question for Gene

Is there any way to directly compare the badnesses of equal
temperaments and linear temperaments and meaningfully ask the
question: Which of the linear temperaments that you found (in the 5-
limit, and whatever other cases you've completed) could be expressed
by an equal temperament, without pushing the badness over the limit
you've computed? 'Cents/error' will always increase,
and 'gens/complexity' will often increase as well, but may
conceivably decrease . . . or maybe this isn't meaningful at
all. . . .?

I wrote,

> without pushing the badness over the limit
> you've computed?

I meant, over the limit you've adopted (500 I think it was . . .)?

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

> Is there any way to directly compare the badnesses of equal
> temperaments and linear temperaments and meaningfully ask the
> question: Which of the linear temperaments that you found (in the 5-
> limit, and whatever other cases you've completed) could be expressed
> by an equal temperament, without pushing the badness over the limit
> you've computed?

Certainly--just recalculate rms error for the new tuning. Complexity will never increase, and if you allow it to decrease (as for instance in the 12-et version of schismic) you recalculate that also, by reducing it mod n, I suppose.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> > Is there any way to directly compare the badnesses of equal
> > temperaments and linear temperaments and meaningfully ask the
> > question: Which of the linear temperaments that you found (in the
5-
> > limit, and whatever other cases you've completed) could be
expressed
> > by an equal temperament, without pushing the badness over the
limit
> > you've computed?
>
> Certainly--just recalculate rms error for the new tuning.

Could you do this please? Which of the twenty (?) linear temperaments
that you found could thus be expressed?

>Complexity will never increase,

Complexity of a larger ET must be more than of a smaller ET,
otherwise my question makes no sense, as you could always find an
infinite number of ETs that pass.

Awaiting a response . . .

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> >
> > > Is there any way to directly compare the badnesses of equal
> > > temperaments and linear temperaments and meaningfully ask the
> > > question: Which of the linear temperaments that you found (in
the
> 5-
> > > limit, and whatever other cases you've completed) could be
> expressed
> > > by an equal temperament, without pushing the badness over the
> limit
> > > you've computed?
> >
> > Certainly--just recalculate rms error for the new tuning.
>
> Could you do this please? Which of the twenty (?) linear
temperaments
> that you found could thus be expressed?
>
> >Complexity will never increase,
>
> Complexity of a larger ET must be more than of a smaller ET,
> otherwise my question makes no sense, as you could always find an
> infinite number of ETs that pass.