Yeah, the way the minor scales are presented in traditional theory is kind of dumb and confusing. Also it ignores the various minor modes that appear in diatonic theory which is very limiting.
Look at it this way...
We start with the Major scale (Ionian mode). This has a set of tones arranged in a specific order... right?
TTSTTTS
Simple enough. Now we create the 7 modes by simply starting on the next step in the pattern, incrementally one note at a time.
So TTSTTTS becomes TSTTTST the first time we do this (which produces the Dorian mode... which BTW is a minor mode). Keep doing that and eventually you end up with all seven modes and then return back to Major Ionian.
The natural minor scale appears on the sixth step of this sequence (it's modal name is the Aeolian mode).
In sequence (The Roman numerals represent the steps of the Major scale):
TTSTTTS I - Ionian (Major Scale/mode)
TSTTTST II - Dorian (minor mode)
STTTSTT III - Phrygian (minor mode)
TTTSTTS IV - Lydian (Major mode)
TTSTTST V - Mixolydian (Major mode - "Dominant")
TSTTSTT VI - Aeolian (Natural Minor Scale/minor mode)
STTSTTT VII - Locrian ("half diminished"/minor* mode)
*I say minor here because Locrian has a minor 3rd which is the distinguishing characteristic of a minor scale/chord/mode but the diminished 5th overides it (which is just an annoying way to say that the fifth has been flatted for much more convoluted advanced theory reasons).
If you squint your eyes you can the semi-tones "scrolling" backwards as we move through the steps. On your keyboard you can play this sequence by playing the C Major scale (only the white keys) up to the octave (C to C) then move up one white key to the D and play the next 8 notes (D to D), then E to E, and so on until you end up at the high C of the C Major scale you originally play. This of course continues all the way up (or down) the keyboard until you run out of keys.
We'll ignore key changes for now because that just muddles up the conversation but the pattern sequence stays the same. You would just add the necessary black keys to acheive the key change.
So the Major scale produce seven distinct scales. The one considered the "natural minor scale" within traditional music theory appears on the 6th step.
When we create the "Harmonic minor scale" all we are doing is slightly altering the tone/semitone pattern of the natural minor scale by nudging the 7th note up by one semitone. This makes it land the exact distance from the root as it would be in the Major (Ionian) scale. In the natural minor scale it is considered a "minor 7th" because it has been flatted. In the Major scale it is considered a Major 7th. In the Harmonic minor scale it is also considered a Major 7th. This naming convention of where notes appear is advanced and confusing but does serve a purpose. That's a little off point but I just wanted to show you that all we have done is take the 7th step of the nat minor scale (a minor 7th) and bump it up a semitone to a Major 7th (which is where the 7th would appear in the major scale).
So let's see how that might look using the method I did above...
TSTTSTT - This is tone/semitone sequence for the Natural minor scale (Aeolian mode)
Now let's just put a plus above the 7th interval to indicate we've added one semitone to second to last interval. THis also means we have to change the last interval to a semitone otherwise we would overshoot the octave (making our root one semitone higher which is no good). On your keyboard you can play the Natural minor scale by play all the white keys from A to A. To play the Harmonic minor all you would do is move last note before A (G) up to the following black key (G#). Everything else remains the same.
+
TSTTSTS - Harmonic minor (or "Aeolian #7" or "Harmonic Aeolian" which are names I use that I'll explain below)
Since we have a new pattern this now creates 7 new modes. Well actually they are the same modes but slightly altered by that bumped up 7th.
The thing that annoys me about this process is that when this is explained it is never really made clear that by changing the Aeolian mode we change all the modes (including the Major scale) which would be much easier to understand if we kept the modes in sequence as we did above. To add to the confusion thse modes have been given all sorts of ridiculous names over the years many of which just make the whole thing even more confusing.
I prefer to just call the by their Major modal names and add "Harmonic" to them (like Harmonic Ionian) or use the most logical traditional naming convention I've seen where they simply add a descriptor of the step changed in the scale such as Dorian #4 (the number sign of course indicating a "sharp" 4th). Unfortunately for the latter naming convention even that doesn't seem to be consistent so I just use my own names and keep an eye out for the various other names used so I have an idea what someone is talking about. Different genres of music have different names for the same scales and some genres use MULTIPLE names for the same scale within their own lingo making things extra confusing. Really annoying.
