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Re: Woolhouse and 730-EDO

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  • Gene Ward Smith
    ... weak in ... intervals are ... decent ... exactly ... All of which is part of why I used to use 612 instead. ... liked ... It s what you get by applying an
    Message 1 of 5 , May 1, 2005
      --- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

      > Now about 730-tone. The fifth is 427 degrees, the third is 235. It's
      weak in
      > 7- and 11-limit, however: 7/4 is 589 and 11/8 is 335, but both
      intervals are
      > a third of a degree sharp. 665-tone (fifth = 389, third = 214) has a
      decent
      > approximation of 7/4 (537 degrees), though 11/8 is horrible, almost
      exactly
      > halfway between 305 and 306.

      All of which is part of why I used to use 612 instead.

      > The comma in 730-tone is 13 degrees, while in 665-tone it's 12 degrees,
      > which of course is divisible by 3 and 4. I'm wondering why Woolhouse
      liked
      > 7/26-comma meantone so much (it of course lies between third- and
      > quarter-comma).

      It's what you get by applying an equally-weighted least squares
      analysis in the 5-limit.

      > <vanity>Now here's a meantone I like: set the generator to
      697.085365 cents
      > (lower the fifth by one-sixth of 896/729), so the augmented fourth
      is 7/5.
      > 105-TET is great for this.</vanity>

      I was calling that the Aaron Johnson fifth a few days back. Do you
      have a prior claim? It's good for playing the Tristan chord in.
    • Gene Ward Smith
      ... (Where ... I dunno, but it seems easier simply to call it (56/5)^(1/6).
      Message 2 of 5 , May 1, 2005
        --- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
        > > <vanity>Now here's a meantone I like: set the generator to 697.085365
        > > cents
        > > (lower the fifth by one-sixth of 896/729)
        >
        > I meant 3584/3645, which is the difference between 729/512 and 7/5.
        (Where
        > in the hell did I come up with 896/729?)

        I dunno, but it seems easier simply to call it (56/5)^(1/6).
      • Danny Wier
        ... Nope, I just came up with the idea a few hours ago. ;)
        Message 3 of 5 , May 1, 2005
          From: "Gene Ward Smith":

          >> <vanity>Now here's a meantone I like: set the generator to
          > 697.085365 cents
          >> (lower the fifth by one-sixth of 896/729), so the augmented fourth
          > is 7/5.
          >> 105-TET is great for this.</vanity>
          >
          > I was calling that the Aaron Johnson fifth a few days back. Do you
          > have a prior claim? It's good for playing the Tristan chord in.

          Nope, I just came up with the idea a few hours ago. ;)
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