Re: Compton/Erlich temperament

On Thu, 18 Jul 2002 01:22:19 -0700 Carl Lumma <carl@lumma.org> writes:

> How do we classify the Compton/Erlich scheme of tuning multiple
> 12-et keyboards 15 cents apart? Some sort of planar temperament
> with the following commas?
>
> 531441/524288 (pythagorean comma)
> 5120/5103 (difference between syntonic comma and 64/63)
>
> Is this right?

I think it's another system, discussed below. The wedgie you find from
the pyth comma and 5120/5103 gives what we are calling a linear
temperament. It is [0,12,12,-6,-19,19], and has a TM reduced basis
<50/49, 3645/3584>. The mapping is

[[12, 19, 28, 34], [0, 0, -1, -1]]

However, the rms optimum is 23.4 cents apart, not 15.

I think what you want is the linear temperament with wedgie
[0,12,12,-6,-19,19], TM reduced basis
<225/224, 250047/250000> and mapping [[12,19,28,34],[0,0,-1,-1]]. You can
use the 72 or 84 ets for this.

By the way, is 250047/250000 not deserving of a little recognition?

Hello
Does anybody know if the mathematic term "rational" means "ritos" in Greek ?
I can't find it in a dictionary now , and I am confused.

--- In tuning-math@yahoogroups.com, Gene W Smith <genewardsmith@j...>
wrote:
>
>
> On Thu, 18 Jul 2002 01:22:19 -0700 Carl Lumma <carl@l...> writes:
>
> > How do we classify the Compton/Erlich scheme of tuning multiple
> > 12-et keyboards 15 cents apart? Some sort of planar temperament
> > with the following commas?
> >
> > 531441/524288 (pythagorean comma)
> > 5120/5103 (difference between syntonic comma and 64/63)
> >
> > Is this right?
>
> I think it's another system, discussed below. The wedgie you find
from
> the pyth comma and 5120/5103 gives what we are calling a linear
> temperament. It is [0,12,12,-6,-19,19], and has a TM reduced basis
> <50/49, 3645/3584>. The mapping is
>
> [[12, 19, 28, 34], [0, 0, -1, -1]]
>
> However, the rms optimum is 23.4 cents apart, not 15.
>
> I think what you want is the linear temperament with wedgie
> [0,12,12,-6,-19,19], TM reduced basis
> <225/224, 250047/250000> and mapping [[12,19,28,34],[0,0,-1,-1]].

This is the same mapping as above. Did you mean for the last term to
be -2, not -1? I know Waage proposed this system; who's Compton?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, Gene W Smith <genewardsmith@j...>
> wrote:
> >
> >
> > On Thu, 18 Jul 2002 01:22:19 -0700 Carl Lumma <carl@l...> writes:
> >
> > > How do we classify the Compton/Erlich scheme of tuning multiple
> > > 12-et keyboards 15 cents apart? Some sort of planar temperament
> > > with the following commas?
> > >
> > > 531441/524288 (pythagorean comma)
> > > 5120/5103 (difference between syntonic comma and 64/63)
> > >
> > > Is this right?
> >
> > I think it's another system, discussed below. The wedgie you find
> from
> > the pyth comma and 5120/5103 gives what we are calling a linear
> > temperament. It is [0,12,12,-6,-19,19], and has a TM reduced basis
> > <50/49, 3645/3584>. The mapping is
> >
> > [[12, 19, 28, 34], [0, 0, -1, -1]]
> >
> > However, the rms optimum is 23.4 cents apart, not 15.
> >
> > I think what you want is the linear temperament with wedgie
> > [0,12,12,-6,-19,19], TM reduced basis
> > <225/224, 250047/250000> and mapping [[12,19,28,34],[0,0,-1,-1]].
>
> This is the same mapping as above. Did you mean for the last term to
> be -2, not -1? I know Waage proposed this system; who's Compton?

That's it. Maybe this should be the Waage or Compton temperament?

Wedgie: <<0 12 24 19 38 22||

TM basis: {225/224, 250047/250000}

TOP tuning: <1200.617051 1900.976998 2784.880964 3368.630668|

TOP error: 0.617051 cents

TOP complexity: 8.548972490

TOP badness: 45.097

Not that the last two of these figures mean much without something to
compare them to.