gut feelings and analytical experiments in 20e

I've been doing a bunch of playing and careful listening experiments
the last couple of days, and I'm more convinced than ever that my
"1/20=28/27" interpretation of 20e, which stemmed from a persistent
feeling that a 0 3 6 8 11 15 16 20 wanted to be interpreted as some
(20e saturated) 4:5:6:7 form of V. - say:

5/4
/ \
/ \
/ 7/4 \
/ \
4/3-------1/1-------3/2-------9/8------27/16

is essentially on the money... And while it's true enough that in a
side by side *tuning* (i.e., non-musical) comparison this assertion is
bound to seem absurd -- as the difference between the two is of
course clear and striking -- and while the 0 3 6 8 11 15 16 20 can
only hpoe to imply the omnipresent periodicity purr of the JI version,
it's also true that the peculiar and very distinct melodic (and IMO
'harmonic') flavor of the 20e is sorely missed in the straight JI
version... but of all the (essentially) simple JI interpretations I've
tried for this particular set of 20e scales, including the "closer"
and more "consistent" approximation of this scale as a major scale
taken F to B on a circle of fifths where the fifth size is
(log(3)-log(2))*(20/log(2)) and each multiple or addition of this
~11.7/20 fifth is then taken as the rounded fraction of e, and where
on a lattice 3/2=12/20, 5/4=7/20, 6/5=5/20, and 25/24=2/20, and the 0
3 7 8 12 15 18 20 major scale is seen as a

B
\
D---A---E
\ / \ / \
F---C---G

at 1/1 10/9 5/4 4/3 3/2 5/3 50/27 2/1, and the 0 3 6 8 11 15 16 20
mixolydian is seen as a

E
\
G---D---A
\ / \ / \
Bb---F---C

at 1/1 10/9 100/81 4/3 40/27 5/3 16/9 2/1, this particular
"1/20=28/27" interpretation, where 20e is seen as:

I II III IV V VI VII
0 1/1 . . . . . .
1 28/27
2 16/15
3 9/8 [9/8] 10/9
4 9/8 8/7
5 7/6 32/27 [32/27] 6/5
6 5/4
7 81/64 9/7
8 21/16 4/3 [4/3] [4/3]
9 4/3 27/20
10 10/7 7/5
11 40/27 3/2
12 3/2 [3/2] 32/21 [3/2]
13 128/81 14/9
14 8/5
15 27/16 5/3 12/7 [27/16]
16 16/9 7/4
17 16/9 [16/9] 9/5
18 15/8
19 27/14
20 2/1 . . . . . .

or,

11------03------15~~~~~~06------18
/\ /\ /\ 10 /\ /\
/ \ / \ / \ /\ / \ / \
/ 01-\--/-13-\--/05~~\~~/~~16\--/-08 \
/ 16/ 08/ \ / \/ \ / 11/ 03
13--05-----17------09----X--20--X--12------04-------15--07
16\ 08\ / \ /\ / \ 11\ 03\ /
\ 12-/--\04~~/~~\~~15/--\-07-/--\-19 /
\ / \ / \/ \ / \ / \ /
\/ \/ 10 \/ \/ \/
02------14~~~~~~05------17------09

seems to me to ring the truest in terms of both my gut feelings and my
analytical experiments.

Dan