2.3.5.17.19 subgroup Pajara/Augmented?

Hi all,

Has anyone ever looked at treating Pajara as a 2.3.5.17.19 subgroup
temperament? I know that it's more often used as a 7-limit
temperament, but I am really digging the 2.3.5.17.19 subgroup
interpretation is what really makes it shine. Specifically, look at
the following pentachord (in 12-tet)

C C# D E F

If you can't hear that C# as anything except for an implied major
third below the fourth, just play the (maybe 15:)16:17:18:20 chunk of
the harmonic series on the piano until it snaps in. The fourth should
be a break away from that and not sound like 16/21 - the point is that
we're taking this 8:9:10 that is C-D-E and splitting the C-D into
16:17:18.

Once you start hearing it as some kind of "Major" extension above the
root, you have it locked in. So play that tetrachord - C C# D E F -
and then create a disjunct tetrachord over G - G G# A B C. Play this
whole scale over and over. If you're anything like me you're tripping
out. If you aren't tripping out I might post some improvisations to
demonstrate the concept. AGAIN - focus on the perception of C# as
being a "rooted" interval over C, and focus on G# as being a "rooted"
interval over G. DO NOT think of the G# as a b6 over C - yet.

Anyway, what we have above is now C C# D E F G G# A B C. This is a
proper MODMOS of augmented[9]. Again, play this scale again until you
get the gist of what's going on: we have this 17-limit otonal
structure over C, and another one over G. In 12-equal, we are done -
we now have the harmonic structure we want. However, in other tuning
systems, like 21-equal, we're not done, because this resulting scale
has some strange properties - since 81/80 doesn't vanish, the
difference between F and G is now 10/9, not 9/8 as we probably want.

This can be accomplished by the addition of one more note - F# - to
the scale, which leads to

C C# D E F F# G G# A B C

This leads to two ridiculously awesome results!

1) The scale is now made up of three tetrachords - C-C#-D-E, F-F#-G-A,
and G-G#-A-B, all of which fit into your newly acquired perception of
16:17:18:20
2) This scale is now one of the Pajara pentachordal scales, and as
such it works in 22-equal.

I can't stop playing this, it's blowing my mind. I feel like I've
discovered new sounds in 12-equal. Has anyone played with this before?
Maybe some "microtonal" 12-tet improvs would better demonstrate the
concept if nobody gets it.

-Mike

--- Mike Battaglia <battaglia01@...> wrote:

> Maybe some "microtonal" 12-tet improvs would better demonstrate
> the concept if nobody gets it.

I've always thought there's still room for innovation in
dimipent in 12-ET. I'd love to hear your subgroup pajara
-inspired results! -Carl