Ch 2 and still thinking out loud. From another thread:
n jazz practice chords are extended in thirds up to a 13th.
For a fully extended C major triad, the most stable sound is the C major 13 (#11).
Put these notes in one octave, and you've got a C Lydian scale.
Hmm.
Stack those perfect 5ths, CGDAEBF#, put those notes in octave, and you've got a C Lydian scale.
Hmmm.
The Lydian scale produces the basic chords used in jazz. [As does the major scale, but...]
Let's see, the next most common source of jazz chords is the melodic minor. If I skip the next P5th (Db), I've got an A melodic minor, but I can't line these chords up with the major scale, I'd have to raise the root. If I reckon from the C Lydian I can line up these chords with their "siblings" and I've got an augmented Lydian scale.
I only have to remember to raise the G to a G#. Starting to look like a palette.
Up another fifth to Eb. Substituting the Eb for the E in the Lydian, I've got a Lydian diminished scale, and the siblings are still lined up.
The next fifth is Bb. B down to Bb in that Lydian, and there's the Lydian dominant scale.
The notes that are change (altered) are also a fifth apart.
The scale names should be consistent to make the matrix easier to memorize and consistent with the first column and the triad on I. How about Lydian, Lydian Augmented, Lydian Diminished, and Lydian Flat Seven.(that last one is nice because it recognizes the use of I7 as the I chord of the blues
To continue, the next scale, AUX.AUG or whole tone scale includes all three 'substitutions' so is a bit further out, i.e.,
I II III #IV #V bVII
The AUX.DIM moving up the cycle introduces the natural IV in combination with bIII #IV and #V for the WH diminished scale.
The AUX.DIM.BLUES adds the last 5th bII , along with bIII #IV and bVII, giving us the HW diminished scale. We have our seven principle scales and the Lydian Chromatic Scale is complete.
Note from Sandy's post on strach's thread the symmetrical divisions:
LYD divides the LCS by 2, LA by 3, LD by 4, AA by 6, and of course the chromatic scale by 12.
(This opens a window to consider the LCC concept in the light of Slomoninsky (sp?) Thesaurus of Scales ... another day)
We're now ready for a look at Example 11:3, The Lydian Chromatic Order of Tonal Gravity.