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

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  • monz
    ... 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, 2007
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      --- 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
    • Jon Szanto
      ... 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, 2007
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        --- 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
      • Gene Ward Smith
        ... Why not? Good name for a girl baby. Can you imagine Eightthousandfivehundredandthirtynine Monzo?
        Message 3 of 13 , May 1, 2007
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          --- 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?
        • monz
          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, 2007
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            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.

            Mama and i had already had a long debate about our
            baby's name and had already picked Lelani by the time
            my mother told me about this. Then i stayed up all night
            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
            already ironic that i had applied my Aunt's name to
            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
          • Andreas Sparschuh
            ... 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, 2007
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              --- 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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