Periods and generators

My previous example with a title like this hasn't shown up, and now I'm trying to follow it up anyway. Nuts!

I was going to add to a previous example of 720 as a period for meantone one of 16/15 as meantone. Assuming the posting does finally show up, continue with this point: I want 16/15 to be my period, so I
take 16/15^81/80 = h5. Now one solution to h5^g = 81/80 is g=h7, which gives us [h5,h7] as our map. We now have a "period" of about 16/15, inside of which is a "generator" of about 25/24. But a more sensible way of looking at it is that 16/15 and 25/24 are both generators, and we do 5-limit meantone by means of a two-dimensional generator lattice.