An example of how I name things...
Harmonic Ionian (or Harmonic Major scale)
or
Ionian augmented 5 (or Ionian Aug5 which is shorter... there is also a symbol for augmenting but it would require me opening my character map... which I ain't doing so you can look it up).
BTW... Augmented means to increase a note by one semitone ABOVE where it would naturally land in the Natural Major scale. So in Ionian Aug 5 the 5th note appears one semitone higher than it would in the Natural Major scale. In this case because all we have done is alter one note in our overall sequence the rest of the scale is exactly identical to a Natural Major scale... but again perhaps I'm getting ahead of myself. I'm just trying to explain why I'm naming things the way I have. I just checked my notes from years ago and it does seem that at least one traditionally used convention for this mode is simply "Ionian Augmented" so that's pretty close... but mine is more descriptive to the performer so probably easier to understand. A better example of a weird name would be what Mixolydian turns into. Apparently some folks call it UltraLocrian which is all sorts of weird and wrong (I was typing up a long winded explanation of why but that would just be even more confusing when you only asked about minor scales... lol).
The other thing to understand is when I add my modifier to sharp or Augment the note I am sharping it from the viewpoint of the mode in question. Not from the viewpoint of the Major scale (which is the more "proper" way to do it but also more confusing and requires more thought to figure out... my way if you know how to play the natural mode you just make that small change and away you go... the other way you have to mentally do the conversion of the mode, into a Major scale, make the change then switch back which is unnecessarily convoluted). Also Augmented means the same thing as Sharp but is used when the note already appears at it's natural state. To make things easier I could have just used sharps to modify everything instead of augmented but that is just a little too outside of tradition so I stuck with augmented when appropriate.
So let's look at our new sequence created from the slight alteration we did to the natural minor scale. I will start in the order the natural modes of the Major scale appear in for consistency but know USUALLY this will be shown starting from the 6th step where the minor scale appears (which IMO is what causes the bulk of the confusion in regards to minor scales).
Just to be totally clear the T with the + sign over top represents a step of a tone + one semitone. So three semitones total for that one step.
+
TTSTSTS - I Ionian Aug5
+
TSTSTST - II Dorian #4
+
STSTSTT - III Phrygian #3 (Phrygian Dominant*)
+
TSTSTTS - IV Lydian Aug2
+
STSTTST - V Mixolydian Aug1 (Having a sharped root note* is very strange indeed... lulz)
+
TSTTSTS - VI Aeolian #7 (Harmonic Minor)
+
STTSTST - VII Locrian #6
It may actually be easier to see how the intervals flow backward that way because you can see the + sign jumping back a notch with each step then jumping to the end of the pattern once it can't go backwards anymore. In modal and key theory there is a lot of this type of flowing and infinite movement. It's kind of cool once you start seeing the patterns.
*I marked off Phrygian Dominant because it is actually far more important than the root scale of harmonic minor. The reason harmonic minor is used traditionally is for the chord created on this step. In natural minor the 5th chord (also known as the "Dominant" chord) is a minor. Someone, somewhere decided that sounded bleak, boring and it stifled creativity so they switched the 5th to a Major chord which adds a completely new flavor to the minor scale and allows for different, and some would say more pleasant, chord progressions. That someone (or someone else) did the math needed to accomodate the new chord progression and the harmonic minor scale was born. It technically isn't meant to be played as a scale... just to create chord harmonies thus the name. However it and its modes can of course be played as scales and often are in metal, jazz and other more adventurous and/or ethnic music. In classical theory it's just for chords with the nat minor and/or melodic minor played over top (booooring... not to mention confusing as hell).
I find a good, simple way to make immediate use of the Harmonic minor scale and to understand it a little better is to play a I, IV, V type progression. The I is a minor chord, the IV is a minor chord and the V is a Major chord.
So in the key of A minor you would use... Am, Dm and E Major.
As you play your progression (you can organize it however you want) use the natural minor scale to improvise a melody over top of the Am and Dm chords. Then when you move the E switch to using the Harmonic minor for your melody. Switch back to natural minor when you move away from the E.
