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Re: Pajara tuning examples

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  • Carl Lumma
    ... In this example not especially, and I think the 7-limit version has nicer bite. ... The better 5-limit parts of 34 and 56 were immediately appreciated.
    Message 1 of 95 , Dec 1, 2006
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      > G B\ D G - 4:5:6:8 - otonal (major) triad
      > C A Eb/ G - 1/12:1/7:1/5:1/4 - utonal tetrad, open position
      > D A C F#\ - 4:6:7:10 - otonal (harmonic 7th) tetrad, open position
      > G B\ D G - 2:5:6:8 - otonal (major) triad
      >
      > First listen to these in JI, so you have some idea what we're
      > trying to approximate. So in 7-limit JI we have:
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-JI7a.mp3
      >
      > Paul Erlich suggested that, since the utonal tetrad isn't as
      > consonant as the otonal, one might prefer an alternate JI tuning,
      > of which the most consonant voicing is 10:12:15:17 (in the first
      > inversion). In the following 17-limit JI version of the previous
      > example, the 2nd chord becomes 10:17:24:30 (in open position):
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-JI17a.mp3
      >
      > Would you agree that this is more consonant that the 7-limit
      > example?

      In this example not especially, and I think the 7-limit version
      has nicer bite.

      > Here's the above progression in 4 different pajara temperaments:
      > 22-ET:
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-22a.mp3
      > 34-ET (using 28deg34 for 4:7):
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-34a.mp3
      > 56-ET (using 46deg56 for 4:7):
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-56a.mp3
      > 34-WT (using 28deg34 for 4:7):
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-34WTa.mp3
      >
      > Note that the 2nd and 3rd chords have two common tones (C and A),
      > which do *not* change in pitch (except that the C's are an octave
      > apart).

      The better 5-limit parts of 34 and 56 were immediately
      appreciated. 7-limit still hard to tell because there's only
      one otonal tetrad in this example. The 22 version had what
      sounded like chorusing here, which I hated.

      > And just for fun, here's a 12-ET example. It's a little lower in
      > pitch (C=261.63) than all of the others (C=264), and it's here
      > simply as a reminder of why we've been looking for alternative
      > tunings.
      >
      > 12-ET:
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-12ab.mp3

      Couldn't get this to download.

      > For the 2nd chord the first JI example has 1/12:1/7:1/5:1/4,
      > while the second example replaces that with 10:17:24:30 (changing
      > only the tenor voice in the 2nd chord), which sounds more
      > consonant, IMO. The JI examples have a couple of shifts in
      > pitch that are tempered out in pajara, and they're here to
      > give a clearer idea of what we're trying to approximate with
      > the temperaments.
      >
      > GROUP B
      > -------
      >
      > Warning: this involves a comma shift in the tenor voice, from
      > A\ to A, which isn't a good pajara progression -- it's here
      > only for comparison with the above.
      >
      > The examples in this group consist of a progression of 4
      > consonant 9-limit chords:
      >
      > G B\ D G - 4:5:6:8 - otonal (major) triad
      > C A\ Eb G - 6:10:14:18 - otonal 9th w/o root, open position
      > D A C F#\ - 4:6:7:10 - otonal (harmonic 7th) tetrad, open position
      > G B\ D G - 2:5:6:8 - otonal (major) triad
      >
      > First in 9-limit JI:
      > http://xenharmony.wikispaces.com/space/showimage/Pajara-JI9b.mp3

      Ditto. I'm getting a "redirection cycle detected" error.

      > Please vote for which of the above 4 pajara temperaments you
      > think is best.

      I would say 34 based on this.

      -Carl
    • George D. Secor
      ... As ... on ... paper in ... pajara ... trying ... the ... weird ... system, ... worth ... very ... Thanks for your suggestion, Gene. Since I m thinking of
      Message 95 of 95 , Dec 26, 2006
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        --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
        wrote:
        >
        > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
        >
        > > First, I want to say "thank you" for your very helpful comments.
        As
        > > a follow-up to my 17-tone paper (for which I had to draw heavily
        on
        > > my own observations and opinions), I hope to write a 34-tone
        paper in
        > > the near future.
        >
        > I think it would be very useful if this paper not only included
        pajara
        > but also discussed keemun, where the seventh is flat. This is 34
        trying
        > to act like 19, not 22. The Kees tunimg here sets the fifth, not
        the
        > third, to be exact and is pretty much the same as 53-et with a
        weird
        > choice of mapping for 7. Hence it is not innately a wide-fifth
        system,
        > but of course it will be tuned to 34, and it seems like a system
        worth
        > exploring to anyone wanting to delve into 34 and with an instrument
        > available to do so.
        >
        > The point of it is, the 7 is not very well in tune, but it's not
        very
        > complex either. The 7 and 11 note MOS make for natural scales.

        Thanks for your suggestion, Gene. Since I'm thinking of this as a 34-
        tone (rather than a pajara) paper, I expect to describe several
        useful scales in 34 that may be created with a generating interval,
        and Keemun will definitely be among them.

        --George
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