in
/tuning/topicId_36877.html#36877
gene wrote,
"
Here is a symmetrical JI scale related to Blackjack, obtained by
detempering Blackjack by what I call "Euclidean reduction", where I
choose the scale step nearest to unity in the symmetrical 7-limit
octave-equivalent lattice. In the one case where there was a tie I
broke
in in favor of 49/40 and 80/49 rather than 60/49 and 49/30; the latter
giving an alternative version.
Here is the scale:
1, 49/48, 15/14, 35/32, 8/7, 7/6, 49/40, 5/4, 21/16, 4/3, 7/5, 10/7,
3/2,
32/21, 8/5, 80/49, 12/7, 7/4, 64/35, 28/15, 96/49
"
i made a lattice, with the broken consonances in gray, here:
/tuning-math/files/Paul/blackjust5.gif
some of the consonances are broken by more than 8 cents (1029/1024),
and there are only four just tetrads.
look at some of my previous detemperings of blackjack, for example
this one
/tuning-math/files/perlich/scales/blackjust4.g
if
keeps all the mistunings under 8 cents (all the breaks are labeled
with the ratio of the mistuning amount), has twice as many just
tetrads, and is also symmetrical about a 1/1!
