10+16 (continued from tuning)

7-limit now . . .

val for 10:

<10 16 23 28]

val for 16:

<16 25 37 45]

wedgie:

<<-6 2 2 17 20 -1]]

According to Gene's file, this has TOP error of 3.740932 and L1
complexity of 14.626943. Not too bad. It just barely, by a hair,
falls outside the bound in my paper. Not too late to change that,
though . . .

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> 7-limit now . . .
>
> val for 10:
>
> <10 16 23 28]
>
> val for 16:
>
> <16 25 37 45]
>
> wedgie:
>
> <<-6 2 2 17 20 -1]]
>
> According to Gene's file, this has TOP error of 3.740932 and L1
> complexity of 14.626943. Not too bad. It just barely, by a hair,
> falls outside the bound in my paper. Not too late to change that,
> though . . .

What is the bound of your paper at the moment?

Paul Erlich wrote:

> 7-limit now . . .
> > val for 10:
> > <10 16 23 28]
> > val for 16:
> > <16 25 37 45]
> > wedgie:
> > <<-6 2 2 17 20 -1]]
> > According to Gene's file, this has TOP error of 3.740932 and L1 > complexity of 14.626943. Not too bad. It just barely, by a hair, > falls outside the bound in my paper. Not too late to change that, > though . . .
>
This is the "Number 82" temperament that I commented on back in January. I still haven't done anything with it, but I've been kind of busy lately.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> > 7-limit now . . .
> >
> > val for 10:
> >
> > <10 16 23 28]
> >
> > val for 16:
> >
> > <16 25 37 45]
> >
> > wedgie:
> >
> > <<-6 2 2 17 20 -1]]
> >
> > According to Gene's file, this has TOP error of 3.740932 and L1
> > complexity of 14.626943. Not too bad. It just barely, by a hair,
> > falls outside the bound in my paper. Not too late to change that,
> > though . . .
>
> What is the bound of your paper at the moment?

It was going to be, for both 5-limit and 7-limit,

(error/16.6667)^(2/3) + (complexity/23.5)^(2/3) < 1

since the bound falls in a nice wide moat in both cases.

As of right now, though, I'm planning to use,

error/10 + complexity/23.5 < 1

partly due to Dave pleading against exponents smaller than 1. No more
moats, which is OK since I don't really have the space for those
graphs anyway.

This change only adds two to the 7-limit list and one to the 5-limit
list, without taking any away.

The units are error = max. over all ratios of (cents error)/lg2(n*d),
complexity = L1 Tenney multival norm in the 7-limit case, but L1
Tenney multival norm multiplied by 2 in the 5-limit case (I can't
really justify that, but the multival has twice as many entries in
the 7-limit case). This would appear to penalize complex 5-limit
temperaments, but Orwell and Amity still make it in.