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Genuine melodic minor has been in existence for at least 300 years now – with raised 6th and 7th scale degrees in both directions. It is enough to open any work in a minor key written by J. S. Bach and see a descending fragment which contains the raised degrees. A most conspicuous example is the contrapuntal passage to the fugue theme in the C minor fugue (WTC, I). Jazz people often claim that it is they who started using genuine melodic minor on a regular basis, but let them hear some Bach music first.
In view of this empirical evidence, it makes no sense to call "melodic minor" the combination of ascending melodic and descending natural minor scale. It would be ridiculous to use the term "melodic minor" for such a hybrid scale and to "invent" a new nickname for the true descending melodic minor which is pretty abundant in the literature.
Of course, the hybrid scale (ascending melodic + descending natural) occurs even more frequently than genuine melodic minor itself, but this is no reason to call it "melodic minor". If some colleagues want to prove that the hybrid scale must be called "melodic minor", let them derive harmony from its "descending portion" and prove that these chords belong to the melodic minor mode. :)
Therefore, I suggest that we stop confusing students worldwide with such statements as, "melodic minor has a different ascending and a different descending version". Instead, we shall explain to them that a melodic minor is a minor scale which has raised 6th and 7th degrees in both directions. As for the combination of ascending melodic and descending natural scale, we can say that this scale is also very frequent; it is easier to use vocally and being fully compatible with the key signature, it frequently neutralizes the modal influence of the opposite major scale.
Let us remind ourselves that the harmonic, melodic and doubly harmonic versions of major and minor are all conspicuous examples of modal mixture. Whether you will say "scale degrees 6 and 7 in minor are raised" or "the upper tetrachord of natural major is borrowed into minor, thus giving rise of melodic minor" – you are saying the same thing.
It is another matter that some teachers still explain to their students that "degrees 6 and 7 in minor are flexible, while their counterparts in major are firm (!), or "minor mode has more chords than major mode because of the flexibility of degrees 6 and 7". I think that such statements should be embarrassing for a professor of music to say...
Conclusion. There is only one scale that can be called "melodic minor", and this is the scale which has degrees 6 and 7 raised in both ascending and descending direction. There is also a hybrid scale which combines the features of melodic and natural minor. Yes, melodic minor versus a hybrid scale. No tradition is broken, no tradition is created. Only the false tradition of uniting two different scales under a single uniform name will go away.
Thank you, and best regards.
Dr. Dimitar Ninov
Texas State University