Modern harmony revolves around tonic-dominant relationships, and part of what makes a V-I or V-i sound convincing to our ears is that the leading tone goes up a half-step to the tonic. In the common-practice era, this is why we see so many examples in minor that seem to be well described by the idea of a melodic minor scale. On the way up, we want to hear that half-step. The scale you're describing doesn't have that, because (in the key of C) it has a Bb rather than a B natural.
To ears that have gotten used to the major-minor system, I suspect that listeners would tend to hear this scale as being in F minor. The notes, F G Ab Bb C D E, are the notes of the ascending melodic minor scale. You can build chords using these scale degrees, and in fact it's fairly common to do so in jazz harmony. You get triads that are i, IV, and V7, which sound pretty familiar to most people's ears.
Of course, you could very easily set up a piece of music in which this scale would clearly be in C. You start and end the melody on C, the bass has heavy-handed emphasis on alternating between C and G, and so on. Then it would probably sound to most people like a piece of music that was in C, but with modal mixtures for effect.
Modal mixture is perfectly fine, it's used frequently, and listeners easily accept it if it's done competently. But people don't normally compose music by picking some set of 7 tones and then building everything on that as some kind of rigid structure that determines everything about the harmony and melody.
The tones must have the least maximum harmonic distance.
Could you explain what you mean by this, or point us to a source that defines this terminology? Is this something to do with psychoacoustic models of dissonance, such as tonotopic models (Kameoka and Kuriyagawa)?
