With hexatonic scales, if I'm looking for any modal doubles of a scale I simply examine the two triads formed by the alternating scale tones. For any non-tertian triads that exist by looking at the scale that way I've created names of my own as mnemonics. Eg. CD CD CD CD CD CD CD CD CD
Eb is "Cm(add9)(no5th)" E is "C ion" or "Cmaj(add2)(no5th)" F is "Dm7(no5th" aka a shell voicing of Dm7. F# is "D7(no5th)" aka a shell voicing of D7. G is Gsus4 or Csus2 Ab is "Ab(add#4)(no5th)" A is "D7(no3rd)" or "Dm7(no3rd)" Bb is "Bbmaj7(no5th) aka a shell voicing of Bbmaj7 B is "B phryg" which is the same chord type as C Db Eb below.
C C# D is "C chrom" C Db Eb is "C phryg" or "Cm(addb2)(no5th)" C Db E is "C(addb2)(no5th)" "C(addb2)(no5th)" or "Dbm(maj7)(no5th)" C Db F is "Dbmaj7(no5th)" C Db Gb is "Gbsus#4" C Db G is "Csusb2" or "C(addb2)(no3rd)" C Db Ab is "Dbmaj7(no5th)" C Db A is "A(add#9)(no5th)" C Db Bb is the same chord as Bb C Db which is found as the same chord type type as C D Eb above. C Db B is the same chord type as C C# D above. [Note: Any non-tertian triad type that contains a min 2nd interval (or a maj7th) can not really be arranged within a triad pair in the standard way, i.e. with alternating adjacent tones of the two triads.] I'm not sure I follow you here. Why did you pick this particular group of triads? it's just an example or it's supposed to be an exhaustive set of some sort? It's the list of all possible non-tertian triads. the names also seem very complex unless you manage to fit things like "Dbm(maj7)(no5th)" in one "box" in your memory. The names are harder to recite or to type than they are to remember. They're all based on the chord quality. the typical stuff that uses two triads with adjacent tones. Eg. Fmaj& Gmaj F A C, G B D, A C F, B D G, C F A, D G B, F A C Etc, etc.
nice. I suppose the same can be done with two four-note groups (e.g. the first four notes of two major pentatonics, say F and G). Four-note patterns seem to be more commonly used. Of course, unless we pick them from a 8 note scale, they will overlap. The triad pairs techniques I've been talking about are based on picking two triads with no common tones and creating lines that swing back and forth between the two triads. Usually we play these lines over a chord on which the notes of both triads happen to not be avoid notes. Eg. The lines we get from manipulating the notes of Fmaj & Gmaj will fit over the following chords: G7sus4, Fmaj7#11, Dm7, F7#11 and B7alt. If you wanted to try a similar technique with pentatonic scales, but it won't be the "same", you'd have to pick 3 notes of the scale and play them in alternation with the remaining 2 notes of the scale. C E G vs D A for example. But it wouldn't have the same qualities as working with a triad pair, especially one that uses standard tertian triads, because each tertian triad has a strong harmonic identity of its own. My teacher, Charlie Banacos, used to call triad pairs "bi-tonal pendulums". In order for the pendulum to be effective each of the two components need to be strong tonal centres in their own right. You could also try playing two pentatonic scales against each other, but they shouldn't share any common tones. Eg. C D E G A vs Db Eb F Ab Bb, Etc. So if we take F G A c and G A B D (usual ascending order) we could get F G A C, G A B D, G A C F, A B D G, A C F G, B D G A, ...
