Catalog of bridgable 7-limit temperaments

Recall that these are the ones with period an octave and generator a
fifth. I list everything I could find with TOP badness less than 100
and TOP error less than 25; the second condition is not needed to
produce a finite list, but it screens out the utter crap. This list
may well be complete, but note the Special Guest Temperament at the
bottom, a hugely complex temperament which nonetheless does not fall
too far below my badness cutoff. In any case I spent a lot of
computing time and went out quite far without finding anything more
than what is here. Meantone comes in #1, and the much-maligned pontiac
#2.

meantone
<<1 4 10 4 13 12|| {81/80, 126/125}
[<1 2 4 7|, <0 -1 -4 -10|]
1201.698520 1899.262910 21.551433

pontiac
<<1 -8 39 -15 59 113|| {4375/4374, 32805/32768}
[<1 2 -1 19|, <0 -1 8 -39|]
1200.074518 1901.872135 22.393674

dominant
<<1 4 -2 4 -6 -16|| {36/35, 64/63}
<<1 2 4 2| <0 -1 -4 2||
1195.228951 1894.576888 28.744954

garibaldi
<<1 -8 -14 -15 -25 -10||, {225/224, 3125/3087}
<<1 2 -1 -3| <0 -1 8 14||
1200.760624 1903.401919 28.818557

father
<<1 -1 3 -4 2 10|| {16/15, 28/27}
[<1 2 2 4], <0 -1 1 -3|]
1185.869125 1924.351908 33.256527

mother
<<1 -1 -2 -4 -6 -2|| {16/15, 21/20}
[<1 2 2 2|, <0 -1 1 2|]
1179.240917 1882.448854 37.746618

mavila
<<1 -3 -4 -7 -9 -1|| {21/20, 135/128}
[<1 2 1 1|, <0 -1 3 4|]
1209.734056 1886.526887 39.824124

sharptone
<<1 4 3 4 2 -4|| {21/20, 28/27}
[<1 2 4 4|, <0 -1 -4 -3|]
1214.253642 1919.106053 42.300771

superpyth
<<1 9 -2 12 -6 -30|| {64/63, 245/243}
<<1 2 6 2|, <0 -1 -9 2||
1197.596121 1905.765059 50.917016

flattone
<<1 4 -9 4 -17 -32|| {81/80, 525/512}
[<1 2 4 -1|, <0 -1 -4 9|]
1202.536419 1897.934872 61.126395

<<1 4 5 4 5 0|| {15/14, 81/80}
[<1 2 4 5|, <0 -1 -4 -5|]
1219.977396 1904.959305 63.370077

kwai
<<1 33 27 50 40 -30|| {5120/5103, 16875/16807}
[<1 2 16 14|, <0 -1 -33 -27|]
1199.680495 1902.108988 64.536859

<<1 -3 -2 -7 -6 4|| {15/14, 64/63}
[<1 2 1 2|, <0 -1 3 2|]
1194.329967 1872.420906 67.416350

<<1 -3 3 -7 2 15|| {28/27, 35/32}
[<1 2 1 4|, <0 -1 3 -3|]
1215.315953 1918.820166 81.102522

schism
<<1 -8 -2 -15 -6 18|| {64/63, 360/343}
[<1 2 -1 2| <0 -1 8 2|]
1195.155395 1894.070901 82.638059

pelogic/hexadecimal
<<1 -3 5 -7 5 20|| {36/35 135/128}
[<1 2 1 5|, <0 -1 3 -5|]
1208.959293 1887.754857 84.341546

<<1 -1 -5 -4 -11 -9|| {16/15, 126/125}
[<1 2 2 1|, <0 -1 1 5|]
1185.210905 1925.395162 90.384580

undecental
<<1 -37 -43 -61 -71 4|| {5120/5103, 235298/234375}
[<1 2 -13 -15|, <0 -1 37 43|]
1199.660960 1902.492367 93.148463

grackle
<<1 -8 -26 -15 -44 -38|| {126/125, 32805/32768}
[<1 2 -1 -8|, <0 -1 8 26|]
1199.424969 1900.336158 99.875370

Special Guest Temperament

<<1 657 -67 1039 -109 -2000|| {|51 -13 -1 10>, |7 -41 2 19>}
[<1 2 275 -25|, <0 -1 -657 67|]
1199.999509 1901.957078 123.391219

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Recall that these are the ones with period an octave and generator
a
> fifth. I list everything I could find with TOP badness less than
100
> and TOP error less than 25; the second condition is not needed to
> produce a finite list, but it screens out the utter crap.

What about something to screen out the hugely complex utter crap?

> This list
> may well be complete, but note the Special Guest Temperament at the
> bottom, a hugely complex temperament which nonetheless does not
fall
> too far below my badness cutoff.

What that proves is that log-flat badness sucks. :-)

> In any case I spent a lot of
> computing time and went out quite far without finding anything more
> than what is here. Meantone comes in #1, and the much-maligned
pontiac
> #2.

Even more such evidence.