another Dictionary update: minor 3rd

For those of you who are particularly fond
of "minor 3rds", I've added a considerable amount
of new detail to that entry:

http://www.ixpres.com/interval/dict/minor3rd.htm

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> For those of you who are particularly fond
> of "minor 3rds", I've added a considerable amount
> of new detail to that entry:
>
> http://www.ixpres.com/interval/dict/minor3rd.htm

That's good, but can I ask, why would anyone care about rational
fractions of a cent, like "274 & 53/91 cents". I think it just
clutters the page.

-- Dave Keenan

> From: Dave Keenan <D.KEENAN@UQ.NET.AU>
> To: <tuning@yahoogroups.com>
> Sent: Friday, July 20, 2001 11:05 AM
> Subject: [tuning] Re: another Dictionary update: minor 3rd
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > For those of you who are particularly fond
> > of "minor 3rds", I've added a considerable amount
> > of new detail to that entry:
> >
> > http://www.ixpres.com/interval/dict/minor3rd.htm
>
> That's good, but can I ask, why would anyone care about rational
> fractions of a cent, like "274 & 53/91 cents". I think it just
> clutters the page.

Ahhh... I knew that eventually *someone* would call me on that!

Well, the reason I started adding rational fractions of a cent
is because I noticed that most EDOs (at least the ones people
actually use) have degrees whose cent-values come out to an
exact rational fractional value. (Thanks to Dan Stearns for
inconspicuously tipping me off to this a couple of years ago.)

For example, here's 11-EDO with the fractional part of the
cent-values given as both decimal and rational:

degree ~cents exact cents

11 1200 1200
10 1090.909091 1090 & 10/11
9 981.8181818 981 & 9/11
8 872.7272727 872 & 8/11
7 763.6363636 763 & 7/11
6 654.5454545 654 & 6/11
5 545.4545455 545 & 5/11
4 436.3636364 436 & 4/11
3 327.2727273 327 & 3/11
2 218.1818182 218 & 2/11
1 109.0909091 109 & 1/11
0 0 0

OK, so I admit that values like ""274 & 53/91 cents"
don't offer a heck of a lot of advantage over decimal.

But in the case of smaller, more comprehensible values,
like the example above, I think using rational fractions
makes it much easier to grasp the essentials of the tuning.

I definitely think that rational fractional values with
denominators under 10 are very useful, and I suppose that
if I were to keep using denominators larger than 10 it would
probably be a good idea to keep the denominator under some
sensible limit, say 16 or 25 or so, and forget about fractions
like "53/91".

I suppose I just got carried away in my search for closer
rational approximations... Does it really clutter the page
enough to make it worthwhile to remove them? I'm always a
firm believer in "redundant coding"... you never know which
representation will resonate with any given individual.

-monz
http://www.monz.org
"All roads lead to n^0"

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