*Correction01* Re: 114 7-limit temperaments

>>>Number 8 Schismic
>>>
>>>[1, -8, -14, -15, -25, -10] [[1, 2, -1, -3], [0, -1, 8, 14]]
>>>TOP tuning [1200.760625, 1903.401919, 2784.194017, 3371.388750]
>>>TOP generators [1200.760624, 498.1193303]
>>>bad: 28.818558 comp: 5.618543 err: .912904
>>>
>>>
>>>Number 9 Miracle
>>>
>>>[6, -7, -2, -25, -20, 15] [[1, 1, 3, 3], [0, 6, -7, -2]]
>>>TOP tuning [1200.631014, 1900.954868, 2784.848544, 3368.451756]
>>>TOP generators [1200.631014, 116.7206423]
>>>bad: 29.119472 comp: 6.793166 err: .631014
//
>> And I don't see how you figure schismic is less complex than
>> miracle in light of the maps given.
>
>Probably the shortness of the fifths in the lattice wins it for
>schismic . . .

After I wrote that I reflected a bit on comma complexity vs. map
complexity. Comma complexity gives you the number of notes you'd
have to search to find the comma, on average (Kees points out that
the symmetry of the lattice allows you to search 1/4 this numeber
in the 5-limit, or something, but anyway...). Map complexity is
the number of notes you need to complete the map *with contiguous
chains of generators*. It's this contiguous-chain restriction
that makes me wonder -- what good is it? I suppose it helps keep
the number of step sizes (mean variety) low in the resulting scales.
But it implies a generator-stacking process that produces linear
temperaments in some (DE/MOS) cases and I'm guessing planar
temperaments otherwise (when there are 3 step sizes)... if so what
relation do these planar temperaments bear to the linear temperaments
arrived at with the same-sized generators?... in the case of Marvel,
Gene says 384:whatever always goes with 225:224, and this notion of
natural planar extensions seems highly interesting... Aside from
the Hypothesis, the link between these two ways of approaching
temperament (chains vs. commas) seems little-explored.

-Carl