let's say your melody (or guitar solo) at that point is rising by step from E to A. With the natural minor you had the notes E F G A. But now with your strong E7- Am progression, you don't want G. You want G# to match the chord tone in your E7 chord and also to take advantage of G#'s leading tone quality.
That means your melody/ solo will be E F G# A. That's fine except that the step between F and G# isn't the prettiest of intervals, (unless you like the sound of Middle Eastern music - which I do :D )
To avoid this ungainly melodic interval, the aptly named melodic minor scale was introduced. (ABCDEF#G#). So you can now make your melodic line E F# G# A. It's now a smooth melodic progression containing the strongly rising leading tone G# as well as avoiding the harmonic minor's awkward interval of an augmented second F- G#.

You can forget the descending form of the melodic minor as it's exactly the same as the natural minor.

I was going to ask something like so, so I'll just 'jack the thread. :D

If I'm a regular garden-variety guitarist, just playing for fun, maybe in a garage band with a few guys to just jam on some songs we've learned and like (not there yet, but hoping...), how would all the scales theory be useful/used? Or is it more required for writing and arranging or bringing diverse instruments and singers together? I broke out my scales, keys, chords, intervals cheat sheets, and re-read Noteboat's book. It all basically makes sense, but how deep does the casual guitarist need to go into it? As far as I've gotten so far with modes is:

I - C Ionian
Don't - D Dorian
Particularly -E Phrygian
Like - F Lydian
Modes - G Mixolydian
A - A Aeolian
Lot - B Locrian

I'm not even sure I have all that right or that there's not a lot more to it. Hence my question for the casual player.

If I'm a regular garden-variety guitarist, just playing for fun, maybe in a garage band with a few guys to just jam on some songs we've learned and like (not there yet, but hoping...), how would all the scales theory be useful/used?

Apart from improving your knowledge of the fretboard, understanding major and minor scales means you can understand how the notes and chords of major or minor keys relate to each other, which in turn allows you to be creative from a position of knowledge, rather than just relying on guess-work and hoping for the best.

The major scale is especially important to know as all chords are named and constructed in reference to it. Minor 6th chords, for example, have the note formula 1-b3-5-6. That means notes 1, 5 and 6 are taken directly from the scale. Note 3 is also from the scale but flatted to make it minor.
e.g C major scale = CDEFGAB
C min6th chord = C Eb G A (1-b3-5-6)

Understanding other scales, modes, pentatonics, exotic scales, etc is useful only to those who want to understand the structure of the various styles of music that feature them.

Apart from improving your knowledge of the fretboard, understanding major and minor scales means you can understand how the notes and chords of major or minor keys relate to each other, which in turn allows you to be creative from a position of knowledge, rather than just relying on guess-work and hoping for the best.

Ah, OK! Like knowing "how and why" to do something instead of just "what to do" based on memory; like being able to read standard notation instead of just tabs.
The major scale is especially important to know as all chords are named and constructed in reference to it. Minor 6th chords, for example, have the note formula 1-b3-5-6. That means notes 1, 5 and 6 are taken directly from the scale. Note 3 is also from the scale but flatted to make it minor.
e.g C major scale = CDEFGAB
C min6th chord = C Eb G A (1-b3-5-6)

Thanks for that explanation. That's stuff I never got to in lessons, but probably should get into. So far I understand the circle of fifths and that the minor starts with the 6th note of the major. Though I don't know why. I guess these are things I need to learn.

I made this cheat sheet that I should study more. I think it's correct.

Understanding other scales, modes, pentatonics, exotic scales, etc is useful only to those who want to understand the structure of the various styles of music that feature them.

OK, that's good to know; I don't have to get stressed worrying about things I won't be getting into until way down the road, if ever.

So far I understand the circle of fifths and that the minor starts with the 6th note of the major. Though I don't know why.

The relative minor starts on the 6th degree of the major because if you build a natural minor scale on that note you'll have exactly the same notes as are used in the major. If you build a natural minor scale on any other note of the major scale you'll have notes that aren't in the major scale.
As the A natural minor scale built on the 6th degree of the C major scale happens to have exactly the same notes as C major, they are closely related, hence the name relative minor.
It works the other way too. C major is the relative major key of A minor. (Relative majors start on the 3rd degree of the minor)

Your chart looks fine, but I see the major chart contains one more piece of information than the minor. It tells you which chords are major, minor and diminished. That's missing from your minor chart. If you don't know what they are and want to include them, they're:
Min, dim, Maj, min, min, Maj, Maj - which is exactly the same series as the chords of the major key but shifted along 6 places (or back 3)

I just can't say it too many times... you guys are the absolute best!

The relative minor starts on the 6th degree of the major because if you build a natural minor scale on that note you'll have exactly the same notes as are used in the major. If you build a natural minor scale on any other note of the major scale you'll have notes that aren't in the major scale.
As the A natural minor scale built on the 6th degree of the C major scale happens to have exactly the same notes as C major, they are closely related, hence the name relative minor.
It works the other way too. C major is the relative major key of A minor.

Ha! You are right! :D If you take C major and use F as the starting note, you don't get the same notes as you do in the "real" F minor scale. Well, I'll be..!
Your chart looks fine, but I see the major chart contains one more piece of information than the minor. It tells you which chords are major, minor and dimished. That's missing from your minor chart. If you don't know what they are and want to include them, they're:
Min, dim, Maj, min, min, Maj, Maj - which is exactly the same series as the chords of the major key but shifted along 6 places (or back 3)

Yes, I was wondering about the series of chords in the minor scales. I was looking through my books and the internet and didn't find them, or I just plain overlooked them. I've added them to my chart. I see how they are shifted. Thank you again!

Actually there is a problem with your chart, which I've just noticed. Some of the the minor keys aren't written as the real relative minor of the majors in the first chart - And C minor is missing completely.

Edit - oops - sorry - I misread it - they're fine. :oops:
Edit - no they're not - The problem is that I can't see both on my screen at the same time so I forget which major key I've just looked at when checking the minors - It's an age thing :(
Anyway, C minor is missing and it should be D# minor instead of Eb minor as D# min is the relative minor of F# major in your major key list above.

Actually there is a problem with your chart, which I've just noticed. Some of the the minor keys aren't written as the real relative minor of the majors in the first chart - And C minor is missing completely.

Edit - oops - sorry - I misread it - they're fine. :oops:
Edit - no they're not - The problem is that I can't see both on my screen at the same time so I forget which major key I've just looked at when checking the minors - It's an age thing :(
Anyway, C minor is missing and it should be D# minor instead of Eb minor as D# min is the relative minor of F# major in your major key list above.

Thanks for catching them, and for the corrections. I already discovered myself, that I'm missing C minor; fixed. I will make the other correction now. I see what you're talking about. Thanks. :) I know about the age thing... I did a lot of copy/cut/paste to make the charts... I'm surprised I got as much right as I did. :D

Your question has been answered really well so I'll just add my grain of sand. In a minor ii-V-i, where the ii chord is half diminished teh V is 7b9 and the i is m7 (like in Blue Bossa: Dm7b5-G7b9-Cm7) Over those three chords you can play C harmonic minor all day and it sounds great.
Have fun