By switching to the Harm minor on that chord alone the scale/melody/improv sounds less "foreign". You get the benefits of the moodier minor chords but a nice "happy" type of movement from the major/dominant chord. Since the nat minor scale fits over top of the two minor chords it sounds good there but it won't over the dom 5th. Switching to the harm minor DOES fit.
Of course that's probably a really bastardized/simplistic way to use it all but it's cool and useful for writing and improvising. It will also give you somewhere to go if you are working with another artist who uses the harmonic minor for their progression.
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Melodic minor
This one is indeed a brain twister. When they say "play it one way ascending and another descending"... well that makes no damned theoretical sense. It's like Shrodinger's cat or in quantum physics when they (used to) say that light is both a wave AND a particle depending on whether you are observing it or not (WHUT?!).
That's why I personally dismiss that nonsense. It's a paradox. I'm sure it makes sense to Juliard graduates and other classical automatons (or they pretend it does) but really... it doesn't make sense in any practical way as far as I can tell. I am of course completely self taught (aside from some pretty lame lessons for a year when I was 12).
It just seems to be a compositional "suggestion" or "style" by some bored long dead composer who may or may not have just been screwing with everyone. Remember that the "modes" other than the Ionian and Aeolian modes were deemed "paganistic/heresy" by the clergy and thus the royals who commissioned and sponsored composers of yore. Of course they still used modes simply by shifting chords throughout a composition but could not make those chords or modes the root. That is why it is speculated those composers came up with such silly things like the harmonic and melodic minor. Essentially to get a bit more creative room withotu getting burned at the stake or losing their royal funding. It is also why traditional music theory is so damned convoluted and confusing when the modal method is more precise and easy to understand (something jazz musicians have long known and how they can create seemingly impossibly complex music).
The best way to look at the melodic minor scale is from the jazz perspective which is to just study it and implement it as the "ascending" version. The descending version is simply the natural minor scale (there is no difference... it is just the natural minor scale/Aeolian mode and behaves exactly the same way).
In fact when viewing it from this angle it is often called the Jazz minor scale which uses the ascending version of the melodic minor in both directions just like you would any other scale or mode.
There are two ways to look at the Melodic minor scale (well this is how I look at it).
The simplest way is to consider it a Major scale (Ionian mode) with a flatted 3rd. So exactly like the Major scale in every way but you drop the third note a semitone.
However considering we are supposed to apply it like we would a minor scale we can view it as the Natural minor scale (Aeolian mode) with a sharp 6th AND a sharp 7th. So in that sense it could even be considered a Harmonic minor with a sharped 6th.
Of course that is when comparing it to those scales. Traditionally we use the Major scale as our metric at all times but as I said earlier that gets too confusing when trying to keep track of modes and chord steps. I much rather avoid those whacky, non stop conversions. You learn the 7 natural modes then alter them as needed to accomodate the modes of Harm and Mel minors.
So let's pretend we are altering the Natural minor scale in its natural modal position which is the 6th step of the Major scale.
First we'll start with the interval step order of the ascending version of the Melodic minor scale which is...
TSTTTTS
Notice that unlike the Harmnic minor there is no tone and a half to create this. We just altered where the two semitones appear. This creates a longer string of whole tones (and thus reducing the number of whole tones in the shorter run of whole tones between the semitones from two down to one).
To clarify this point further here is the natural minor...
TSTTSTT
and again here is the melodic minor...
TSTTTTS
The three whole tone series has been turned into a four whole tone series and the two whole tone series is reduced to one single whole tone.
Now let's take the interval sequence and create the 7 modes of melodic minor just as we did before with both the natural and harmonic minor scales.
In this sequence I will view it from the perspective that we have altered the Natural minor scale so the Melodic minor will appear at the 6th step of the sequence...
TTTTSTS - I Ionian #4/#5
TTTSTST - II Dorian #3/#4
TTSTSTT - III Phrygian #2/#1
TSTSTTT - IV Lydian #1/#2
STSTTTT - V Mixolydian #7/#1
TSTTTTS - VI Aeolian #6/#7 (Melodic minor)
STTTTST - VII Locrian #5/#6
This time I did not bother doing the sharp/augmented conversion because I've been typing this for too long as it is but essentially you just take the natural mode listed and sharp the steps indicated to acheive the Melodic minor mode for that step.
