Correction in Paul's blackjack lattice

We have discovered a slight error in Paul Erlich's blackjack lattice,
which, otherwise, really looks great! I've been staring at it for
hours!

The correction replaces A< (6th tone low) with A[ (quarter tone low.)

In this lattice, because of the nature of the 6 "interlocking" 12-
tET "bicycle chains," all the chained fifths should have the SAME 72-
tET alterations.

Therefore, 1/4 down the page to the left one should find:

D[ A[ E[ B[

and, similarly, you will find the same needed correction half way
down the page at the left. (A[ replaces the A<, of course)

At the very bottom of the page, you will note that the link of fifths
is, in that instance, correct... and also the same chains in the
MIDDLE of the page...

_________ __________ ________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> We have discovered a slight error in Paul Erlich's blackjack
lattice,
> which, otherwise, really looks great! I've been staring at it for
> hours!
>
> The correction replaces A< (6th tone low) with A[ (quarter tone
low.)

Thanks, Joseph, I've made the correction.

Go to /tuning/files/perlich/scales/ and
download bjlatt.ZIP. The image blackjack0.bmp is the corrected
version. And I've added blackjack3.bmp, which shows one (arbitrary)
way the lattice can be broken down into identical 21-tone periodicity
blocks. Half of the consonant tetrads are broken in this process -- I
know I can do better, but perhaps not if C is forced to be at the
exact center of each block . . .