Erv Wilson Orwell generator: attn Jacques Dudon

Erv Wilson considered the positive real root of x^10-2x^7-128 as a generator. This would work as an Orwell generator, and the ratios of associated linear recurrences converge. I wonder if Jacques would like to venture an opinion about it?

Gene wrote :

> Erv Wilson considered the positive real root of x^10-2x^7-128 as a > generator. This would work as an Orwell generator, and the ratios > of associated linear recurrences converge. I wonder if Jacques > would like to venture an opinion about it?

A very pretty one, -c, equal-beating, and allowing many creative rational sequences. Being so open (10 numbers to give) I think it could also share the road with other algorithms of lower exposants, that would add other qualities, in other limits.
Funnily I was just working on Orwell/Sabra etc., which I like a lot, and I found a myriad of new ones, but still have to resolve the solutions.
What would you consider as good forks for 11-Limit Orwell ? and other limits ?
What about including 13th harmonic with +12 ? and also the 19th h. with +10 ? these two would open the game nicely.

I also found a more anecdotic thing, with this Orwell generator :
1.709511291351 = octave / pure fifth proportion.
It means that some Orwell generators, even bad ones, could eventually serve as close-to-pure fifth meta-temperaments,
such as this hardly-Orson one : x^2 - 14x + 21 (x = 7 - 2sqrt(7) = 1.708497377872) that suggests a Schismatic temperament of 497.6284 c.
- - - - - - -
Jacques

Jacques Dudon <fotosonix@...> wrote:

> What about including 13th harmonic with +12 ? and also
> the 19th h. with +10 ? these two would open the game
> nicely.

The 13th harmonic can be done a lot more accurately as
-19. That also means the intervals of 13 are distinct from
11-limit intervals, as a trade-off for the increased
complexity. So the neutral third between 11:9 and 3:2 is
16:13 with the -19 approximation. With +12, 11:9 and 16:13
approximate to the same interval, and the other neutral
third gets no better than 27:22.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Jacques Dudon <fotosonix@...> wrote:
>
> > What about including 13th harmonic with +12 ? and also
> > the 19th h. with +10 ? these two would open the game
> > nicely.
>
> The 13th harmonic can be done a lot more accurately as
> -19. That also means the intervals of 13 are distinct from
> 11-limit intervals, as a trade-off for the increased
> complexity. So the neutral third between 11:9 and 3:2 is
> 16:13 with the -19 approximation. With +12, 11:9 and 16:13
> approximate to the same interval, and the other neutral
> third gets no better than 27:22.
>
>
> Graham

Thanks for these informations. Actually, for some fractal reasons I was working on a smaller generator (~270c...) than in the recommended Orwell range and I was quite happy with these mappings of the 13th and 19th harmonics (and also 7/6...) But of course this is less optimal for others then ;)
- - - - -
Jacques

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:

> What would you consider as good forks for 11-Limit Orwell ? and other
> limits ?

I'm afraid I don't know what you mean by a "fork".

> What about including 13th harmonic with +12 ? and also the 19th h.
> with +10 ? these two would open the game nicely.

As Graham remarks, this reduces the accuracy of the temperament. But it's an interesting idea; it tempers out 66/65, 99/98, 105/104 and 121/120, and 31edo is a good tuning choice. Graham's -19 works better with the more accurate 53edo. It also tempers out 99/98 and 121/120, but not 66/65 or 105/104, rather 275/273 and 176/175. Winston temperament, perhaps (from Winston Smith, the protagonist of Orwell's 1984?)

> I also found a more anecdotic thing, with this Orwell generator :
> 1.709511291351 = octave / pure fifth proportion.

That would be 1/log2(3/2), or log base 3/2 of 2.

> It means that some Orwell generators, even bad ones, could eventually
> serve as close-to-pure fifth meta-temperaments,
> such as this hardly-Orson one : x^2 - 14x + 21 (x = 7 - 2sqrt(7) =
> 1.708497377872) that suggests a Schismatic temperament of 497.6284 c.

I don't know how you got from 1.708 to 497.6.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
>
> > What would you consider as good forks for 11-Limit Orwell ? and other
> > limits ?
>
> I'm afraid I don't know what you mean by a "fork".

I see, you don't use that in english. In french une "fourchette" can be this thing the kings had this stupid idea to use for eating - and also a "range" for anything, that's more what I meant here (a minima and and a maxima)...

> > What about including 13th harmonic with +12 ? and also the 19th h.
> > with +10 ? these two would open the game nicely.
>
> As Graham remarks, this reduces the accuracy of the temperament. But it's an interesting idea; it tempers out 66/65, 99/98, 105/104 and 121/120, and 31edo is a good tuning choice.

I noticed that.

Graham's -19 works better with the more accurate 53edo. It also tempers out 99/98 and 121/120, but not 66/65 or 105/104, rather 275/273 and 176/175. Winston temperament, perhaps (from Winston Smith, the protagonist of Orwell's 1984?)

Sure, if you say it.

> > I also found a more anecdotic thing, with this Orwell generator :
> > 1.709511291351 = octave / pure fifth proportion.
>
> That would be 1/log2(3/2), or log base 3/2 of 2.

That's it.

> > It means that some Orwell generators, even bad ones, could eventually
> > serve as close-to-pure fifth meta-temperaments,
> > such as this hardly-Orson one : x^2 - 14x + 21 (x = 7 - 2sqrt(7) =
> > 1.708497377872) that suggests a Schismatic temperament of 497.6284 c.
>
> I don't know how you got from 1.708 to 497.6.

1200 - (1200/1.708497377872) - just an idea. But I'm not sure I will spend time to make it work. Waiting for better ones.