Here are the four largest commas on my list of 32, and the temperaments they lead to.

27/25

Map:

[ 0 1]

[ -2 2]

[ -3 3]

Generators: a = 2.0104 / 9; b = 1

badness: 359

rms: 35.6 cents

g: 2.16

errors: [-38.1, 9.5, 47.6]

16/15

Map:

[ 0 1]

[ -1 2]

[ 1 2]

Generators: a = 2.9479 / 8; b = 1

badness: 129

rms: 45.6 cents

g: 1.414

errors: [55.9, 55.9, 0]

135/128

Map:

[ 0 1]

[-1 2]

[ 3 1]

Generators: a = 10.0215 / 23; b = 1

badness: 46.1

rms: 18.1

g: 2.94

errors: [-24.8, -17.7, 7.1]

25/24

Map:

[ 0 1]

[ 2 1]

[ 1 2]

Generators: a = 4.9722 / 17; b = 1

badness: 81.6

rms: 28.9

g: 1.414

errors: [0, -35.3, -35.3]

Neutral thirds

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> 135/128

> badness: 46.1

Should be 461.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> 135/128

>

> Map:

>

> [ 0 1]

> [-1 2]

> [ 3 1]

>

> Generators: a = 10.0215 / 23; b = 1

>

> badness: 46.1

> rms: 18.1

> g: 2.94

> errors: [-24.8, -17.7, 7.1]

Many theorists associate this with Pelog. Would you mind calculating

the optimal version of this where the octave is _not_ constrained to

be exactly 1200 cents?

I wrote,

> Would you mind calculating

> the optimal version of this where the octave is _not_ constrained

to

> be exactly 1200 cents?

Could you do this for the first one (based on 27/25), too?

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

> Many theorists associate this with Pelog.

Hmmm...anyone tried 23-et gamelan music?

Would you mind calculating

> the optimal version of this where the octave is _not_ constrained to

> be exactly 1200 cents?

This is what I got fitting to {2,3,5,3/2,5/2,5/3}:

a = .43763, b = 1.0113

errors:

2: 13.6

3: 0 (exactly)

3/2: -13.6

5/4: -24.4

6/5: 10.8

4/3: 27.1

5/3: 2.7

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

> Could you do this for the first one (based on 27/25), too?

Map:

[ 0 1]

[-2 2]

[-3 3]

Generators: a = .21545; b = .99207

Errors:

2: -9.5

3: -38.1

3/2: -28.6

5/2: 19.0

4/3: 19.0

5/3: 47.6

5/4: 28.6

6/5: -57.0

Pretty radical stuff.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

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

>

> > Many theorists associate this with Pelog.

>

> Hmmm...anyone tried 23-et gamelan music?

Lots of people have.

> Would you mind calculating

> > the optimal version of this where the octave is _not_ constrained

to

> > be exactly 1200 cents?

>

> This is what I got fitting to {2,3,5,3/2,5/2,5/3}:

>

> a = .43763, b = 1.0113

>

> errors:

>

> 2: 13.6

> 3: 0 (exactly)

> 3/2: -13.6

> 5/4: -24.4

> 6/5: 10.8

> 4/3: 27.1

> 5/3: 2.7

Thanks a lot, Gene!

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

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

>

> > Many theorists associate this with Pelog.

>

> Hmmm...anyone tried 23-et gamelan music?

>

> Would you mind calculating

> > the optimal version of this where the octave is _not_ constrained

to

> > be exactly 1200 cents?

>

> This is what I got fitting to {2,3,5,3/2,5/2,5/3}:

>

> a = .43763, b = 1.0113

>

> errors:

>

> 2: 13.6

> 3: 0 (exactly)

> 3/2: -13.6

> 5/4: -24.4

> 6/5: 10.8

> 4/3: 27.1

> 5/3: 2.7

What if you include 4, 4/3, and 5/4 as well? At least including 4 and

4/3 would seem logical. I'd even include 4/2 also!

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> 135/128

>

> Map:

>

> [ 0 1]

> [-1 2]

> [ 3 1]

>

> Generators: a = 10.0215 / 23; b = 1

>

> badness: 46.1

Is this a typo? Should this be 461? I might revise my badness cutoff

now . . .

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

> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> > badness: 46.1

>

> Is this a typo? Should this be 461? I might revise my badness cutoff

> now . . .

I was cross-eyed again, but so where you--you missed my correction. :)

If you want to keep this, 500 is working for you. Do you think I've missed anything, by the way?

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

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

> > --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...>

wrote:

>

> > > badness: 46.1

> >

> > Is this a typo? Should this be 461? I might revise my badness

cutoff

> > now . . .

>

> I was cross-eyed again, but so where you--you missed my

correction. :)

> If you want to keep this, 500 is working for you. Do you think I've

missed anything, by the way?

Why, are you done with the list?