Taxonomies of xen approaches
One possible taxonomy of approaches to xen:
JI-based approaches either use JI directly, or interpret all pitches in a system as JI ratios. Formalized JI-agnostic and non-stacking-based approaches to xenharmony are more recent than JI-based RTT approaches.
Stacking-based approaches obtain all pitches by stacking a finite set of intervals. Non-stacking based approaches do not think of pitches in systems this way, even if e.g. edos are trivially stacking-based.
- JI-based, stacking-based: Traditional, JI-based RTT is a major approach that belongs to this, in JI-based RTT the JI interpretations of two intervals stack according to the temperament mapping. So is prime-limited or lattice-based JI.
- JI-based, non-stacking-based: Primodality and nejis.
- JI-agnostic, stacking-based: Uninterpreted mosses and k-step scales. This could be thought of as RTT but with abstract intervals instead of JI. The goal of these systems is not to approximate JI (though close JI intervals can be considered sometimes), but to give the pitch system or scale a regular structure (e.g. a finite number of scale steps or a maximum variety condition such as mosses.) For more (in context of edos), see EDO vs ET#Temperament-agnostic EDO paradigms.
- JI-agnostic, non-stacking-based: This is a more wide-open area.