We want (for dimensions above linear temperaments) a standard form of the mapping so as to be able to calculate generator steps. Perhaps taking Hermite form first, and then doing a Minkowski reduction on the non-octave part of the lattice (excluding the first column) would be a good plan. The reduction could be with regard to the weighted distance function Paul likes. The problem with it all is that it's hard to compute; an LLL reduction would be much easier. Anyone care to weigh in on this?

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...>

wrote:

> We want (for dimensions above linear temperaments) a

>standard form of the mapping so as to be able to calculate

>generator steps. Perhaps taking Hermite form first, and then

>doing a Minkowski reduction on the non-octave part of the

>lattice (excluding the first column) would be a good plan. The

>reduction could be with regard to the weighted distance

>function Paul likes. The problem with it all is that it's hard to

>compute; an LLL reduction would be much easier. Anyone care

>to weigh in on this?

what about the TM reduction?