Cents to Ratio

Am I missing the obvious, but surely continued fractions are the best way
of getting the ratio from cents, to increasing accuracy?

Mark

Mark Gould wrote:

> Am I missing the obvious, but surely continued fractions are the best way
> of getting the ratio from cents, to increasing accuracy?

Provided you don't care about the prime limit. In some contexts, 25:18 and 36:25 are the simplest tritones, but a continuous fraction won't give them as an approximation to 600 cents. Neither will walking the Stern-Brocot tree (I think this converges more slowly than a continued fraction, but all values of the continued fraction are there). Which may be why Gene said on [tuning] that he goes straight to Farey sequences and removes intervals outside the prime limit.

Graham

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <graham@m...> wrote:

> Which
> may be why Gene said on [tuning] that he goes straight to Farey
> sequences and removes intervals outside the prime limit.

I don't know of any better algorithm, but this might be a fruitful
area to research. I doubt it has been studied, but it may have been.

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, Graham Breed <graham@m...>
wrote:
>
> > Which
> > may be why Gene said on [tuning] that he goes straight to Farey
> > sequences and removes intervals outside the prime limit.
>
> I don't know of any better algorithm, but this might be a fruitful
> area to research. I doubt it has been studied, but it may have
>been.

i'm pretty sure our own robert walker has done some work in this
area.