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Re: 11/13 limit bridges

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  • Mats Öljare
    ... These are great!I´ll see what i can do with these...Thanks! -=-=-=-=-=-=- MATS ÖLJARE http://www.angelfire.com/mo/oljare
    Message 1 of 8 , Feb 8, 2001
      >100:99
      >245:243,
      >441:440,
      >and
      >896:891
      >
      >Back in November, I created some 13-limit periodicity blocks for Justin
      >White based on the five unison vectors
      >
      >100:99,
      >105:104,
      >196:195,
      >275:273,
      >and
      >385:384

      These are great!I�ll see what i can do with these...Thanks!

      -=-=-=-=-=-=-
      MATS �LJARE
      http://www.angelfire.com/mo/oljare
      _________________________________________________________________________
      Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com
    • D.Stearns
      Mats Öljare wrote, I ve used this rather odd
      Message 2 of 8 , Feb 8, 2001
        Mats Öljare wrote,

        <<I hope you can give good examples of some,other than 105/104 which
        is the only one i´ve explored so far.>>

        I've used this rather odd 7-tone scale as a sort of bridged/tempered
        3-7-11 lydian hybrid...

        ,1/1.
        .' | `.
        32/21-------8/7----+---12/7------9/7------27/14
        |
        7/5

        The way I see it this scale makes interesting and selective use of the
        441/440 and the 540/539 and allows for the 243/242 to disappear as
        well...

        1/1 8/7 9/7 7/5 32/21 12/7 27/14 2/1
        1/1 9/8 11*9 4/3 3/2 27/16 7/4 2/1
        1/1 12*11 32/27 4/3 3/2 14/9 16/9 2/1
        1/1 12~11 11~9 11*8 10/7 18~11 11~6 2/1
        1/1 9/8 81/64 21/16 3/2 27/16 11*6 2/1
        1/1 9/8 7/6 4/3 3/2 18*11 16/9 2/1
        1/1 28/27 32/27 4/3 16*11 128/81 16/9 2/1

        (The ratios separated by the asterisks are the theoretically bridged
        intervals and those separated by the tilde are the theoretically
        tempered ratios.)

        --Dan Stearns
      • graham@microtonal.co.uk
        ... example, on ... I considered 243:243, but decided it didn t really simplify anything. Although it can be approximated with a high degree of accuracy. For
        Message 3 of 8 , Feb 9, 2001
          Paul H. Erlich wrote:

          > We've discussed quite a few 11-limit ones on this list -- for
          example, on
          > Graham's page http://www.microtonal.co.uk/lattice.htm you'll see
          >
          > 121:120
          > and
          > 243:243

          I considered 243:243, but decided it didn't really simplify anything.
          Although it can be approximated with a high degree of accuracy. For
          most purposes, 243:242 is preferable.

          For the 13-limit, 144:143 may be useful. That's between the two
          neutral sixths 13:8 and 18:11. An alternative is 352:351, between
          13:8 and the extended 11-limit neutral 6th of 44/27 (=(4/3)*(11/9).
          Using both bridges also gives you a 243:242.

          With only the 352:351, a neutral triad will still contain only
          13-limit intervals.


          Note: a law of electronic discussions states that this post will
          contain a numerical error.


          Graham
        • jpehrson@rcn.com
          ... http://groups.yahoo.com/group/tuning/message/18486 ... anything. Although it can be approximated with a high degree of accuracy. That s pretty funny....
          Message 4 of 8 , Feb 9, 2001
            --- In tuning@y..., graham@m... wrote:

            http://groups.yahoo.com/group/tuning/message/18486
            >
            > I considered 243:243, but decided it didn't really simplify
            anything. Although it can be approximated with a high degree of
            accuracy.

            That's pretty funny....

            _____ _____ _____ _
            Joseph Pehrson
          • Paul H. Erlich
            Graham wrote, ... ha ha . . . that was a joke, right?
            Message 5 of 8 , Feb 9, 2001
              Graham wrote,

              >I considered 243:243, but decided it didn't really simplify anything.
              > Although it can be approximated with a high degree of accuracy. For
              >most purposes, 243:242 is preferable.

              ha ha . . . that was a joke, right?
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