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.