The sound of the opening of Poema armónico is *minor 7 chord*, with little inflections to 027. To extend this sound through the chromatic space we have the octotonic option, transposing by multiples of 3, the minor third cycle. There are other ways to transpose the minor 7 chord through the chromatic space. 3 is not the only interval.
I'm not afraid of a wee whiff of octotonic, but composing with the octotonic scale or jamming on the octotonic scale is too easy. Moreover, the 3 cycle extensions of the minor 7 chord is a lovely post-tonal way to extend that harmony, but the behavior of the octotonic scale is so predictable that I prefer to lace minor third extensions with other transpositions, particularly more tonal ones. I get encouragement here from the wonderful things Terry Riley does in his Y Bolanzero.
Also, at this moment I am exploring the large, "public" entities:
Octotonic (with great caution)
Augmented scale (012589), aka "E Hexachord"
Diatonic septachord (diatonic collections *with tritones*)
Crossings between a collection where a pitch has fewer relationships to the others to one with a wealth of relationships is a meaningful crossing.
E hexachord 014589 has
6 major 3rds
3 minor thirds
The diatonic septachord enjoys this wonderful dynamic:
3 major 3rds
4 minor 3rds
In the ancient world of 12-tone music these large "public" collections were thought to lack specificity that some rows & partitios offer. On the other hand, a composer can constellate the interplay of larger elements in ways that are absolutely unique to a given piece of music, matching the specificity of 12-tone music.
The behavior of rows has become problematic, but arrays and especially counterpoints of arrays showed us the way out of that. My way, at this moment comes from experience with super-arrays.