Re: solution of cubic

HI there,

Just sent a post to the freelists.org - all the posts
sent here get echoed there.

Anyway in summary it has a link to

http://tunesmithy.netfirms.com/japplets/iterative_solution_of_quintic.htm

where I have put up a solution to the quintic that I did
basically for fun and because when I looked for
on-line pages for solving the quintic I couldn't find any,
so it might be somethign of a gap in the range of Web javascripts
available right now.

Of course you can use it for solving a cubic by setting
the first two coefficients to 0.

That page also has links to a couple of other pages on the web about the
modern solution of the cubic, and its history.

I don't know of any relevance of my page to tuning but did use
solutions of cubic when exploring fibonacci tonescapes
- to find appropriate ratios to use such that if you
go up by one ratio and down by another ratio on the
long and short beats of a fibonacci rhythm, then
in the long term (like hours) you want the pitch
to wander not too far from the original 1/1.

If you choose the numbers right then even after an hour
or so, even with small ratios, you can stay within a
fraction of a cent of the original 1/1.

If you follow that through you end up with a
cubic equation to solve.

Robert

HI there,

Sorry getting muddled. When you have two beats
in the pattern you just need to solve a quadratic.
The cubics come in when you look for ratios to use
for fibonacci tonescapes with three beat
fibonacci rhythms.

I expect if one went up to fibonacci patterns
built up using four or more beats you would probably need the quartic
and quintic - that's just a guess as I haven't
worked it out.

Robert