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.