Pitch Set Harmonization

Pitch Set Harmonization is a method of building harmony based on a set of pitches which act as the fundamental pool of intervals that can be combined to make a consonant chord. It is a form of secondual harmony in that the chords are based on seconds rather than thirds or fourths. The most basic example is taking the first three pitches of a mos mode and using those as your pitch set. The advantage of this is that not only does it solve the problem of mos not having major and minor triads, but it allows for a more modern, creative approach to harmonizing mos scales without being totally in the dark about it.

Mavila

Mavila in 16edo can be harmonized by taking the first three pitches of the scale and placing the ninth on top producing chords of 000-225-375 called Hard, 000-150-375 called Soft, and 000-125-300 called Symmetrical. In addition, the first inversion is needed to create a full range of harmonization possibilites. Something, however, happens with Mavila and other mos scales that doesn't happen with inversions of tertian triads: The first inversion can be considered a chord in it's own right apart from the Root position. This means that if you have a chord of CED then EDC with E as the root can be considered a resolved sonority. First inversion triads in Mavila have a cool metallic sound which is more xen than the regular Root position chords. Therefore, there are two types of triads: Open - 1st inversion and Closed - root position.

Below is an example of Mavila Harmonized entirely with Open chords:

Mike's note - original SoundCloud link is broken

And another Example of harmonization using both types of chords:

Mike's note - original SoundCloud link is broken

Options for extended harmony exist as well and can add more interesting color to the triads, this too is more interesting with the open position chords. For example, a chord of 000-975-825 can be extended by adding another stacked interval of either a large or small seventh.