Its a square world

To AMILton,

More information is below:

<SNIP>

Howdy tuners!

I was just skimming through the math stuff on the list and was reminded of a
puzzle/pattern that fascinates me. It's the old tic-tac-toe (or turtle back)
number pattern that adds up to the same thing in all directions, like this...

8 1 6
3 5 7
4 9 2
-------------
15's

expanded...

17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
---------------------------
65's

It always fascinates me because of how easy it is to generate these matrices
if you know the pattern. Just as long as it is square and has an odd length
on its side, it works, and it is possible to generate infinitely huge (and
seemingly complex (to me anyway)) matrices.

It occurred to me that there are some really cool tunings in there.

Has anybody done any work with something similar?
Am I way out in left field? (I wouldn't know if i was/am)

<UNSNIP>

It's funny that you should say this, but I have now calcualted two tunings
on something called the squared square, this being a parent square divided
up inot a smaller number of daughter squares, and packed with no overlap.

No two daughter squares have the same size, and the lowest number possible
is 21.

This is also known as the PLUPERFECT square.

Like pretty much of most of what I do, I extend upon ideas that have
occurred to me, and I dreampt up pluperfect quasi-hexes,
pluperfect-quasi-cubes, and woundered what the sides might add up to if each
cell in the parent square was given a value.

I will be mapping the pluperfect square to music when I buy the sampler.

The temperament is thus:

1, 1.0416666666, 1.08333333333, 1.104166666666, 1.125, 1.14583333, 1.1875,
1.270833333333, 1.2916666666, 1.3125, 1.33333333333, 1.3541666666666,
1.45833333333, 1.47916666666, 1.5208333333,1.5625, 1.645833333333, 1.6875,
1.72916, 1.8333333333333, 2

Pluperfect square matrix temperament:

Below is shown the pluperfect square matrix temperament, cut into three to
find it into this once was Word97 document:

2 4 6 7 8 9 11 15
2 1 2 3 3.5 4 4.5 5.5 7.5
4 0.5 1 1.5 1.75 2 2.25 2.75 3.75
6 0.333333 0.666667 1 1.166667 1.333333 1.5 1.833333 2.5
7 0.285714 0.571429 0.857143 1 1.142857 1.285714 1.571429 2.142857
8 0.25 0.5 0.75 0.875 1 1.125 1.375 1.875
9 0.222222 0.444444 0.666667 0.777778 0.888889 1 1.222222 1.666667
11 0.181818 0.363636 0.545455 0.636364 0.727273 0.818182 1 1.363636
15 0.133333 0.266667 0.4 0.466667 0.533333 0.6 0.733333 1
16 0.125 0.25 0.375 0.4375 0.5 0.5625 0.6875 0.9375
17 0.117647 0.235294 0.352941 0.411765 0.470588 0.529412 0.647059
0.882353
18 0.111111 0.222222 0.333333 0.388889 0.444444 0.5 0.611111 0.833333
19 0.105263 0.210526 0.315789 0.368421 0.421053 0.473684 0.578947 0.789474
24 0.083333 0.166667 0.25 0.291667 0.333333 0.375 0.458333 0.625
25 0.08 0.16 0.24 0.28 0.32 0.36 0.44 0.6
27 0.074074 0.148148 0.222222 0.259259 0.296296 0.333333 0.407407 0.555556
29 0.068966 0.137931 0.206897 0.241379 0.275862 0.310345 0.37931 0.517241
33 0.060606 0.121212 0.181818 0.212121 0.242424 0.272727 0.333333 0.454545
35 0.057143 0.114286 0.171429 0.2 0.228571 0.257143 0.314286 0.428571
37 0.054054 0.108108 0.162162 0.189189 0.216216 0.243243 0.297297 0.405405
42 0.047619 0.095238 0.142857 0.166667 0.190476 0.214286 0.261905 0.357143
50 0.04 0.08 0.12 0.14 0.16 0.18 0.22 0.3

16 17 18 19 24 25 27
8 8.5 9 9.5 12 12.5 13.5
4 4.25 4.5 4.75 6 6.25 6.75
2.666667 2.833333 3 3.166667 4 4.166667 4.5
2.285714 2.428571 2.571429 2.714286 3.428571 3.571429 3.857143
2 2.125 2.25 2.375 3 3.125 3.375
1.777778 1.888889 2 2.111111 2.666667 2.777778 3
1.454545 1.545455 1.636364 1.727273 2.181818 2.272727 2.454545
1.066667 1.133333 1.2 1.266667 1.6 1.666667 1.8
1 1.0625 1.125 1.1875 1.5 1.5625 1.6875
0.941176 1 1.058824 1.117647 1.411765 1.470588 1.588235
0.888889 0.944444 1 1.055556 1.333333 1.388889 1.5
0.842105 0.894737 0.947368 1 1.263158 1.315789 1.421053
0.666667 0.708333 0.75 0.791667 1 1.041667 1.125
0.64 0.68 0.72 0.76 0.96 1 1.08
0.592593 0.62963 0.666667 0.703704 0.888889 0.925926 1
0.551724 0.586207 0.62069 0.655172 0.827586 0.862069 0.931034
0.484848 0.515152 0.545455 0.575758 0.727273 0.757576 0.818182
0.457143 0.485714 0.514286 0.542857 0.685714 0.714286 0.771429
0.432432 0.459459 0.486486 0.513514 0.648649 0.675676 0.72973
0.380952 0.404762 0.428571 0.452381 0.571429 0.595238 0.642857
0.32 0.34 0.36 0.38 0.48 0.5 0.54

29 33 35 37 42 50
14.5 16.5 17.5 18.5 21 25
7.25 8.25 8.75 9.25 10.5 12.5
4.833333 5.5 5.833333 6.166667 7 8.333333
4.142857 4.714286 5 5.285714 6 7.142857
3.625 4.125 4.375 4.625 5.25 6.25
3.222222 3.666667 3.888889 4.111111 4.666667 5.555556
2.636364 3 3.181818 3.363636 3.818182 4.545455
1.933333 2.2 2.333333 2.466667 2.8 3.333333
1.8125 2.0625 2.1875 2.3125 2.625 3.125
1.705882 1.941176 2.058824 2.176471 2.470588 2.941176
1.611111 1.833333 1.944444 2.055556 2.333333 2.777778
1.526316 1.736842 1.842105 1.947368 2.210526 2.631579
1.208333 1.375 1.458333 1.541667 1.75 2.083333
1.16 1.32 1.4 1.48 1.68 2
1.074074 1.222222 1.296296 1.37037 1.555556 1.851852
1 1.137931 1.206897 1.275862 1.448276 1.724138
0.878788 1 1.060606 1.121212 1.272727 1.515152
0.828571 0.942857 1 1.057143 1.2 1.428571
0.783784 0.891892 0.945946 1 1.135135 1.351351
0.690476 0.785714 0.833333 0.880952 1 1.190476
0.58 0.66 0.7 0.74 0.84 1