Reticular Intonation (RI) is the theory and practice of using an interval audibly (very) distinct from 2/1 (or its multiples) directly as the base of a just or tempered scale (said interval here assumed the interval of equivalence of this scale). In theory, the interval chosen may be any member of this infinite set. However, the practical utility of most intervals as bases of RI scales is limited by their being either so narrow as to seriously muddy the close voicings of triads (e. g. the fifth) or so wide as to create scales which do not entirely cohere (e.g. the tritave).
Largely in theory, then, the types of RI are the following:
- Orthogonal and pseudo-orthogonal: based on an interval audibly not very distinct from the product of unequal positive integer powers of integers (the Bohlen-Pierce Lambda scale is the canonical example of this type)
- Diagonal: based on any other interval (the family of edfs supporting the temperament based on a cycle of 5/4s is the canonical example of this type)
For entirely practical purposes, however, only the diagonal type contains intervals which have unlimited utility as the base of a scale; a seventh entirely and a sixth partially being too wide to seriously muddy close voicings of triads and a tenth being narrow enough to create a scale which entirely coheres. Incidentally, therefore, 2/1 is not the axis of symmetry of this region, being in fact significantly flat of that interval, itself not even being a simple fraction of 2/1 (although essentially, if not exactly 2 degrees of 3edt).