For Kraig -- Blackjack scale in the Wilson/Grady style (I think)

This is intended as aa gesture of respect for your musical
philosophies, Kraig. Please give it an honest and impersonal
evaluation.

21-tone Constant Structure

Pitches Steps
sm. lg.
------- ---- ----

1/1 21:20
21/20 50:49
15/14 21:20
9/8 64:63
8/7 21:20
6/5 55:54
11/9 45:44
5/4 21:20
21/16 64:63
4/3 21:20
7/5 50:49
10/7 21:20
3/2 64:63
32/21 21:20
8/5 45:44
18/11 22:21
12/7 49:48
7/4 22:21
11/6 45:44
15/8 21:29
63/32 64:63
2/1

Note that if 22/27 is taken as an auxillary to 11/9, the scale is
inversionally symmetrical about this pair of auxillaries.

I wrote,

> Note that if 22/27

I meant 27/22

> is taken as an auxillary to 11/9, the scale is
> inversionally symmetrical about this pair of auxillaries.

And about the dyad 1/1-3/2.

I wrote,

> 15/8 21:29

21:29 was a typo -- should be 21:20.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_30814.html#30814

> This is intended as aa gesture of respect for your musical
> philosophies, Kraig. Please give it an honest and impersonal
> evaluation.
>
>
>
> 21-tone Constant Structure
>
>
> Pitches Steps
> sm. lg.
> ------- ---- ----
>
> 1/1 21:20
> 21/20 50:49
> 15/14 21:20
> 9/8 64:63
> 8/7 21:20
> 6/5 55:54
> 11/9 45:44
> 5/4 21:20
> 21/16 64:63
> 4/3 21:20
> 7/5 50:49
> 10/7 21:20
> 3/2 64:63
> 32/21 21:20
> 8/5 45:44
> 18/11 22:21
> 12/7 49:48
> 7/4 22:21
> 11/6 45:44
> 15/8 21:29
> 63/32 64:63
> 2/1
>
> Note that if 22/27 is taken as an auxillary to 11/9, the scale is
> inversionally symmetrical about this pair of auxillaries.

So, I guess this means that these are the closest just ratios to the
Blackjack scale, yes? So that means they are off by about 3 cents
from Blackjack...??

Of course, a "nice" interlocking lattice couldn't be made of this in
the same way as the tempered Blackjack.

What would a lattice like this look like? Similar to the Blackjack
lattice but with a break around the whole thing, or something
different??

Just curious...

JP

--- In tuning@y..., jpehrson@r... wrote:

> So, I guess this means that these are the closest just ratios to
the
> Blackjack scale, yes?

Not necessarily -- you can always find closer ones if you allow more
complex ratios. But these are pretty much the simplest ratios for
it, if you start on G (in the new standard "key")

> So that means they are off by about 3 cents
> from Blackjack...??

No . . . only the _consonant intervals_ will be that close . . .
_pitches_ may end up further away . . .
>
> Of course, a "nice" interlocking lattice couldn't be made of this
in
> the same way as the tempered Blackjack.

It would be finite, rather than infinitely repeating.
>
> What would a lattice like this look like?

Kraig put one up, but that only shows the prime intervals, and not
consonances like 5:3, 7:3, 7:5, etc. . . . I can make one if you
like . . . there are very similar ones already in the 'Files'
section.

> Similar to the Blackjack
> lattice but with a break around the whole thing, or something
> different??

Basically . . . if you pick one and only one occurence of each note
in the original Blackjack lattice, you will have constructed the
lattice for a JI rendition of Blackjack . . . of course my original
lattice was only 7-limit, so caveats apply . . .