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epimoric bisection 81:80=(441:440)(99:98) was Re: Werckmeister's "Septanarius"

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  • Andreas Sparschuh
    ... Dear Margo, Werckmeister s so called 11-limit septenarian 99:98 Comma amounts (81:80):(441:440) 11-limit septenarian 441:440 Schisma amounts
    Message 1 of 69 , Jul 1, 2008
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      --- In tuning@yahoogroups.com, Margo Schulter <mschulter@> wrote:

      Dear Margo,

      Werckmeister's so called
      11-limit "septenarian" 99:98 Comma amounts (81:80):(441:440)
      11-limit "septenarian" 441:440 Schisma amounts (81:80):(99:98)
      if understood that ratios as epimoric bisection of the SC=81:80.

      the following well-tuning uses that as epimoric bi-scetion:

      F 440:441 G = F 881:882 C 880:881 G inbetween F-C-G

      and the trisection
      inbetween the violin empty strings G-D-A-E consisting in

      G 98:99 E = G 276:279 E subdivided into 3 epimoric factors:

      G 296:297 D 295:296 A 296:297 E

      and respectively for the schisma B 32768:32805 F within

      E 3968:3969 B F# C# G# 2510:2511 Eb 3764:3765 Bb 4704:4705 F

      into 4 another superparticular ratios
      in order to conclude the cycle of 5ths by
      the totally amount of an PC=3^12/2^19.

      meanwhile my good-old piano got tuned in that refinement :

      F 881:882 C 880:881 G 296:297 D 295:296 A 296:297 E

      with the interim product inbetween FCGDAE = 80:81 = SC and

      E 3968:3969 B F# C# G# 2510:2511 Eb 3764:3765 Bb 4704:4705 F

      for yielding the Schisma=2^15/5/3^8=32768:32805.

      that's expanded:
      > Start at an minor-tone (10:9) below Scheibler:
      > G; (7*7=E6:27=49 E8:27=98 <) 99G2 198G3 396G4 := 440Hz*(9:10)
      > D; (E6:9=147 E8:9=294 < 295=A5:3 <) 296D4 (<297 = G2*3)
      > A; (E6:3=441 E8:3=882 <) 885A5 just as Margo proposes
      > E; 1323E6
      > B; 31B0...3968B7(<3969=E6*3=49) lowest pitch on 5string doublebass
      > F#; 93F#2 := B0*3
      > C#; 279C#4 := F#2*3
      attend the modifications from here on:
      G#; 887G#5 := C#4*3
      Eb; 1255Eb6 2510Eb7 (< 2511 := G#5*3)
      Bb; (F2:3=29.4 .. F6:3=470.4<)470.5Bb4 941Bb5 1882Bb6 (3765:=Eb6*3)
      F; (C4:3 = 88.1 <) 88.2F2
      > C; (G1:3=33 ... G4:3=264 <) 264.3C4
      > G; 99G2 = 33*3
      Hence the
      > Chromatically
      improved values
      >on the keys in frequencies as absolute-pitchs:
      do arise a tiny little bit on the corresponding notes:
      > 264.3_C4
      > 279___C#4
      > 296___D4
      313.75 > instead formerly 313.5_Eb4
      > 330.75E4
      > 352.5_F4
      > 372___F#4
      > 396___G4
      418.5 > instead formerly 418___G#4
      > 442.5_A4
      470.5 > instead fromerly 470___Bb4
      > 528.6_C5
      all others pitches remain unchanged.

      please forget about my obsolte
      > !sparschuh885A5.scl
      and replace it by the more elaborate:

      Sparschuh's 80:81 inbetween F-C-G-D-A-E and 32768:32805 in E B...Bb F
      6275/2463 ! was > 3135/2463 formerly
      6615/4926 ! (5:4)(882:881)
      3524/2463 ! (4:3)(882:881) was > 3525/2463 ! (4:3)(3525:3524)
      3960/2463 ! (3:2)(880:881)
      4185/2463 ! was > 4180/2463 formerly
      4705/4700 ! was > 4700/2463 fromerly

      attend the exact JI haltone E 16:15 F that is
      shifteted 882:881 upwards versus the unison 1:1,
      because the 4th F-C and the 3rd C-E
      turn out to be the same 882:881 sharper than JI.

