A puzzle for scale builders

I am in the process of revising an old article. It
concerns a scale with the following properties:

(1) There are seven pitch classes in the system,
which I will number ascending from 1 to 7. Octave
equivalence is assumed, but may actually vary to
create beating for coloristic or perhaps a
vibrato-like effect to cover the difference of the
tuning from a small-number-ratio just intonation.

(2) There are three distinct pentatonic 'keys',
beginning at degrees 1 (12 456), 2 (23 567) and
5 (56 123) of the seven tone system, that is to
say, at 'fifths' apart.

(3) the intervals 1-5, 2-6 and 3-7 are recognizable
as 'fifths' (let's say +/- 25 cents of a 3/2) and =

are used as dyads.

(4) 5-2', 6-3', and 4-1' _may_ be recognizeable as
fifths. The interval 7-4' is not used as a dyad.

(5) the intervals 1-2, 2-3 and 5-6 are between 80
and 190 cents apart.

(6) the intervals 1-2-3, 4-5-6, and 5-6-7
encompass an interval between an 8/7 and a 6/5.

(7) the interval 1-2 is smaller than 2-3 and the
interval 5-6 is smaller than 6-7. (The relationship
between the intervals 4-5 and 5-6 is not so fixed). =

=

I am interested in what kinds of tunings others can
come up with that will meet the above specifications
in order to find out if the set of specifications
above is sufficient and necessary. Anyone game to try?

Best regards,

Daniel Wolf
Frankfurt =