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Re: Blackwood's Microtonal Etudes in Tonescape (was: seeking...)

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  • Gene Ward Smith
    ... How does he classify 22? Paul Erlich thought his 22 was about the weakest of the bunch, because it is a kind of cockeyed diatonic piece. I thought it was
    Message 1 of 19 , Feb 1, 2007
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      --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

      > But that's exactly why i want those research notes:
      > Blackwood divides scales into two broad categories,
      > diatonic and symmetric, and goes into great detail
      > about the types of harmonic progressions he found
      > available in each EDO.

      How does he classify 22? Paul Erlich thought his 22 was about the
      weakest of the bunch, because it is a kind of cockeyed diatonic
      piece. I thought it was interesting, and amusing in something the way
      the Candide Overature is. But things like the recent "Blue Monk" in
      22 seem to be more intrinisic to the character of 22. I think maybe
      Paul was objecting to the impression he left, that his 22 etude is
      what the tuning is *like*, rather than something it makes possible.

      > The problem is how to design the Lattice for each EDO.
      > Having all that info would help me a great deal in
      > deciding what to use for the Lattice axes: how many
      > dimensions should the Lattice have, which prime-factors
      > should define each axis, and in fact are there generators
      > other than prime-factors which would be better?

      Interesting questions. For the 23, for instance, I think taking it as
      half a 46 might be better. The 16 etude seems to have a diminished
      temperament concept to it. What the hell you or anyone can do with 13
      is a question. You could look at the chords he was using as, more or
      less, consonances to try to sort it out.

      > EDO prime-factors
      > 13 . 11
      > 14 . 29

      29?? I'd do what I suggested, and look at his chords.

      > Well, it's nice that Blackwood put a legend at the beginning
      > of each Etude which shows the notation *and* the EDO degree
      > number!

      What do you think of his notations? Scala doesn't use them, but of
      course it would be relatively easy to produce a Scala version in some
      other notation.
    • Herman Miller
      ... The 13 etude uses the 8-note MOS scale which he calls subminor , based on a generator of 5 steps (461.538 cents). The thirds of that scale could be
      Message 2 of 19 , Feb 1, 2007
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        Gene Ward Smith wrote:

        > Interesting questions. For the 23, for instance, I think taking it as
        > half a 46 might be better. The 16 etude seems to have a diminished
        > temperament concept to it. What the hell you or anyone can do with 13
        > is a question. You could look at the chords he was using as, more or
        > less, consonances to try to sort it out.

        The 13 etude uses the 8-note MOS scale which he calls "subminor", based
        on a generator of 5 steps (461.538 cents). The "thirds" of that scale
        could be considered as, very roughly, approximations of 7/6 and 5/4.
      • Gene Ward Smith
        ... based ... If I take that seriously, and assume the generator is a sort of fourth, I end up with
        Message 3 of 19 , Feb 1, 2007
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          --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

          > The 13 etude uses the 8-note MOS scale which he calls "subminor",
          based
          > on a generator of 5 steps (461.538 cents). The "thirds" of that scale
          > could be considered as, very roughly, approximations of 7/6 and 5/4.

          If I take that seriously, and assume the generator is a sort of fourth,
          I end up with <13 21 30 37| as a val, which is as good as you can do
          for the 7-limit with 13. It has a TM basis {25/24, 28/27, 160/147}, and
          if we take 28/27 and 160/147 as kernel elements, we get <<1 7 3 9 2 -13|
          as a wedgie. This looks like a Herman Miller temperament to me. You get
          a Fibonacci thing going with 8, 13, 21, 34, 55, 89 ... since (3-sqrt
          (5))/2 of an octave, eg 600*(3-sqrt(5)) cents, is a poptimal generator
          (so is 13/34, 21/55 etc.)
        • monz
          ... Thanks, Rich. I had already found that before you posted it, called, and got his email from the person who answered. Hopefully i ll be hearing from him.
          Message 4 of 19 , Feb 1, 2007
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            --- In tuning@yahoogroups.com, Rich Holmes<rsholmes@...> wrote:
            >
            > Rich Holmes<rsholmes@...> writes:
            >
            > > There's a phone number listed here: http://music.uchicago.edu/?dir
            >
            > ... which on closer examination turns out to the be the Music
            > Department main office number, but presumably whoever answers
            > that could help.



            Thanks, Rich. I had already found that before you posted it,
            called, and got his email from the person who answered.

            Hopefully i'll be hearing from him.


            -monz
            http://tonalsoft.com
            Tonescape microtonal music software
          • monz
            Hi Gene, ... Well ... i don t know, because that s one of the parts of the book that i don t have. As i said, i only have the sections on 15-, 16-, and 18-edo.
            Message 5 of 19 , Feb 1, 2007
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              Hi Gene,


              --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
              wrote:
              >
              > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
              >
              > > But that's exactly why i want those research notes:
              > > Blackwood divides scales into two broad categories,
              > > diatonic and symmetric, and goes into great detail
              > > about the types of harmonic progressions he found
              > > available in each EDO.
              >
              > How does he classify 22?


