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Re: Defining Just intonation

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  • David C Keenan
    ... Thanks John, I was avoiding that for as long as I could. One day at a time sweet jesus. Many tunings (both static and dynamic) try hard to be JI while
    Message 1 of 96 , Nov 30, 2000
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      John deLaubenfels wrote:

      >In the discussion between Monz, Dave K., and others, I haven't seen one
      >very large aspect of tuning addressed: if an interval targets a
      >particular low integer ratio, yet is allowed to deviate somewhat from it
      >for purposes of horizontal (melodic) stability, is it still "JI"? How
      >much deviation is allowed? Zero point zero zero cents?

      Thanks John,

      I was avoiding that for as long as I could. One day at a time sweet jesus.

      Many tunings (both static and dynamic) try hard to be JI while compromising
      for various reasons. Merely trying hard isn't good enough. But then tunings
      which are intended to be strictly JI are used on instruments (even
      electronic ones) whose resolution and stability is such that +-0.5c
      deviations are common.

      I propose that for now, in ordinary circumstances, we accept deviations of
      +-0.5 cents from strict harmonic coincidence as still being JI. This would
      be convenient since it would let us round all our cents values to the
      nearest whole number of cents.


      ------------------
      Jacky Ligon wrote:

      > Just for the sake of deepening my understanding of this fascinating
      > thread, I would like to humbly ask the following question: "Out of
      > tune" relative to what (I realize you did say "A lot of the time")?
      > Our preconceptions of 5 limit harmony - or 12tET? Seems like this
      > could be just a little subjective (please take the liberty of
      > correction if seen fit).

      Hi Jacky,

      What Paul attributed to me is correct.

      You'd have to subject me to a long time of some particularly hideous
      torture* before I'd say that 12-tET was "in tune". (* like deprive me of my
      computer for a week)

      But you're right. If we relied only on a description of just intervals as
      being "in tune", it would be highly subjective. Here's how we avoid that.

      We define it in terms of what you can _do_ to experience it.

      --------------------------------------------------------------------------
      Injunctive definition of "JI interval"

      Take a sustained harmonic timbre such as human voice or strings (or almost
      any timbre if it's played loud enough). While sounding one tone at constant
      pitch, very slowly sweep another tone up from that. Some times you hear
      "wah wah". Notice when the "wah wah"s slow down and eventually stop before
      speeding up again. Those sharply defined points where the "wah wah"s stop
      are the "just intervals", "justly intoned intervals", "JI intervals", "pure
      intervals".
      --------------------------------------------------------------------------

      Any definition of JI that isn't based on an injunction very like the one
      above, is breaking with its historical and musical roots.


      -----------
      Dear Margo,

      It is clear that we both recognise the same distinctions. We only disagree
      about what words to use for them.

      I feel that the musical distinction between pure and impure intervals is
      far too important to leave to the vagaries of a capital letter,
      particularly when people already use "Just" versus "just" for other
      purposes unrelated to your proposal.

      And we have a well-respected dictionary that claims a definition dating
      from 1811 establishing "just" as synonomous with "harmonically pure".

      As Joe Monzo pointed out, we already have a word for the mathematical
      property of being tuned in a whole number ratio, "rational".

      For "an interval that is not necessarily pure but arises in a just scale" I
      suggest simply "JI-scale interval". The hyphen is important to avoid the
      interpretation "JI scale-interval".

      For "an interval that is definitely not pure, in a just scale" I suggest
      "non-just JI-scale interval".


      ----------------------------
      Snappy-but-rough definitions
      ----------------------------

      It's natural to want a snappy definition of JI, even if it's only
      approximate. But "tuning by whole number ratios" isn't just rough, it's
      just wrong.

      I'm pleased that John Chalmers has repudiated "tuning by whole number
      ratios". Here's where David Doty makes the same mistake John did.

      Short version
      http://www.dnai.com/~jinetwk/whatisji.html
      Long version (first chapter of David Doty's Just Intonation Primer).
      http://www.dnai.com/~jinetwk/primer2.html

      "Tuning by small whole number ratios" is much better, but as Dave Beardsley
      pointed out, "small" can mean anything from 10 to 200 depending heavily on
      harmonic context.

      How about:
      -------------------------
      JI is tuning by harmonics
      -------------------------

      Regards,
      -- Dave Keenan
      -- Dave Keenan
      http://uq.net.au/~zzdkeena
    • ligonj@northstate.net
      ... Paul, When I discovered the mistake, I found that the FFT size for the data was set to 4096 rather than 65536, which would ve likely caused this much
      Message 96 of 96 , Dec 5, 2000
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        --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
        > Well, whatever.

        Paul,

        When I discovered the mistake, I found that the FFT size for the data
        was set to 4096 rather than 65536, which would've likely caused this
        much deviation. The "729.202" was not found(!); proving how important
        these resolution settings are.


        Thanks again,

        Jacky
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