Notating temperaments by chains of fifths

Suppose we have an r2 ("linear") temperament. It seems to me we can
divide these into five kinds so far as notation using fifths goes:

(1) The period is an octave, and the fifth is a generator. In this
case we can use standard notation.

(2) The period is an octave, and the fifth is not a generator. In this
case, seven nominals plus # and b will give us a subgroup; we will
have islands defined by the chains of fifths, and we can get a
notation for the whole thing if we have a consistent way of filling in
the spaces between the islands. For instance with miracle the islands
are at muliples of six secors, and so we need a way of naming steps up
and down of one and two or three secors.

(3) The period is not an octave, and the fifth is a generator. For
this, we need symbols for the period and its multiples.

(4) The period is not an octave, and the fifth is a multiple of a
generator. Now we need a way of notating periods, plus of filling in gaps.

(5) The period is not an octave, and the fifth is not a generator or a
multiple of a generator. This case, exemplified by ennealimmal, is the
most difficult for the chain of fifths plan. Finding a generator which
is a consonance, if possible, and using that in the chains, and then
using relationships of the fifth just to construct or help construct
an initial basis for the chain might be a way to proceed. At least in
ennealimmal it could work; we can take a chain of fifths, from
Eb to B, say, and then use this as the start of nine chains of minor
third generators. Of course, we don't need to think of this in terms
of consonant generators if using smaller ones works better.