Four funky ones

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?