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Re: Moving on [to Cameron and others]

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  • lobawad
    ... Basically, the way something is used, not just the stuff from which it is made. Using the ditone of 41-edo would be a different modality, for example, and
    Message 1 of 124 , Mar 1, 2012
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      --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
      >
      > On Thu, Mar 1, 2012 at 2:50 AM, lobawad <lobawad@...> wrote:
      > >
      > > --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
      > > >
      > > > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
      > > >
      > > > Uh... a far cry from what? I don't understand the question.
      > > > It seems like you're saying that once somebody uses an equal
      > > > >temperament, we should also give them credit for every higher-rank
      > > > >temperament consistent with it. For example if somebody uses 31tet >to
      > > > approximate the 7 limit, then we should give them credit for >cynder, for
      > > > valentine, for miracle... simply because they used a >temperament in which
      > > > the appropriate commas vanish. Is this not what >you're saying?
      > > >
      > > > Keenan
      > >
      > > A far cry "from 3125/3072 or "five major thirds make a perfect twelfth"",
      > > your own words.
      > >
      > > Were 41-edo not wielded with the appropriate modalities, "3125/3072 or
      > > "five major thirds make a perfect twelfth"" would indeed be a far cry away,
      > > or, better said, these things would be deeply buried.
      >
      > Can you define "modality?"

      Basically, the way something is used, not just the stuff from which it is made. Using the ditone of 41-edo would be a different modality, for example, and it would not effect "magic temperament". Even using the Just approximations of 41-edo, there is an enormous amount of music which would not implement "magic" in a tangible way.

      >
      > Did Janko ever say specifically that he wanted to use 41-EDO because
      > 3125/3072 vanishes in it?

      Not that I know of. As far as I know, that is a happy accident. One thing he did say, between the lines, was that tempering out the syntonic comma was not a concern for him.

      >
      >
      > > As far as questions of "credit", the most appropriate response to that is
      > > "WTF?". Effecting a temperament, probably by accident, doesn't constitute
      > > having created one of the systems which are called "temperaments" here.
      >
      > I agree, but you seemed above to be saying the opposite; that Janko
      > gets credit for discovering magic because he used 41-EDO.

      Nowhere did I say that. I said "the earliest implementation", nothing about discovery or even intent (I even added "by happy accident, it seems" to make that clear).

      It is appropriate modalities (music of Janko's time provides plenty of these) applied to 41-edo that bring the temperament tempering-out-the-difference-between-P12-and-five-M3's to life.

      >
      > > If we want to give "credit" for first thinking of "magic", we'd have to give it
      > > Helmholtz, as he seems to be the first to describe 3072:3125 as the fifth
      > > less 5 major thirds.
      >
      > Yeah, but did he ever consider tempering that comma out?

      I don't know. Whether or not he did consider doing so, he chose not to temper it out.

      Once again I suggest that you read older literature for yourself. It is dripping with interesting things.
    • Graham Breed
      ... The link shows that Wilson was still looking at the Cassandra/Schismatic (29&41) mapping. There s something to be said for that because it maps the 43
      Message 124 of 124 , Mar 14, 2012
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        kraiggrady <kraiggrady@...> wrote:
        > I have uploaded
        > this document which is not yet cataloged in the archives
        > [i will probably add to the treasure section at some
        > point] http://anaphoria.com/PartchMappedTo41.pdf if you
        > look especially on page 6 even though the document was
        > done in 2001 he references Secor. So in this case i think
        > George might be giving more credit elsewhere than maybe
        > he should.

        The link shows that Wilson was still looking at the
        Cassandra/Schismatic (29&41) mapping. There's something to
        be said for that because it maps the 43 notes of the Genesis
        scale to 41 distinctly tempered notes with the only
        ambiguity being the unavoidable one from 11/10 and 10/9
        mapping to the same pitch. This means we have to ignore
        100:99. (Two notes disappear because each pitch occurs
        with its octave complement.)

        You may recall that each of the 43 pitches is distinct in
        Miracle (31&41) temperament. For the earlier Exposition on
        Monophony scale, these 43 distinct pitches are included in
        the first 45 Miracle generated pitches.

        I've been looking at the ambiguous 41 note temperings
        again. The coincidence of 43 just pitches mapping to a 41
        note MOS doesn't hold with Cassandra and the Exposition
        scale. 49/48 maps to 29 fifths.

        To get exactly 41 tempered pitches, a rank 2 mapping has to
        be consistent with 41-equal and temper out 100:99. It must
        have an 11-limit complexity of no more than 20. The
        highest complexity for an 11-limit pitch will then be 20
        generators from the 1/1. Each pitch occurs with its octave
        complement in the diamond, and the 11-limit diamond is a
        subset of either Partch scale, so there will be 40
        generators between these two worst-case pitches. 40
        generators means 41 pitches.

        The only mappings that comply with these conditions are
        those for Cassandra, Octacot (31&27e), and Magic (19&22).
        It turns out that Octacot needs 57 generated notes to
        approximate either 43 note scale. But Magic needs exactly
        41 for either scale. So both scales correspond to
        periodicity blocks that detemper the 41 note Magic MOS with
        two ambiguous pairs of pitches. Only Magic works like this
        for both scales. Only Magic and Cassandra work like this
        for either scale.

        The discrepancy between the Genesis and Exposition scales
        amounts to an interval of 245:243. Tempering out 245:243
        is the same as ignoring the difference between the two
        scales. Combining this with the 100:99 that allows us to
        fit the 11-limit diamond into 41 pitches is consistent with
        these temperaments:

        http://x31eq.com/cgi-bin/uv.cgi?uvs=100%3A99+245%3A243&limit=11

        The most accurate are Bohpier (41&8d), Magic, Octacot, and
        Varan (41&5e). This is another way of producing a shortlist
        that includes Magic.


        Graham
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