Now as to the usage of the melodic minor. In classical is where you will find that weird ascending/descending thing. Of course this has bled into more modern music but that concept seems to be rarer. Actually it seems to more manifest itself by way of non diatonic scales with little chromatic runs in it like the bebop/mixoblues scales. I honestly haven't spent a lot of time trying to understand the ascending descending nonsense so a classically trained individual would have to chime in.
As far as using the pure ascending version, like they do in jazz, I personally find the melodic minor scale (which in this sense is more likely to be referred to as the Jazz minor scale) kind of... well not really useful. It kind of comes off as hokey, wandering and pointless unless played just so. It's a good variation to toss in while improvising but all in all I don't like it. Some of the modes however are cool and analyzing the chord sequence produced by it is very interesting from a theoretical perspective.
Really it has been a while since I sat down and really played with melodic minor so I can't provide you any good progressions to try.
The modes of melodic minor and some of it's derivatives have some interesting names based in some really mind twisting theory but it really is easier to just think of the natural modes and raise the necessary notes to get it all absorbed mentally (it's easier to remember this way) and THEN worry about all that other silliness later. At least it was for me.
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Conclusion.
So that was a rather rambling (and mostly unedited) post that seems to ahve turned into an almost mini lesson/article.
To sum it all up and make it easier to absorb do this.
Learn the Major scale in C Major.
Now learn all the modes of C Major.
That is all just playing on the white keys octave to octave going from C to C, D to D, E to E, etc. Very simple.
Now make sure to number each of those steps in your mind from 1 to 7 (the 8th step of course bringing you back to C Major an octave higher than where you started).
Learn and memorize the name of the natural modes which are, in order:
I Ionian (Natural Major)
II Dorian
III Phrygian
IV Lydian
V Mixolydian
VI Aeolian (Natural minor)
VII Locrian
Now always remember that the minor scale appears on the 6th step of your modal sequence.
To "solve" the harmonic modes add one semitone to the 7th step of the Aeolian mode (natural minor).
Now the notes will never change for any of the keys. Just the starting point of the scale.
So since we are adding a semitone to the 7th note of the Aeolian mode of C major we end up with...
A B C D E F G# A
We now can just move through all the modes one starting note at a time. To get back to Ionian we move up to the C which gives us...
C D E F G# A B C
Which we could call Harmonic Ionian or Ionian Augmented 5th or Ionian #5 or the way it seems to be called in traditional theory simply Ionian Augmented (which is woefully lacking in description for my taste).
Then you can simply start moving through the notes one at a time to create the modes of harmonic minor just like we did with the natural modes.
To change keys just take the tone/semitone pattern of harmonic minor and apply it to the correct note (so if you want to create G harmonic minor start on G, plug in the tone/semitone pattern and repeat what we have just done... you'll end up with a different amount of black keys in different locations as you move through each key but the pattern and concept stays the same).
To acheive melodic minor do the exact same thing except this time sharp the 6th and 7th notes of the natural minor scale/Aeolian mode. Then move through everything as we have been doing keeping track of where those sharped notes appear.
Of course with melodic minor you could also take the Major scale (Ionian mode) sequence and flat the third by a semitone. You do however have to remember that you are NOT altering the Ionian mode so you cannot label it as if you were. It needs to be conceptual considered the 6th step of sequence. This gets particualrly confusing because in traditional theory when you switch to minor scales the VI becomes the I BUT it still appears at the same position in the sequence... which is why I hate the way that crap is taught. It shoudl ALWAYS be first thought of as the VI step of the Major scale then translated from there.
Also many commonly used names from jazz and other theories will skew things further because they will name some of these harmonic and melodic minor modes simply based on their similarities to their natural mode counterparts instead of the actual position in the 7 mode sequence.
For example the I mode in the melodic minor sequence is often referred to as Lydian Augmented even though it occupies the I spot which is where Ionian is in the natural modes. The only reason this is is because it is more physically similar to the lydian mode except with an augmented (sharp) 5th. This is extremely misleading and puts everything completely out of order. That is only one example.
So keep your modes straight in your head, where they appear, how they appear and make your modifications from there. THEN go scout out the various dumb names used.
Math first.
Cheers... and sorry if that is too long or confusing. I normally edit this kind of crap down when writing my actual lesson stuff but perhaps it will be helpful figuring this nonsense out... and believe me it is indeed unnecessarily nonsensical.