Again, there is no such scale. What you're referring to is chromaticsm, yes, but as stated before, there is no such. If/When asking about the intervallic relationship, yes, there is one.
Originally Posted by dwest2419
And I need to correct you.
C-C# = augmented unison =/= minor second - C-Db, however is your minor second.
C#-D would be a minor second
D-D# again is an augmented unison =/= minor second
The relationship between C-D# is an augmented second =/= minor third; this makes up the harmonic minor scale as there is an A2 between note six and seven (despite it sounding like a minor third; however, C-D-Eb-F-G-Ab-B (natural)-C) As you can see the raised seventh is a half-step below the tonic - hence why it is called the "leading tone" which is why you see V7s in minor keys and not minor V7s; you may, but they aren't as strong. (ie: Summertime)
But that is what chromaticism consists of: Augmented Unisons when ascending (C-C#) - while the diminshed octave occurs when descending (C-Cb)
Granted, C-Cb sounds like C-B, but just as the augmented second =/= minor third (C-C# =/= C-Db) the diminished octave =/= major seventh. (C-Cb =/= C-B)
Oh, and make sure to link the proceeding note to the one that precedes it:
Likewise, but using the diminished octave when descending:
Does this help?