Fwd: Two 21-tone JI scales: detemperings of blackjack

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
Here's a JI convex detempering of blackjack that seems to give the
most possible pure 4:5:6:7 chords (six of them). Is that right?

Go to

/tuning-math/files/perlich/scales/

and download

blackjack6.gif

The JI scale is as follows:

ratio note cents
1/1 E[ 0
50/49 Ev 35
15/14 F< 119
320/147 F 147
8/7 Gbv 231
7/6 Gb^ 267
60/49 G 351
5/4 G> 386
21/16 Ab^ 471
4/3 A[ 498
7/5 A> 583
10/7 Bb< 617
3/2 B[ 702
32/21 Bv 729
8/5 C< 814
80/49 C 849
5/3 C> 884
7/4 Db^ 969
25/14 D[ 1004
15/8 D> 1088
40/21 Eb< 1116

The step sizes are

50/49
21/20
64/63
21/20
49/48
360/343
49/48
21/20
64/63
21/20
50/49
21/20
64/63
21/20
50/49
49/48
21/20
50/49
21/20
64/63
21/20

If change the note G by 2400:2401 we have this lattice instead:

Go to

/tuning-math/files/perlich/scales/

and download

blackjacksup.gif

The scale is

ratio note cents
1/1 E[ 0
50/49 Ev 35
15/14 F< 119
320/147 F 147
8/7 Gbv 231
7/6 Gb^ 267
49/40 G 351
5/4 G> 386
21/16 Ab^ 471
4/3 A[ 498
7/5 A> 583
10/7 Bb< 617
3/2 B[ 702
32/21 Bv 729
8/5 C< 814
80/49 C 849
5/3 C> 884
7/4 Db^ 969
25/14 D[ 1004
15/8 D> 1088
40/21 Eb< 1116

with step sizes

50/49
21/20
64/63
21/20
49/48
21/20
50/49
21/20
64/63
21/20
50/49
21/20
64/63
21/20
50/49
49/48
21/20
50/49
21/20
64/63
21/20

This could satisfy Kraig Grady, and perhaps even Pierre Lamothe,
despite the loss of a tetrad relative to the first scale. Pierre, any
comments on this last version?
--- End forwarded message ---

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

> This could satisfy Kraig Grady, and perhaps even Pierre Lamothe,
> despite the loss of a tetrad relative to the first scale.

What do Kraig and Pierre need to make them happy?

--- In tuning-math@y..., genewardsmith@j... wrote:
> --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:
>
> > This could satisfy Kraig Grady, and perhaps even Pierre Lamothe,
> > despite the loss of a tetrad relative to the first scale.
>
> What do Kraig and Pierre need to make them happy?

Kraig loves CS scales with all steps as superparticular ratios. As
for Pierre . . . I'll let him speak for himself.