--- 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.