I have no doubt that the Mark Levine book is a great reference. thanks for the heads up.
I still think there is special sauce involved in this music theory. After adding harmonic minors and melodic minors there are 252 keys? I explain my reasoning below.
If I start on the circle of 5ths or the circle of 4ths, there are 12 keys, (some say there are 14 keys, maybe more). To stay with the spelling, where the notes are A,B,C,D,E,F,G, and the associated accidentals. there probably more keys, (I can think of Cb for one, that is not described on the circle, but is considered a valid jazz scale) but for the sake of discussion, we stick to the 12 keys, following what I believe there are only 7 scales to work with, and those are defined by the piano's white keys, so there only 7 keys to worry about. then as you explain above there are three mode groups to worry about, Major scale, Harmonic minor and Melodic minor ascending. So you have 21 scales (modes?). However, when you switch to harmonic minor or melodic minor ascending, accidentals are required to define the scales, so now the black keys are available as well as the double flats and double sharps, as we know spelling is important, I have never run into triple flats or triple sharps, so in the world of quantum music theory, they might exist [a little humor on my part]).
Expand the keys to accepted major scales found on the circle of 5ths or 4ths, you have 12 major keys, since within the defined modes, relative minors are included, we wouldn't double count. 12 major keys, and each key has a dorian, Ionian, etc., associated with it. That's how I got 84 scale-modes. I believe the math is straight forward. I accept your addition without argument that Harmonic minor and Melodic minor are acceptable scales, now take the dorian, the Ionian, etc., from each one, you get 252 scales-modes.
And we haven't spoken about super Locrian, Lydian augmented, and Lydian dominant, and other permutations. Its my understanding, the three special scale-modes, I just mentioned can be called by other scale-modes, per Dan Erksine, a contributor on another website.
Special sauces are made from known ingredients, its the mix of the ingredients that make it special sauce.
In the case of music theory, in western music, we have 12 notes in a chromatic scale, and how they are mixed really how they are spelled make up the incantations we call scales-modes. I am just a mediocre bass-player with a junior high music education, that out of curiosity conjured up devils because I thought a self study of music theory would be beneficial to my playing.
(By the way, I have taken some liberties in my word selection, using such phrases as "special sauce, incantations, etc,.)
To me, the term mode should have stuck to using, the white keys on the piano. (Which wasn't invented when the equiv white key pitches were the only game in town, in western music).
- is lacking that knowledge.
