Tuning Dictionary: EDO 11-odd-limit error

i've created a new "error" page for the Dictionary,
this time with an applet showing the %-EDO-step error
for all EDOs from 10 to 41 and then the most significant
higher-cardinality ones (43, 46, 53, 55, 72, 768) in
the 11-odd-limit:

http://sonic-arts.org/dict/edo-11-odd-limit-error.htm

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> i've created a new "error" page for the Dictionary,
> this time with an applet showing the %-EDO-step error
> for all EDOs from 10 to 41 and then the most significant
> higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> the 11-odd-limit:
>
> http://sonic-arts.org/dict/edo-11-odd-limit-error.htm

... which makes it quite obvious what's so special about
72edo for the 11-limit, and 31edo too for that matter.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > i've created a new "error" page for the Dictionary,
> > this time with an applet showing the %-EDO-step error
> > for all EDOs from 10 to 41 and then the most significant
> > higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> > the 11-odd-limit:
> >
> > http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
>
>
>
> ... which makes it quite obvious what's so special about
> 72edo for the 11-limit, and 31edo too for that matter.

namely:

- that for 72edo, no errors are greater than 24% of
one degree of 72edo, and most are under 10%;

one outlying pair with the largest error, which
still isn't too bad at ~23.5%: (1/9, 9/1)

then two pairs between 15% and 18%:
(1/5, 5/1; 11/9, 9/11)

the rest are clustered under 13% in the following groupings:

five pairs between 7.9% and 13%:
(3/1, 1/3; 7/1, 1/7; 9/7, 7/9; 11/1, 1/11; 11/5, 5/11)

five pairs with error between 3.8% and 6.2%:
(5/3, 3/5; 7/5, 5/7; 9/5, 5/9; 11/3, 3/11; 11/7, 7/11)

one pair with error of ~1.3%: (3/7, 7/3)

- and that for 31, no errors are greater than 29% of
one degree of 31edo, and many are around 10% or less:

31edo represents four pairs of 11-odd-limit ratios
(5/1, 1/5; 1/7, 7/1; 5/7, 7/5; 11/9, 9/11) with less
than 5%-edo-step error,

four pairs with edo-step-error between 10% and 16%:
(1/3, 3/1; 5/3, 3/5; 7/3, 3/7; 3/11, 11/3),

and six pairs with edo-step-error between 21% and 29%:
(1/9, 9/1; 5/9, 9/5; 7/9, 9/7; 1/11, 11/1; 5/11, 11/5;
7/11, 11/7)

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> i've created a new "error" page for the Dictionary,
> this time with an applet showing the %-EDO-step error
> for all EDOs from 10 to 41 and then the most significant
> higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> the 11-odd-limit:
>
> http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
>
>
>
>
> -monz

beautiful shapes there monz!

couple comments:

it says "MouseOver the cardinality names of the various EDOs to see a
bingo-card lattice of them showing the error from the closest EDO
approximation to JI."

but i don't see any bingo-card lattices there! probably thank
goodness, since it would have to be a high-dimensional one!! :)

secondly, as i offered with respect to a similar page of yours on
tuning-math, mind if i get into the html and extend some stuff so
that it relates to consistency? or maybe just a one-liner?

thanks,
paul

hi paul,

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > i've created a new "error" page for the Dictionary,
> > this time with an applet showing the %-EDO-step error
> > for all EDOs from 10 to 41 and then the most significant
> > higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> > the 11-odd-limit:
> >
> > http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
> >
> >
> >
> >
> > -monz
>
> beautiful shapes there monz!
>
> couple comments:
>
> it says "MouseOver the cardinality names of the various
> EDOs to see a bingo-card lattice of them showing the error
> from the closest EDO approximation to JI."
>
> but i don't see any bingo-card lattices there! probably thank
> goodness, since it would have to be a high-dimensional one!! :)

oops, my bad. thanks for that. i had simply copied the
HTML code from the bingo webpage and missed that.

> secondly, as i offered with respect to a similar page of
> yours on tuning-math, mind if i get into the html and
> extend some stuff so that it relates to consistency?
> or maybe just a one-liner?

feel free to add whatever you want. i'd like to have
considerations of consistency be a part of all my
descriptions of "error from JI".

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_48467.html#48467

> i've created a new "error" page for the Dictionary,
> this time with an applet showing the %-EDO-step error
> for all EDOs from 10 to 41 and then the most significant
> higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> the 11-odd-limit:
>
> http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
>
>
>
>
> -monz

***This is very interesting, but I find it hard to use even in "full
screen" mode. It's too bad that the numbers to select can't be on
the *side* (since the graph isn't *that* big...). Then it would be
easier to select and compare them and one wouldn't have to keep
moving up and down between the numbers and the graph. (Unless
somehow this is a big HTML problem, but I don't believe it is...)

Thanks!

J. Pehrson

on 11/14/03 9:25 AM, monz <monz@attglobal.net> wrote:

> i've created a new "error" page for the Dictionary,
> this time with an applet showing the %-EDO-step error
> for all EDOs from 10 to 41 and then the most significant
> higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> the 11-odd-limit:
>
> http://sonic-arts.org/dict/edo-11-odd-limit-error.htm

I see no entry for this in the index though, which will be important so we
don't all have to save this email to find it again. I would expect to find
it near the EDO prime error entry.

