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Re: Decatonic scales: temperaments with relatively just thirds and fifth?

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  • George D. Secor
    ... test ... Hi Torsten, I thought it was about time I replied directly to one of your messages about a couple of things that weren t completely answered. ...
    Message 1 of 46 , Apr 1, 2008
      --- In tuning@yahoogroups.com, Torsten Anders <torstenanders@...>
      wrote:
      >
      > Thank you all very much for your replies!! I had no time yet to
      test
      > all your recommendations, but I definitely will :)

      Hi Torsten,

      I thought it was about time I replied directly to one of your
      messages about a couple of things that weren't completely answered.

      > On Mar 27, 2008, at 6:28 AM, Petr ParĂ­zek wrote:
      > > If you want thirds and fifths to be closer to just, then you'll
      get
      > > only a very poor approximation to 7/4 because the same interval
      is
      > > also used here to approximate 16/9.
      >
      > Does there also exist a variant where the intonation of the
      septimal
      > intervals is optimised (possibly to the detriment of thirds and
      > fifths) like the (major) thirds are optimised in meantone (to the
      > detriment of the fifths)?

      It looks as if that would have to be something very close to 22-
      equal. Because ~7/5 is fixed at 600 cents in pajara (with pure
      octaves; but, in any case, something very close to that), further
      decreasing the error of 7/4 (by lowering it) causes the error of 5/4
      (which also must go lower) to increase further in error. A major 3rd
      that's narrower than in 22-equal is not very good melodically, which
      I suspect is one of the things that caused you to look for
      alternatives to 22-equal (in addition to the heavily tempered fifths).

      > ...
      > On Mar 27, 2008, at 7:37 AM, Graham Breed wrote:
      > > Well temperament -- make the tuning more lumpy. You can
      > > make some chords better in tune at the expense of others.
      > > Naturally you'll probably want the most important chords to
      > > be well tuned. As a bonus you can get the temperament to
      > > circulate, so that you can modulate over a fixed number of
      > > notes. 22 and 34 are the most obvious choices.
      > I have never created a well temperament yet -- is there
      some "gentle
      > introduction" to this subject available I could read?

      Please do check out the 34-tone well-temperament that I discussed
      here, because (in its dozen or so best keys) it doesn't damage 7/4
      nearly as much as does 34-equal:
      http://groups.yahoo.com/group/tuning/message/68032

      I've tried (on several occasions) to construct some sort of 22-tone
      well temperament, but I wasn't able to come up with anything
      satisfactory.

      --George
    • Torsten Anders
      On Mar 28, 2008, at 4:20 PM, Carl Lumma wrote: Original Subject: Re: [tuning] Re: Decatonic scales: temperaments with relatively just thirds and fifth? ...
      Message 46 of 46 , Apr 16, 2009
        On Mar 28, 2008, at 4:20 PM, Carl Lumma wrote:
        Original Subject: Re: [tuning] Re: Decatonic scales: temperaments
        with relatively just thirds and fifth?

        > George Secor wants to preserve the common usage of these terms.
        > However, since the common usage isn't precise (uses these
        > terms interchangeably), I don't think that's a good idea.

        Just remembered that we were discussing this terminology already a
        year ago. In summary I feel instead of redefining established terms
        it might be a better idea to use new terms or common terms with
        additional qualifiers in order to avoid confusion.

        Best
        Torsten

        --
        Torsten Anders
        Interdisciplinary Centre for Computer Music Research
        University of Plymouth
        Office: +44-1752-586219
        Private: +44-1752-558917
        http://strasheela.sourceforge.net
        http://www.torsten-anders.de
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