How do I arrange chords after mixing pentatonic modes?

TL;DR

There are four combinations of major and minor pentatonics which create the entire diatonic collection.

• Two minor pentatonics a whole step apart
• Two major pentatonics a whole step apart
• One minor and one major pentatonic a half step apart
• One minor and one major pentatonic a perfect fourth apart

However, any one of these formulations will suffice, as they all have identical pitch content.

Deconstructing diatonic modes into pentatonics

Let's restart from the inverse question: how can diatonic modes be deconstructed into two pentatonic scales?

Since all diatonic modes are rotations of each other, it's sufficient to consider a single mode, so let's use ionian (major).

Here is a map of the ionian mode on C along with the diatonic scales that can be derived from it. The numbers indicate the starting points of the nth mode, where ionian and major pentatonic are, respectively, mode 1.

  1 2 3 4 5 6 7 1 2 3 4 5 6 7 1
  C D E F G A B C D E F G A B C
1 * * *   * *   * * *   * *   *
2   *   * * *   * *   * * *   *
3     *   * * *   * *   * * *  
4       * * *   * *   * * *   *
5         * * *   * *   * * *
6           *   * * *   * *   *

What this table shows is ionian can be composed from:

• min pent on ionian deg 2 + min pent on ionian deg 3 (2-4-5-6-1 + 3-5-6-7-2)
• min pent on ionian deg 2 + maj pent on ionian deg 5 (2-4-5-6-1 + 5-6-7-2-3)
• min pent on ionian deg 3 + maj pent on ionian deg 4 (3-5-6-7-2 + 4-5-6-1-2)
• maj pent on ionian deg 5 + maj pent on ionian deg 4 (5-6-7-2-3 + 4-5-6-1-2)

But consider that the pentatonics built on ionian degrees 1/6, 2/4, and 3/5 contain identical pitch content, respectively. Further the pitches missing from 1/6 form a tritone, which is not contained in any maj/min pentatonic scale. This means there is really only one way to build the entire ionian (and by extension, diatonic) collection:

• minor pentatonic on X + minor pentatonic on (X + M2)

Constructing diatonic modes from pentatonics

Now let's consider the minor pentatonic scale and look at how to construct the diatonic collection. The X axis is the diatonic collection, the Y axis is modes of the minor pentatonic. (Note that this is equivalent to considering the major pentatonic, with appropriate rotation.)

                       V____________________V
  1  2  b3 4  5  b6 b7 1  2  b3 4  5  b6 b7 1
  A  B  C  D  E  F  G  A  B  C  D  E  F  G  A
1 *     *  *  *     *  *     *  *  *     *  *
2                *  *  *     *  *     *  *  * 
3 *  *     *  *     *  *  *     *  *     *  *
4             *     *  *     *  *  *     *  *
5       *  *     *  *  *     *  *     *  *  *

As can be seen, the only minor pentatonic mode that can be mapped to diatonic degree 2 is mode 3, and only modes 2 and 5 can be mapped to diatonic degree b6. But the pitch content of modes 2 and 5 is identical; thus, we have

• diatonic collection = minor pentatonic mode 2 + minor pentatonic mode 3,

which is identical to the formulation in the previous section.

Incorrect formulation

The Aeolian formulation is correct, but Locrian can not be decomposed into a minor pentatonic and a minor pentatonic a half-step up, regardless of the modes used.

Minor pentatonic = 1 b3 4 5 b7
Minor pentatonic + m2 = b2 3 b5 b6 7

Sum = 1 b2 b3 3 4 b5 5 b6 b7 7 (Too many pitches)

I don't really do this kind of music, but I've been watching videos about techniques like triad pairs and constructing scale patterns with seemingly arbitrary rules, so the system described here seemed somewhat interesting. Triad pairs... scale pairs?

I tried to produce a modal sound using a system where a pair of pentatonic scales is selected so that when their notes are combined, all seven notes of a diatonic scale are covered. As a target mode, I selected B Locrian, and as the two pentatonic scales, (1) the 4th mode of E minor pentatonic, i.e. root on B, and (2) the 5th mode of D minor pentatonic, root on C. Then I tried to construct licks with these two scales.

Here's a one-octave box of scale 1:

And scale 2, close to the same position:

First, a lick using the B-rooted scale, the 4th mode of E minor pentatonic scale.

Then a lick using the C something scale, which is also the 4th mode of F major pentatonic, and the 5th mode of D minor pentatonic scale.

(In Guitar Pro, the C something scale seems to be called "C Mixolydian Pentatonic". But in what sense is that C Mixolydian anything, if there's no Bb or E in it? It makes no sense to me.)

But does this combination work? In my opinion, in order to sound like B Locrian, at least B, C, D and F should be felt to exist in the harmonic context, maybe A as well. With our first pentatonic scale, we can reach B, D and A, but no C or F. But with the second scale, we get C, D, F and A. So if we could rely on someone else playing a low B, or if B has been imprinted in the listener's harmonic context as a root note very deeply some other way, we could be quite Locrian by simply using the C something pentatonic scale.

When writing the licks, I tried to emphasize the relevant notes of the selected "pentatonic modes", so that e.g. the C something lick wouldn't sound like it's in E minor, when played alone. The C something scale doesn't have a third in it, so it's hard to hear it as a mode as in "Church modes".

Anyway, if we play the two licks together and end the whole thing on a B note, the final note sounds like a home-note resolution.

All in all, I think it's a plausible way of constructing lines, looking at a pair of pentatonic scales like a pair of chords that, when put together, form a modal scale.