## Re: tina - unit of interval measurement: 8539-edo

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• ... I ve added to my tina webpage http://tonalsoft.com/enc/t/tina.aspx a table of the tina values for all of the commonly used intervals, in all of the
Message 1 of 13 , May 1 2:07 AM
--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> The fact that one degree of 12-edo falls almost
> midway between 711 and 712 tinas also doesn't bother
> me much, because i've found that the error of the
> 12-edo 5th (4981 tinas) is only - 8 & 1/3 % of a
> tina, which means that you'd have to go to 6 5ths
> to reach an error of half a tina. That's accurate
> enough for me.
>
> There are some interesting discrepancies among the
> meantones. The 1/4-comma meantone 5th maps to 4957
> tinas, while that of 31-edo maps to 4958 tinas, and
> the 1/6-comma meantone 5th maps to 4969 while that
> of 55-edo maps to 4968.

I've added to my tina webpage

http://tonalsoft.com/enc/t/tina.aspx

a table of the tina values for all of the commonly used
intervals, in all of the standard keys, in some of the
most important EDO meantones. The intervals are listed
as a chain-of-5ths, in decreasing generator order, with
the tonic of each key as the zeroth generator. 53-edo
is also shown for comparison, as a representation of
pythagorean tuning.

The percentage errors for 12-, 55-, and 31-edo are quite
low, those for 43-, 50-, and 19-edo not as good, and the
error for 53-edo almost as bad as it can get, at 49%
(i.e., the 5th of 53-edo is almost midway between two
tina values, at ~4994.5094) -- the values shown in the
53-edo column are actually quite accurate for real
pythagorean JI tuning.

You can easily see the divergence for 12-edo, where
the diminished-2nd (i.e., C:Dbb for example) maps to
one degree higher than zero, and the augmented-7th
(i.e., C:B# for example), which represents the
pythagorean-comma, maps to one degree lower than zero.

-monz
http://tonalsoft.com
Tonescape microtonal music software
• ... Oh, for crap s sake, be useful and go change a diaper. No one needs tinas right now... Cheers, Jon
Message 2 of 13 , May 1 2:24 AM
--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> I've added to my tina webpage

Oh, for crap's sake, be useful and go change a diaper. No one needs
tinas right now...

Cheers,
Jon
• ... Why not? Good name for a girl baby. Can you imagine Eightthousandfivehundredandthirtynine Monzo?
Message 3 of 13 , May 1 3:02 AM
--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > I've added to my tina webpage
>
> Oh, for crap's sake, be useful and go change a diaper. No one needs
> tinas right now...

Why not? Good name for a girl baby. Can you imagine
Eightthousandfivehundredandthirtynine Monzo?
• Hi Gene, ... Ha, good one! :-) Actually, it s really ironic that you say that, because i have an Aunt Tina who is almost 90 years old and she never married or
Message 4 of 13 , May 1 9:30 AM
Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@> wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > > I've added to my tina webpage
> >
> > Oh, for crap's sake, be useful and go change a diaper.
> > No one needs tinas right now...
>
> Why not? Good name for a girl baby. Can you imagine
> Eightthousandfivehundredandthirtynine Monzo?

Ha, good one! :-)

Actually, it's really ironic that you say that, because
i have an Aunt Tina who is almost 90 years old and she
never married or had any children, and the last few of
my generation who were born were all boys (including me),
so she never got to have a baby named after her.

Friday night making my webpage about 8539-edo, calling
the unit "hepticent", and just before going to bed
early Saturday morning i read Dave Keenan's message
here and decided i liked George and Dave's name "tina"
for it a lot better.

So when Lelani was born less than a day later, it was
something else that was my "baby" (the idea to use
8539-edo as a measurement unit).

Anyway guys, i'm only here typing on the tuning list
while i'm home alone and Mama and Lelani are still
resting in the hospital. Take advantage of the fact
that i have this time to be here now ... pretty soon,
when they're home, i *will* be too busy changing
diapers and stuff like that. ;-P

-monz
http://tonalsoft.com
Tonescape microtonal music software
• ... agreed, hence that kind of erroes should be called more apt as meta -Cents in a metaphorically sense. ... also right, in that case it makes also more
Message 5 of 13 , May 3 12:04 PM
--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> These aren't errors in cents at all; they are
> errors in terms of what I used to call relative
> cents until Paul objected.
agreed, hence that kind of erroes should be called more apt
as "meta"-Cents in a metaphorically sense.

> If you take an error
> e in cents, then n*e/12 is a percentage error,
> which we've been using a lot lately as Dave and
> George seem to like it.
also right, in that case it makes also more sense to
express that deviations also in percent units too.

> But why do we care
> in particular about the errors in the Pythagorean
> comma when evaluating a notational edo? If we divide
> it by 12 yet again, we get the percentage error in 3,
> which seems a more reasonable thing to look at.

also an truism, refer it back to the fundamental root
of 3-imit: the plain 5th.
The resulting PC: 3^12/2^19 is dervied from a dozen 5ths.

>
> > 190 537 * ln( 3^12 / 2^19) / ln(2) = ~ 3 724.999 998 76...deg
> > ======> 3725 / 3 724.999 998 7... = ~ 1.000 000 003 ...
>
> It has a 21 % error in the 5-limit, a 23 % error in
> the 9-limit, a 49 % error in the 11-limit, and past
> that isn't consistent. I conclude that it's useless
> for the purposes of most people looking at these things.
hence appearenty irrelevant for the aims that group here.
May be not comletely futil:
Rather something for physicists that do want to convert:
http://en.wikipedia.org/wiki/Stoney_units#Stoney_units
into
http://en.wikipedia.org/wiki/Planck_units
by the "3-limit?":
http://en.wikipedia.org/wiki/Fine-structure_constant
rational or logarithmic(base 2) approximations:
alpha = ~ (12*40/41)^-2 = ~ ((2^(3*3*757/190537))/12)^2
>
> It is, however, a denominator for a convergent to
> log2(3). Those things are trivial to find.

Alike if one knews already the:
http://en.wikipedia.org/wiki/Bohr_model
then especially the
http://en.wikipedia.org/wiki/Balmer_series
spectra turns out to be an trivial sub-case.
>
A.S.
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