The algebraic generator for sensi is 340 cents

POTE generator: ~9/7 = 443.383
Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.

I am displeased!

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> POTE generator: ~9/7 = 443.383
> Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.
>
> I am displeased!

Hopefully Jacques Dudon will show up and give us the right answer.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > POTE generator: ~9/7 = 443.383
> > Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.
> >
> > I am displeased!
>
> Hopefully Jacques Dudon will show up and give us the right answer.

For now I've replaced it with the real root of x^5+x^4-4x^2+x-1, which weighs in at 443.378 cents.

BTW, do you know if these generators lead to equal-beating or
proportional-beating chords?

-Mike

On Fri, Sep 2, 2011 at 7:52 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > POTE generator: ~9/7 = 443.383
> > > Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.
> > >
> > > I am displeased!
> >
> > Hopefully Jacques Dudon will show up and give us the right answer.
>
> For now I've replaced it with the real root of x^5+x^4-4x^2+x-1, which weighs in at 443.378 cents.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> BTW, do you know if these generators lead to equal-beating or
> proportional-beating chords?

Mostly not.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> POTE generator: ~9/7 = 443.383
> Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.
>
> I am displeased!
>
> -Mike
>

That is the incorrect quadratic equation. The correct one should read x^9-x^7-4=0.

This gives a generator of 442.737761 cents.

Ryan

On Fri, Sep 2, 2011 at 9:38 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > BTW, do you know if these generators lead to equal-beating or
> > proportional-beating chords?
>
> Mostly not.

I see I worded that strangely: I was asking if they lead to
equal-beating chords, or if they lead to proportional-beating chords.
Your reply, "mostly not," makes me think that they don't lead to
anything. Are you saying they have nothing to do with proportional
beating or isoharmonicity?

-Mike