I have been working on listing all the possible diatonic scales in order of degrees, the number of accidentals in the scale. The first is the ionian ( major ), since there are zero accidentals. The next would be the mixolydian (b7), then a scale with a b6th, etc., etc.
The harmonic minor doesn't fit the definition of a diatonic scale, because of the minor 3rd interval between the b6th and the natural 7th, but I decided to include it, since it does contain seven tones, and does not contain three or more simultaneous semitones ( 3rd, 4th and b5th, for example) . In doing so, I found two more scale families, each with seven new modes. Im sure that these scale sets have names, but I have not yet found them.
The first contains a scale with a b6. I thought it might be called Harmonic Major, but Im only guessing. The other contains a scale with a#2,#4,b7. I just call it a lydian dominant #2.
How do I determine what the primary scale is ( as is the ionian in the major scale ), and do these scale families have specific names, like, for instance, the Melodic minor, or Major scale?
Also, am I using the term "degrees" correctly? For example, how many degrees in a scale like this:
C Db Eb Fb Gb Abb Bbb (h W h W h W mi3rd)
Is it 3, since the Fb, Abb, and Bbb are enharmonically natural notes, or is it 6, since all six notes are altered?