15 microtemperaments supported by 270

The point posting this isn't simply to annoy people; it seems to me
that 270 is an obvious route to notating the 13-limit. I am sure thet
it has a Saggital method worked out for it already, but I see that a
generator of 44/39, and a period of 1/2 octave, for instance, might be
a good way to work with the 13-limit. We also find the plausible ways
to extend ennealimmal and hemiennealimmal to the 13 limit in this way,
and it is nice to know they are out there. There's a lot of
ten-nominal stuff lurking in the underbrush as well. On the bottom
line is Graham complexity, TOP error, and the resultant logflat badness.

[22, 48, -38, -34, -54, 25, -122, -130, -167, -223, -245, -303, 36,
-11, -61]
[[2, 7, 13, -1, 1, -2], [0, -11, -24, 19, 17, 27]]
102 .078096 173.897744

[50, 60, 110, 70, 0, -21, 34, -62, -185, 87, -45, -222, -184, -407, -259]
[[10, 14, 21, 24, 32, 37], [0, 5, 6, 11, 7, 0]]
110 .093739 236.724371

[72, 108, 72, 36, -54, 4, -88, -192, -352, -136, -290, -525, -148,
-418, -320]
[[18, 28, 41, 50, 62, 67], [0, 4, 6, 4, 2, -3]]
198 .049207 330.980012

[12, 63, 102, 6, 81, 72, 128, -32, 84, 60, -204, -45, -336, -150, 258]
[[3, 4, 3, 2, 10, 6], [0, 4, 21, 34, 2, 27]]
102 .149522 332.943641

Hemiennealimmal
[36, 54, 36, 18, 108, 2, -44, -96, 38, -68, -145, 51, -74, 170, 307]
[[18, 28, 41, 50, 62, 65], [0, 2, 3, 2, 1, 6]]
108 .144410 353.701213

[16, 84, 46, 98, 108, 96, 28, 100, 112, -129, -63, -60, 116, 133, 11]
[[2, 4, 9, 8, 12, 13], [0, -8, -42, -23, -49, -54]]
108 .149522 366.221101

Ennealimmal
[18, 27, 18, -126, -81, 1, -22, -262, -195, -34, -386, -288, -416,
-294, 186]
[[9, 15, 22, 26, 26, 30], [0, -2, -3, -2, 14, 9]]
162 .076135 366.527988

[2, -57, -28, 46, 81, -95, -50, 66, 121, 95, 304, 399, 226, 331, 110]
[[1, 1, 19, 11, -10, -20], [0, 2, -57, -28, 46, 81]]
138 .102172 376.526707

[34, 111, 64, -28, 27, 97, 6, -162, -83, -163, -449, -348, -300, -161,
197]
[[1, 7, 20, 13, -1, 8], [0, -34, -111, -64, 28, -27]]
139 .104131 388.394328

[92, 78, 62, -44, -54, -90, -160, -388, -426, -75, -372, -414, -338,
-381, -24]
[[2, 26, 24, 21, -4, -6], [0, -46, -39, -31, 22, 27]]
238 .044086 402.962652

[24, -9, -66, 12, 27, -70, -172, -64, -46, -128, 59, 96, 262, 320, 49]
[[3, 2, 8, 16, 9, 8], [0, 8, -3, -22, 4, 9]]
114 .152174 407.862914

[52, 3, 82, 116, 81, -116, -16, 4, -64, 182, 259, 177, 42, -76, -149]
[[1, -4, 2, -6, -9, -5], [0, 52, 3, 82, 116, 81]]
116 .152722 421.372278

[20, -30, -10, -80, 0, -94, -72, -196, -74, 61, -82, 111, -190, 37, 296]
[[10, 16, 23, 28, 34, 37], [0, -2, 3, 1, 8, 0]]
120 .151497 442.287562

[74, 51, 44, 82, 27, -91, -138, -126, -231, -41, 14, -126, 78, -87, -210]
[[1, -25, -16, -13, -26, -6], [0, 74, 51, 44, 82, 27]]
148 .110293 456.719330

[70, 30, 100, -10, 0, -115, -38, -258, -259, 148, -127, -111, -374,
-370, 37]
[[10, 13, 22, 24, 35, 37], [0, 7, 3, 10, -1, 0]]
150 .117374 497.041042

Gene,

please, please, PLEASE ... write an explanation of
"logflat badness" that the layperson can understand
... feel free to include all the heavy math stuff
at the end, but keep the beginning easy. thanks.

-monz