              Well ... i don't know, because that's one of the parts
              of the book that i don't have. As i said, i only have
              the sections on 15-, 16-, and 18-edo. In fact, the chapters
              are not arranged in order of EDO, and the first few are
              on 15, 19, 13, 15 again, 16, 18, and 22 ... so you see
              that my copy breaks off just before the chapter on 22-edo.

              There are 10 pages of introductory material where he
              does make general comments, and 22 is included there,
              but i haven't read all of it yet. I prefer to keep typing
              it out so that it's easier to read.


              > Interesting questions. For the 23, for instance, I think
              > taking it as half a 46 might be better. The 16 etude seems
              > to have a diminished temperament concept to it.


              Blackwood's main classifications of the different types
              of scales available in the EDOs from 13 to 23 (which
              tunings were the subject of his NEH grant research project
              of which the Microtonal Etudes are the result) are these:

              (i give examples beginning on C, but transpositions
              are also assumed to be included)

              . recognizable diatonic scales: C D E F G A B C
              edos: 12, 17, 19, 22, 24

              . "nearly just" diatonic (i.e., 2 sizes of "whole-tone")
              edos: 15, 18, 20, 22

              . 6-note symmetric mode: C Eb E G Ab B C
              edos: 12, 15, 18, 21, 24

              . 8-note symmetric mode: C D Eb F F# G# A B C
              edos: 12, 16, 20, 24

              . 10-note symmetric mode
              edos: 15, 20

              . 12-note symmetric mode
              edos: 18, 24

              . 14-note symmetric mode
              edos: 21


              The 6-note symmetric mode is what we were calling
              "augmented" and the 8-note is "diminished" ... i haven't
              kept up with the changes of temperament-family names,
              so i'm not sure if they are still current or not.

              But 16-edo is indeed one of the tunings which Blackwood
              as an example of the 8-note symmetric mode, which i
              know as the "diminished scale".


              > What the hell you or anyone can do with 13 is a
              > question. You could look at the chords he was using
              > as, more or less, consonances to try to sort it out.


              Blackwood gives a table showing essentially the same
              data i put in my table above, then concludes:
              "From this it appears that the most alien tunings
              are those of 13, 14, and 23 notes".



              > > EDO prime-factors
              > > 13 . 11
              > > 14 . 29
              >
              > 29?? I'd do what I suggested, and look at his chords.


              Yes, sure, i'd be able to make a much better Lattice
              after i analyze the piece and see what he used as his
              harmonic basis. I only chose 29 for now because, as
              you'll see if you look at my graph

              http://tonalsoft.com/enc/e/edo-prime-error.aspx#14

              there are no lower primes than 29 which come anywhere
              near as close in accuracy in 14-edo as its approximation to 29.


              > > Well, it's nice that Blackwood put a legend at the beginning
              > > of each Etude which shows the notation *and* the EDO degree
              > > number!
              >
              > What do you think of his notations? Scala doesn't use them,
              > but of course it would be relatively easy to produce a
              > Scala version in some other notation.


              I've always thought his notations were a little strange,
              but given the fact that he did a lot of research into
              all 11 of these EDOs, i suppose that he put a lot of
              thought behind them.

              One thing i never liked was the way he put a circle
              near the bottom of the arrow for the notes which use
              that symbol for the accidental -- my preference would
              be to just use a plain arrow. But that's just a very
              minor detail. Anyway, i'll have a clearer opinion
              after i study the pieces more.

              I look forward to the day when Tonescape can do
              Sagittal notation, because then it will be easy to
              see the already-done .tonescape files of Blackwood's
              pieces in Sagittal.

              He also says a bit about notation in the NEH research
              notes, but again, i only have a small part of that work
              ... i actually have only pages 1-24 and 93-218 --
              that's only 150 pages of a 512-page book.



              -monz
              http://tonalsoft.com
              Tonescape microtonal music software
            • monz
              Hi Herman, ... How do you know that? ...! Have you analyzed the piece, or is there some info available somewhere that i d like to read which i don t know
              Message 6 of 19 , Feb 1, 2007
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                Hi Herman,


                --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

                > The 13 etude uses the 8-note MOS scale which he
                > calls "subminor", based on a generator of 5 steps
                > (461.538 cents).


                How do you know that? ...!

                Have you analyzed the piece, or is there some info
                available somewhere that i'd like to read which
                i don't know about?