      Who in that group here dares to try that on his/hers own instrument?
      Are there any proposals in order to improve even that once more again?

      Yours Sincerely
    • Ozan Yarman
      Dear Mike, my apologies for the very late reply. As I have stated in my recent message to Margo Schulter, I had been enjoying a well deserved summer s rest. To
      Message 69 of 69 , Aug 10, 2008
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        Dear Mike, my apologies for the very late reply. As I have stated in
        my recent message to Margo Schulter, I had been enjoying a well
        deserved summer's rest.

        To answer your enquiry, here are some links to older messages to this
        forum on the subject of masters of Turkish maqam music:




        The names of some of the prominent masters have been listed in these
        messages. A search in amazon.com could yield links to the performances
        of masters themselves.

        Fusion type endeavours in "world music" does occasionally result in
        original productions worthy of approval. However, for a crash course
        in maqam music, you need to listen to acclaimed executants and
        venerable exponents of the tradition, not syntheses.

        Direct personal experience of Allah is very much ingrained in Sufi
        music. Most of the known neyzens in Turkiye are into tasavvuf. You are
        likely to enjoy the Erguner brothers, the elder of which, Kudsi, has
        done world fusion too if I heard correctly:


        If you are into the Turkish ney for the love of its trancendental
        sound, here are acknowledged quotidian performers of the instrument:




        On Jun 28, 2008, at 7:42 AM, Mike Battaglia wrote:

        > On Fri, Jun 27, 2008 at 8:15 PM, Ozan Yarman <ozanyarman@...
        > > wrote:
        >> I think the theory of Maqam music and other "ethnic" genres around
        >> the
        >> world are much neglected by the alternative tuning list community.
        >> Most of the discussions are centered around either historical or
        >> contemporary microtonalisms for furthering Western music culture
        >> alone. While I appreciate the contributions by the West to musical
        >> art, I believe the Western quarter (pun intended) can account for
        >> only
        >> a fraction of the actual music-making in the globe. One of the
        >> greatest traditions is right next door: A venerable monophonal Middle
        >> Eastern culture based on maqamat, destgaha and raga. This "exotic"
        >> culture has been influenced by a thousand years of Islamic atmosphere
        >> to inspire such styles and practices as Mevlevi rites, Qawwali
        >> performances, peshrevs, taqsims, gazels, etc... Your penchant to
        >> discover more of the theories and styles of exotic traditions is
        >> admirable.
        >> Though my experience is most inadequate to describe the musical
        >> wonders of the Islamic Civilization, my presence in the tuning list
        >> as
        >> a fresh academician should be construed as an oppurtunity to discover
        >> a glimpse of at least the Turkish branch of this grand culture.
        > Well hey man, if you have a listening list of stuff you can recommend,
        > I think we'd all love to check it out. World music is one of the most
        > fascinating things in the, well, the world. Mainly because you have
        > thousands of years of musical development behind most of these
        > cultures and styles, and so they are usually very much advanced.
        > Jeff Buckley did a Qawwali-inspired song, "Dream Brother," in which he
        > mixed pop/rock with traditional Qawwali elements, and it's one of my
        > favorite songs. I started looking for some traditional Qawwali
        > recordings when I heard that song, and I didn't really find much.
        > Any time there is an old, ancient branch of music that has reached as
        > high of a level of artistic development as the one we're talking about
        > here, people will be interested. I just think many don't know about it
        > yet.
        > One interesting thing to note is that the religious music of all of
        > the world sounds very, very, very similar. Perhaps not the music that
        > is "associated" with various churches and such - but the music that
        > monks sing, the music that is sung to draw people closer to the
        > experience of God.
        > -Mike
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