Here is an overview of the Melodic Minor in the key of C, using the CAGED system.
When playing these 5 scale positions it can be useful to be aware of when to shift position. The more you are used to it the easier the arpeggios and the other scale positions will be to play.
Practicing Scales and finding useful exercises
If you want to learn scales then you need to practice them in the right way. These posts will help you evaluate and improve how you work on scales in your practice routine
How to practice your scales and why – Positions
Practice Major Scales like this and you will get more out of it!
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Is there a reason why you describe the melodic minor as a Natural Minor with raised 6th and 7th rather than Dorian mode with only a raised 7th?
I find it easier to think of raising one note instead of two.
The Dorian mode is not really a part of tonal harmony so it makes more sense to relate things to different scales related to the minor key instead of a mode which is really something else.
Does that make sense?