Two weird and degenerate temperaments

Since we are trying to approximate 5-limit harmonies, I don't think it makes sense to try to temper out 6/5,5/4,4/3 or 3/2; that leaves
10/9 and 9/8 as things to consider if we want to go past my cut-off.

10/9

Map:

[ 0 1]
[-1 2]
[-2 3]

Generators: a = .339; b = 1.

The generator is a sharp (by 20.5 cents) major third, which makes it a better third than the "official" third given by the map.

badness: 211
rms: 74.5
g: 1.414
errors: [91.2, 0, -91.2]

This is not making any sense.

9/8

Map:

[ 0 2]
[ 0 3]
[ 1 4]

Generators: a = .2794, b = 1/2

The generator is a sharp (20 cents) minor third which once again is better than what the map gives.

badness: 314
rms: 72.1
g: 1.633
errors: [-102, -51, 51]

Again, this may not have much to do with what someone who actually used this tuning would do with it.

This was supposed to go to the math list, where even though it might not make much sense it would make *more* sense.

Gene,

I cannot say that I follow many of the "particulars" (bad pun) of what you are doing here, but your reference to "weird and degenerate" has sparked my curiousity. Are your results below of a type that had not (yet) appeared when considering other intervals?

Is it possible to summarize (in general terms) what occurs in these cases?

J Gill

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Since we are trying to approximate 5-limit harmonies, I don't think it makes sense to try to temper out 6/5,5/4,4/3 or 3/2; that leaves
> 10/9 and 9/8 as things to consider if we want to go past my cut-off.
>
> 10/9
>
> Map:
>
> [ 0 1]
> [-1 2]
> [-2 3]
>
> Generators: a = .339; b = 1.
>
> The generator is a sharp (by 20.5 cents) major third, which makes it a better third than the "official" third given by the map.
>
> badness: 211
> rms: 74.5
> g: 1.414
> errors: [91.2, 0, -91.2]
>
> This is not making any sense.
>
> 9/8
>
> Map:
>
> [ 0 2]
> [ 0 3]
> [ 1 4]
>
> Generators: a = .2794, b = 1/2
>
> The generator is a sharp (20 cents) minor third which once again is better than what the map gives.
>
> badness: 314
> rms: 72.1
> g: 1.633
> errors: [-102, -51, 51]
>
> Again, this may not have much to do with what someone who actually used this tuning would do with it.