Re: Draft of FAQ

Here is a contribution to the FAQ

How to convert cents to ratios and vice versa:
http://homepage.ntlworld.com/robertwalker/fts/cents_to_from_ratios.htm

I could also do "how to calculate the cents values for a mean tone scale from
the size of the comma"

Robert

Robert Walker wrote,

<<Here is a contribution to the FAQ>>

Beautiful job Robert! I've always wished I had some computer savvy so
as to be able to create some of these nifty little conversion
calculators... I think these are really nice and *ultra*
user-friendly, a great contribution to the FAQ indeed.

A nice compliment to the continued fraction approximation method might
be some brute force type sieve that also fills in the continued
fraction method gaps with the smaller ratios that are successively
closer approximations... though I'm unsure how easy this would be to
set up.

<<I could also do "how to calculate the cents values for a mean tone
scale from the size of the comma">>

Absolutely, please do! Any of these that you could set up like this
would be wonderful... the ones I'd personally want to see, in other
words my own LFAQ (least frequently asked questions) pet projects <G>,
would be conversion calculators for the two- and three-term indexes,
and for the equaltone series... actually I bet these would all be
quite easy now... ?

wishing out loud,

--Dan Stearns

Hi Jeff,

> > I could also do "how to calculate the cents values for a mean
> > tone scale from the size of the comma"

> Please do! It certainly belongs in a FAQ since it is one
> of the better ways IMHO of really defining what we mean by
> meantone in a practical sense.

Okay, here it is:

How to calculate the cents values for a mean tone scale from
the size of the comma
http://homepage.ntlworld.com/robertwalker/fts/mean_tone_in_cents.htm

It focusses purely on the practical aspect of how to calculate the numbers.

Hi Dan,

> Beautiful job Robert! I've always wished I had some computer savvy so
> as to be able to create some of these nifty little conversion
> calculators... I think these are really nice and *ultra*
> user-friendly, a great contribution to the FAQ indeed.

Thanks!

> A nice compliment to the continued fraction approximation method might
> be some brute force type sieve that also fills in the continued
> fraction method gaps with the smaller ratios that are successively
> closer approximations... though I'm unsure how easy this would be to
> set up.

Yes, one could easily do a brute force search of all the small ratios up to
say, quotient of 100,000 or something.

One just works out the corresponding denumerator for each value of the
denominator, getting two values, one above and one below the target
value. Then keep track of the closest ratio found so far, and show a
new ratio whenever one finds one that is closer than any of the previous ones.

So it is quite fast, though not nearly as fast as the continued
fractions approach as one has to test every denominator in turn.

In fact, I'm sure that I've actually programmed that before, or something
very like it at least, but don't quite remember the context right now.

<<I could also do "how to calculate the cents values for a mean tone
scale from the size of the comma">>

> Absolutely, please do! Any of these that you could set up like this
> would be wonderful... the ones I'd personally want to see, in other
> words my own LFAQ (least frequently asked questions) pet projects <G>,
> would be conversion calculators for the two- and three-term indexes,
> and for the equaltone series... actually I bet these would all be
> quite easy now... ?

> wishing out loud,

That's fine, I'll do a few.

I've done occasional ones in FTS, "least used options" that don't have any
buttons, but just a bit of description somewhere in the help about how to do them,
because it is the easiest way to do them, as everything is already set up for it.

For instance, I've got a hypermos generator I use in FTS by typing #hypermos
into one of the boxes, which will also do my alternating generator trivalent
scales. Also set it up to do your undertone to overtone scales as well, when
I was doing those timbre experiments with them.

I'll convert those into javascript for you, perhaps some time over the weekend,
or the start of next week, when I also plan to give myself some time to slowly read
through your recent post and Pierre's new one too.

Conversion is fairly easy as javascript is close to c in many ways.

I don't yet fully understand your two and three term indexes, mainly because I
just haven't yet given myself time to read through your posts and think about
them. When I do, will adapt the hypermos generator to make them too.

Thanks!

Robert

Hi Robert,

<<I also plan to give myself some time to slowly read through your
recent post and Pierre's new one too.>>

You'll need the time for Pierre's <!>, but mine is remarkably
simple... somewhere along the line I got hung up on the hyper-MOS type
idea and abandoned my own intuition, big mistake!

In one of the very first posts I put up in response to Paul Erlich's
original question I mentioned the L-out-of-M-out-of-N idea as a likely
answer, and then I never bothered to check it (!), and took off on
down the MOS lookalike route... well that was equal parts fun and
frustrating, and I bounced around some stuff which I at least find
interesting and even useful, but it turned out that my original guess
was actually the answer all along...

Anyway, I'd be thrilled silly if these were turned into javascript
type calculators, so let me know how I can help!

thanks,

--Dan Stearns