I'm studying scales and came across the natural, harmonic, and melodic minors. I understand the patterns for each scale but what other important differences exist between the three?
There are at least some differences in how they're used:
Natural minor is a kind of default.
In the common practice era a dominant chord usually contains the leading note, which is a semitone below the tonic, because that note has a strong tendency to resolve to the tonic. So, from the harmony point of view, the 7th degree of the natural minor scale should be raised in these cases, and you get the harmonic minor scale. Using a "flat" leading note makes the music sound modal, and was used both before and after the common practice era (probably also during it in folk music and such).
Raising only the 7th degree causes the scale to have an augmented second between the 6th and 7th degrees. This is a difficult interval to sing and also sounds like a jump, unlike the other intervals in the scale. So, from the melodic point of view, if you need the raised 7th and want to go up melodically, you also raise the 6th degree to make things more fluid.
Since the raised 7th degree is a leading note you usually go melodically upwards when using it. If you're going downwards you're probably not in a dominant harmony and thus you use the natural minor. Another reason for using the natural minor when going downwards is that if you take the upwards melodic minor and play that downwards it'll only start sounding like a minor after the fifth note or so.
In short, you start with the natural minor scale. You use the harmonic minor scale when you need a dominant chord, and modify it to be the melodic minor if you need the leading note in the melody. This all is, of course, simplified but should give the basic idea.
I'm going to expand upon the answer already provided just to give some further clarification on the history and usage of each scale.
- The Natural Minor scale is also known as the Aeolian Mode, one of the church modes from the plainchant period before the Renaissance. This particular scale can be created by starting on the 6th degree of any major scale, and playing an octave away from that, keeping the key signature the same. Thus:
C Major = C D E F G A B C
A Minor = A B C D E F G A
This is true for all natural minor scales.
The Harmonic Minor scale developed out of the practice of Musica Ficta, where performers and composers of chants were beginning to experiment and understand cadences. By raising the 7th degree, performers and composers were able to create additional tension / resolution for a tonal center, which led to a more satisfying result.
This created a problem however as rules of counterpoint were being developed during the early Renaissance. Moving an augmented interval in any one particular voice was considered incorrect voice-leading as it did not facilitate the smoothest possible voice-leading and was therefore jarring to the ear. The Melodic Minor scale was the solution to this problem.
As the scale ascends, the 6th and 7th degrees are raised in order to dissolve the augmented interval between the normally b6 and #7 scale degrees and create a leading tone that resolves strongly to a tonic. Thus:
A Melodic Minor = A B C D E F# G# A (ascending)
As the scale descends, it becomes a natural minor scale, with the 6th and 7th degrees now moving back to their original formation.
A Melodic Minor = A B C D E F G A (descending)
Hope that helps.
The differences are not very meaningful to music, but very prominent in musical pedagogy (unfortunately). In the Major (de:Dur, hart, lat: durus, en:hard) "gender", there are 7 fixed pitches, whereas in Minor (de:Moll, weich, lat: mollus, en:soft) two of them come in two flavours: the 6th and 7th can be minor or major. All of these combinations are in use, but there are some stereotypes, that lead to preferred sequences. So, for instance, in rising scales the major flavours are more often used than the minor ones. The natural Minor scale isn't very convincing by itself because its material is undistinguishable from Major, if there are no other clues.
You should know these three kinds of Minor, for examination purposes. But it's maybe more important to be aware, that there are no compositions at all in either of them.
If you look at Bach - who had surely a well-established feeling for Major and Minor - you'll see mostly only scale parts in use. Their ends or turning points are often the key dissonance for the Minor tonality: the diminished sixth. In the following example, I picked from Wikipedia, you see a scale part falling to the Major 7th, an upward jump by the diminished 6th, followed by another scale part:
So the sizes of the 6th and 7th in Minor are not controlled by one of "the three scales of Minor", but instead by the tonal (or musical) context (or purpose).
All of the minor scales you mentioned have something different. Let's take the C minor scale for example:
C natural minor scale is C D Eb F G Ab Bb C.
the natural minor scale, also known as Aeolian scale, taken by itself. When a major scale and a natural minor scale have the same key signature, they are relative keys. A natural minor scale has the same notes as its relative major scale, but is built starting from the sixth note of the relative major scale. via Wikipedia
C harmonic minor scale is C D Eb F G Ab B C.
C melodic minor scale is (ascending) C D Eb F G A B C (descending) C Bb Ab G F Eb D C
A harmonic minor scale differs from a natural minor scale in that the seventh note is raised one semitone. Melodic minor scales raise both the sixth and seventh notes one semitone when ascending, but when descending, the sixth and seventh notes are flattened, producing the natural minor scale. [..] The notes of the harmonic minor scale are the same as the natural minor except that the seventh degree is raised by one semitone, making an augmented second between the sixth and seventh degrees.
So, you could use any minor you like, depending on what you like.
One of the answers noted that the natural minor scale is the Aeolian mode. But the harmonic minor scale isn't one of the seven modes. The seven modes come from cyclically permuting the interval sequence
Major / Ionian: W W H W W W H
Dorian: W H W W W H W
etc. Just keep moving the first letter to the end, until you come back around to Ionian again. As noted above, one of those is the natural minor scale.
But the harmonic minor scale takes the natural minor's W H W W H W W and raises the seventh, giving you this:
W H W W H (W+H) H
That three-semitone interval between the 6th and 7th makes it a fundamentally different beast.
Then, as also noted above, the melodic minor scale raises the 6th as well, giving
W H W W W W H
This is also not a mode (not a cyclic permutation of W W H W W W H). But it removes the three-semitone interval. As noted above, this is commonly used only for ascending notes, with natural minor being used for descent.