Thanks,
Kurt

>
>
>
>
> -monz
>
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on 11/15/03 2:19 PM, Joseph Pehrson <jpehrson@rcn.com> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_48467.html#48467
>
>> i've created a new "error" page for the Dictionary,
>> this time with an applet showing the %-EDO-step error
>> for all EDOs from 10 to 41 and then the most significant
>> higher-cardinality ones (43, 46, 53, 55, 72, 768) in
>> the 11-odd-limit:
>>
>> http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
>>
>> -monz
>
> ***This is very interesting, but I find it hard to use even in "full
> screen" mode. It's too bad that the numbers to select can't be on
> the *side* (since the graph isn't *that* big...). Then it would be
> easier to select and compare them and one wouldn't have to keep
> moving up and down between the numbers and the graph. (Unless
> somehow this is a big HTML problem, but I don't believe it is...)

It worked well for me in Mac OS 9 with a 960-pixel-high screen, both in IE
5.0 and in Mozilla without having to get rid of the extra pieces of my
browser window. By getting rid of the address bar, etc. I think it would
work ok down to about 800 pixels high but don't want to try it because it
messes up the icons on my desktop to do that. By reducing the browser text
also it looks like it would work down to about 700 pixels high. On a
480-high screen it would be pretty difficult no matter what you do, but most
people have better resolution than that nowadays. What resolution were you
using?

The idea of putting the float-over key on the left might be a good one, and
definitely html-doable - easy for me to say, not doing the work myself.

-Kurt

>
> Thanks!
>
> J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_48467.html#48467
>
> > i've created a new "error" page for the Dictionary,
> > this time with an applet showing the %-EDO-step error
> > for all EDOs from 10 to 41 and then the most significant
> > higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> > the 11-odd-limit:
> >
> > http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
> >
> >
> >
> >
> > -monz
>
>
> ***This is very interesting, but I find it hard to use even
in "full
> screen" mode. It's too bad that the numbers to select can't be on
> the *side* (since the graph isn't *that* big...). Then it would be
> easier to select and compare them and one wouldn't have to keep
> moving up and down between the numbers and the graph. (Unless
> somehow this is a big HTML problem, but I don't believe it is...)

thanks, Joe, great suggestion. take a look now.

-monz

hi Kurt,

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 11/14/03 9:25 AM, monz <monz@a...> wrote:
>
> > i've created a new "error" page for the Dictionary,
> > this time with an applet showing the %-EDO-step error
> > for all EDOs from 10 to 41 and then the most significant
> > higher-cardinality ones (43, 46, 53, 55, 72, 768) in
> > the 11-odd-limit:
> >
> > http://sonic-arts.org/dict/edo-11-odd-limit-error.htm
>
> I see no entry for this in the index though, which will
> be important so we don't all have to save this email to
> find it again. I would expect to find it near the
> EDO prime error entry.

after all the work i did on the 11-odd-limit error page itself,
i decided to take a one-day break before going into the
index page and amending it ... especially since i hosted
a recital of my students today. and someone had to go and
notice ... OK, it's done now.

(but thanks for writing anyway and reminding me ... it's
*not* my usual practice to take a break like that. normally
i just go in and change and upload the index page right after
creating a new Dictionary page.)

-monz

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

/tuning/topicId_48467.html#48483

On a
> 480-high screen it would be pretty difficult no matter what you do,
but most
> people have better resolution than that nowadays. What resolution
were you
> using?
>

***Thanks, Kurt!

It's 800 X 600, but I only have a 15 inch monitor...

> The idea of putting the float-over key on the left might be a good
one, and
> definitely html-doable - easy for me to say, not doing the work
myself.
>

***I think it would only be in it's own left-hand cell or some such.
That would work much better since one could quickly move from one to
another and it would make for more interesting comparisons...

But, it's usable as is, of course...

J. Pehrson

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_48467.html#48484

> > ***This is very interesting, but I find it hard to use even
> in "full
> > screen" mode. It's too bad that the numbers to select can't be
on
> > the *side* (since the graph isn't *that* big...). Then it would
be
> > easier to select and compare them and one wouldn't have to keep
> > moving up and down between the numbers and the graph. (Unless
> > somehow this is a big HTML problem, but I don't believe it is...)
>
>
>
> thanks, Joe, great suggestion. take a look now.
>
>
>
> -monz

***Hi Monz,

Oh... now this is wonderful! They "jump around" great now going from
one to another... :)

jP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_48467.html#48486

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
> /tuning/topicId_48467.html#48483
>
> On a
> > 480-high screen it would be pretty difficult no matter what you
do,
> but most
> > people have better resolution than that nowadays. What
resolution
> were you
> > using?
> >
>
> ***Thanks, Kurt!
>
> It's 800 X 600, but I only have a 15 inch monitor...
>
>
>
> > The idea of putting the float-over key on the left might be a
good
> one, and
> > definitely html-doable - easy for me to say, not doing the work
> myself.
> >
>
> ***I think it would only be in it's own left-hand cell or some
such.
> That would work much better since one could quickly move from one
to
> another and it would make for more interesting comparisons...
>
> But, it's usable as is, of course...
>
> J. Pehrson

***Sorry, Monz... I see this is a done deal, or fait accompli, or
whatever...

jP