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Double Bass Melodic Minor

I just looked at first few bars of Eccles 11 sonata, which is a classical student piece. Seems to me that the melodic minor rule is breached as often as it is kept. See for yourself:
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(sorry for the ugly Win+Shift+S adjustment)

To me it's actually very interesting question to think about. Knowing a rule, does it help create something, or does it stand in a way?
The "rule" is broken in those instances because the chords under the melody are moving towards D minor, which is why you start seeing E-naturals, F-naturals, and C-sharps. In the first two bars (which are solidly in G minor), the solo part only uses F-sharps

Regarding the original post, the way it was explained to me in music school was that for pure harmonic resolution, the strongest resolutions are the half-step movement from b6>5 and 7>1 (and 2>b3, but that's not really relevant here), which is why in minor our cadential figures are iv (or iimin7b5) > V7 > i. When building harmonies (and staying in one key), composers tend towards harmonic minor as the default so that you have both the b6 and 7 at your disposal. When creating melodies you still want to emphasize that harmonic movement sometimes, but having that augmented second in the scale is really jarring. In this situation, if you have a melody that is emphasizing a 7>1 resolution you want to use 6 instead of b6 because that leads towards 7>1; if you have a melody that is emphasizing b6>5, you use b7 instead of 7 because b7 leads towards b6>5.

Hope this makes sense!
 
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Yes of course Dorian is a very important minor form, but not really considered part of the minor key and it's derivation from the sub-mediant of the major key. What is interesting is that Dorian mode can 'represent' the sub-dominant of the minor key (4th mode of natural minor), but thanks to the availability of major 6ths and 7ths in the minor key, the Phrygian mode with the tricky minor 2nd and 3rd can be legitimately avoided as representing the Dominant. That's why I believe it is important to consider everything diatonic - it avoids getting bogged down in academic debates over borrowed chords, parallel modes and so on - it's all just minor!.
You seem to know your theory. Do you have a favorite book on the subject? I have a bunch that I have not gotten through including Jazz Harmony by David Berkman, Training The Ear by Armen Donelian, and a Schoenberg volume I have yet to crack. But I like to hear what others have used to really understand theory.
 
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I think the reason we jazz guys are attracted to minor sounds is their ambiguity and plasticity. If you've got a root and a minor 3rd, you're in minor and the rest is up to you and your fellow improvisors. That's why when you get tunes that spend a while on one sonority it's usually some flavor of minor. It doesn't necessarily have to go anywhere like dominant sounds do, and there's more freedom than major sounds. The 3 types of minor scales we all learned in school are just a reflection of that. They're just a way to get all the chromatics in between the 5th and the root. Scales are just a way to practice really, not building blocks of music. My personal opinion, of course.
 
You seem to know your theory. Do you have a favorite book on the subject? I have a bunch that I have not gotten through including Jazz Harmony by David Berkman, Training The Ear by Armen Donelian, and a Schoenberg volume I have yet to crack. But I like to hear what others have used to really understand theory.

I have quite a few, but they are old-school and mainly in the Classical tradition, which is my background. I suspect most of my books on theory and harmony are no longer in print :-( I started with this stuff through formal training from quite an early age (~7 until my voice broke) so to some extent it is ingrained. But here's a sample...
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I was divided on whether this was a theory question or an orchestral question. In either event, it's an academic one. I understand and use melodic and harmonic minor scales and harmonies, but:

Can anyone explain to me why in classical pedagogy, the altered notes are only altered when you are ascending and the relative minor notes are used when descending?

I've always known, but not understood this. I've kind of decided that from a jazz standpoint, it's irrelevant, but I probably shouldn't do that without understanding why it is standard in classical rudiments materials.
The answer is simpler than any kind of explanation.
It's called melodic.

On C minor, you play C than B, you want to go back to C, you play C than Bb, you want to go to Ab.
You play A, you want to go to B. You play Ab, you want to go to G.

If you want to know more, check "la règle de l'octave" from Rameau I guess.
Not Jean-Philippe Rameau but François Campion in 1716 !
I learnt to play the keyboard and figured basses with this lonely exercise.

It's all about gravity between Tonic and Dominant, when you play modal your foot never touches the floor.
 
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The reason why melodic minor has two forms comes from rule of the octave.

Sorry, I didn't see someone mentioned it.

But he's just trying to reinvent the wheel.

Everything is there.

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OK, it's French but you can read music.

We had to learn it in three positions.

It was tricky but now I play the piano more than 20 hours a week.
 
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The rule of the octave isn't a really a "rule." It's just an old name for which harmonies go with which bass notes in stepwise bass lines. There are lots of versions of the "rule" and there is not a tradition of "this one is right, that one is wrong." If you compare a few versions, the underlying voice-leading principles are apparent.
Good translation from French, thanks.