                -monz
                http://tonalsoft.com
                Tonescape microtonal music software
              • Carl Lumma
                ... The NY Public library has a copy. -Carl
                Message 7 of 19 , Feb 2, 2007
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                  > Well ... i don't know, because that's one of the parts
                  > of the book that i don't have. As i said, i only have
                  > the sections on 15-, 16-, and 18-edo. In fact, the chapters
                  > are not arranged in order of EDO, and the first few are
                  > on 15, 19, 13, 15 again, 16, 18, and 22 ... so you see
                  > that my copy breaks off just before the chapter on 22-edo.
                  >
                  > There are 10 pages of introductory material where he
                  > does make general comments, and 22 is included there,
                  > but i haven't read all of it yet. I prefer to keep typing
                  > it out so that it's easier to read.

                  The NY Public library has a copy.

                  -Carl
                • Herman Miller
                  ... The liner notes for the CD mention that even this tuning contains a strange mode best described as sub[-]minor . I put the hyphen in brackets since it s
                  Message 8 of 19 , Feb 2, 2007
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                    monz wrote:
                    > Hi Herman,
                    >
                    >
                    > --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
                    >
                    >> The 13 etude uses the 8-note MOS scale which he
                    >> calls "subminor", based on a generator of 5 steps
                    >> (461.538 cents).
                    >
                    >
                    > How do you know that? ...!
                    >
                    > Have you analyzed the piece, or is there some info
                    > available somewhere that i'd like to read which
                    > i don't know about?

                    The liner notes for the CD mention that "even this tuning contains a
                    strange mode best described as "sub[-]minor"." I put the hyphen in
                    brackets since it's at the end of the line and it's not clear whether
                    "subminor" or "sub-minor" is intended.

                    I haven't analyzed the whole piece, but I did look at the first part of
                    it, and I noticed the 8-note scale. I guess I don't know specifically if
                    this is the "mode best described as sub-minor", but that's what I was
                    assuming. I tuned it up in Scala and "show data" reveals that it has
                    Myhill's property, with generators of 461.5385 and 738.4615 cents. You
                    can play along with the recording in this scale, until it eventually
                    modulates into another "key" (but even then many of the notes are shared
                    with the "tonic" key).
                  • Herman Miller
                    ... I recall thinking that his 16-ET notation was strange, but then a while back I realized that the major thirds are the best intervals of 16-ET, and with the
                    Message 9 of 19 , Feb 2, 2007
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                      monz wrote:

                      > I've always thought his notations were a little strange,
                      > but given the fact that he did a lot of research into
                      > all 11 of these EDOs, i suppose that he put a lot of
                      > thought behind them.

                      I recall thinking that his 16-ET notation was strange, but then a while
                      back I realized that the major thirds are the best intervals of 16-ET,
                      and with the exception of C-E, Blackwood's notation of major thirds is
                      consistent with traditional notation. (In that respect it's similar to
                      my porcupine-based notations for 15-ET and 22-ET.) I still find his
                      23-ET notation very confusing.
                    • monz
                      Hi Herman, ... I ve read the first 22 pages of Blackwood s _NEH Research Notes_ so far, and he does go into some detail about how he devised his notations. He
                      Message 10 of 19 , Feb 3, 2007
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                        Hi Herman,


                        --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
                        >
                        > monz wrote:
                        >
                        > > I've always thought his notations were a little strange,
                        > > but given the fact that he did a lot of research into
                        > > all 11 of these EDOs, i suppose that he put a lot of
                        > > thought behind them.
                        >
                        > I recall thinking that his 16-ET notation was strange,
                        > but then a while back I realized that the major thirds
                        > are the best intervals of 16-ET, and with the exception
                        > of C-E, Blackwood's notation of major thirds is consistent
                        > with traditional notation. (In that respect it's similar
                        > to my porcupine-based notations for 15-ET and 22-ET.)
                        > I still find his 23-ET notation very confusing.


                        I've read the first 22 pages of Blackwood's
                        _NEH Research Notes_ so far, and he does go into
                        some detail about how he devised his notations.

                        He places a lot of importance on enharmonic equivalence,
                        drawing parallels to how it works in 12-edo.

                        So far i've only really read about 15-edo, and the
                        way he devised his notation for that tuning, he
                        shows how considering 5-edo as a series of very
                        sharp 5ths (720 cents) makes a series of five 5ths
                        upward enharmonically equivalent: thus, in the
                        sequence C - G - D - A - E - B, the C and B are
                        the same pitch. Similarly for G/F# in G-D-A-E-B-F#,
                        F/E in F-C-G-D-A-E, etc. And of course 15-edo
                        contains 5-edo, so this is significant to him.

                        He also examines the symmetric modes in detail,
                        again drawing parallels with how they work in 12-edo.


                        -monz
                        http://tonalsoft.com
                        Tonescape microtonal music software
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