Semistandard vals

I've been calling the p-limit n-et val obtained by rounding
n*log2(q) for all primes q up to p to the nearest integer the standard
p-limit n-et val. The standard val has the nice property that if we
take its distance in val space from n*JIP it is minimal. See

http://66.98.148.43/~xenharmo/top.htm

for the terminology.

However, the standard val is not always uniquely minimal. I propose
calling any val which is minimal a semistandard val; then the standard
val is semistandard, but not necessarily conversely. For 64 in the
7-limit we have the following four semistandard vals:

<64 101 148 179|, <64 101 148 180|, <64 101 149 179|, <64 101 149 180|

Of these four, the first two seem to be the best; they have a maximum
error over the 7-limit diamond of 12.576 cents, occuring at 8/7 and 7/4.
The standard val is the fourth val.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

One area where the definition of semistandard vals could be useful is
in searches for temperaments; searching all pairs of semistandard vals
over some limit is much more likely to be a complete search than
simply confining ourselves to pairs of standard vals. Another use is a
more canonical method of associating edos to temperaments; if there is
any semistandard val we can count it, instead of simply requiring the
val be standard. For septimal meantone, for example, that picks up
<117 185 272 239|, which is a perfectly fine meantone, about 4/19
comma. We also get an extra contorted meantone in the form of twice
50, which is semistandard but not standard.

Gene,

Your usage of semi- has good precedent.
(group, semigroup; ring; semiring ...)

But I wonder whether there's much gained
by using another". longer term to describe a
"minimal val"?

I suppose it may be useful by way of analogy.

Regards,
Yahya

-----Original Message-----
...
However, the standard val is not always uniquely minimal. I propose
calling any val which is minimal a semistandard val; then the standard
val is semistandard, but not necessarily conversely.

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--- In tuning-math@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> Gene,
>
> Your usage of semi- has good precedent.
> (group, semigroup; ring; semiring ...)
>
> But I wonder whether there's much gained
> by using another". longer term to describe a
> "minimal val"?

Well, but it's only sort of optimal. You might call it minimal, but I
think another term would be better.