Calculating errors

Hi!

Do you people use least squares method or sum of absolute values of
errors (or perhaps something else) when calculating the optimal
values for generators?

I know least squares is used in statistics but to me it seems that
absolute values would be much more appropriate in tuning
calculations. Fokker used least squares. Paul Erlich too I suppose.
What is the idea behind using them and not absolute values or
something else?

Thanks,
Kalle

In-Reply-To: <afc162+lumk@eGroups.com>
kalleaho wrote:

> Do you people use least squares method or sum of absolute values of
> errors (or perhaps something else) when calculating the optimal
> values for generators?

I use either unweighted least squares, or the worst absolute error.

> I know least squares is used in statistics but to me it seems that
> absolute values would be much more appropriate in tuning
> calculations. Fokker used least squares. Paul Erlich too I suppose.
> What is the idea behind using them and not absolute values or
> something else?

I think the worst error is the most appropriate, because it tells you how
bad the temperament can get. But I use least squares in the automated
calculations because it's faster to calculate. See
<http://x31eq.com/temper/method.html>. When evaluating all
pairs of 10 equal temperaments, a slight improvement in the optimisation
calculation does make a difference. There's a danger I might hit the
limit where my ISP kills the CGI process (so many CPU seconds).

A more advanced calculation would weight the most important intervals more
highly. For example, ignore the most complex ones because they're not so
likely to be played. Then you can find temperaments that work well in a
subset of the limit you're interested in.

Graham

--- In tuning-math@y..., "kalleaho" <kalleaho@m...> wrote:
> Hi!
>
> Do you people use least squares method or sum of absolute values of
> errors (or perhaps something else) when calculating the optimal
> values for generators?

very often max error is used.

> I know least squares is used in statistics but to me it seems that
> absolute values would be much more appropriate in tuning
> calculations. Fokker used least squares. Paul Erlich too I suppose.
> What is the idea behind using them and not absolute values or
> something else?

least squares is a nice compromise between max error and sum of
absolute values of errors.