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Werckmeister's "Septanarius" again refined and modernized, was: Re: discer...

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  • Andreas Sparschuh
    ... My intrest comes form Werckmeister s: http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html
    Message 1 of 69 , Jun 30, 2008
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      --- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
      >
      Dear Margo:
      >
      > Thank you for posting your temperament with one wide fifth based on
      > complex integer ratios, a technique that fascinates me, and which I
      > have used in rather different stylistic settings.
      >
      My intrest comes form Werckmeister's:
      http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html
      http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings
      http://launch.groups.yahoo.com/group/tuning/message/69750
      in his
      "Musicalische Temperatur"
      http://diapason.xentonic.org/ttl/ttl01.html
      there on p72.


      ! septenarius.scl
      ! Werckmeister's #6 in string-lenghts on the monochord
      !
      C196 C#186 D176 D#165 E156 F147 F#139 G131 G#124 A117 B110 H104...
      !
      12
      !
      98/93 ! := 196/186 = C/C#
      196/176 ! = C/D
      196/165 ! = C/D#
      49/39 ! := 196/156 = C/E = (5/4)*(196/195)
      4/3 ! := 196/147 = C/F
      196/139 ! = C/F#
      196/131 ! = C/G = (3/2)*(392/393)
      49/31 ! :=196/124 = C/G#
      196/117 ! = C/A
      98/55 ! =196/110 = C/B
      49/26 ! =196/104 = C/H
      2/1
      !

      later
      http://www.tuningforktherapy.com/about.html
      "In 1834, J.H. Scheibler presented a set of 54 tuning forks covering
      ranges from 220 Hz to 440Hz."
      http://www.apogeelearning.com/acutone/historytuningfork_1_2.html
      "J. H. Scheibler in Germany in 1834 presented a set of 54 tuning forks
      covering the range from 220 Hz to 440 Hz, at intervals of 4 Hz."
      or
      http://www.cosmeo.com/viewArticle.cfm?guidAssetId=A44930C3-53BA-4646-AD2C-B6AA4F1A62ED&&nodeid=
      "The German physicist Johann Heinrich Scheibler (1777-1838) made the
      first accurate determination of pitch corresponding to frequency and
      proposed the standard A equals 440 in 1834."

      for that purpose of defineing his 440Hz standard
      S. appearently referred to above Werckmeister's
      original Monochord-lenghts C196...C'98 (Upper-case letttes) on p.73
      but now instead in reverse pitch-order
      interpreted as absolute frequncies
      (here denotated in lower-case letters):

      g1 = 49 C'98 C196
      d3 = F147 := 49*3
      a2 = 55 B110 220 440 (<441 = 147*3) hence Scheibler's choice of 440cps
      e3 = D#165 := 55*3
      b0 = 31 62 G#124 248 496 (!>! 497 = 165*3) attend the wide 5th !
      f#2 = 93 186C#
      c#3 = F#139 278 (<279 = 93*3)
      g#1 = 52 H104 208 416 (<417 = 139*3)
      eb1 = 39 78 E156 := 52*3
      bb2 = A117 := 39*3
      f1 = 44 88 D176 352 (!>! 351 = 117*3) another wirde 5th !
      c3 = G131 (<132 = 44*3)
      g1 = 49 C'98 C196 392 (<393 = 131*3)

      with the invariant 5ths against change from lenghts to frequency:
      1. 392:393 for G-C & c-g
      2. 278:279 for F#-C# & f#-c#

      completely:
      C392:393~G131:132~D352:351~AEH416:417~F#278:279~C#G#496:495~D#B440:441~F-C

      c392:393~gd440:441~ae496:495~bf#278:279~c#416:417~g#eb-bb352:351~f131:132c

      !reverseSeptenarius.scl
      !
      W's monochord-lengths backwards in reverse direction as frequencies
      !
      139/131 ! c#3/c3
      147/131 ! d3 /c3
      156/131 ! eb3/c3
      165/131 ! e3 /c3 =(5/4)*(132/131)
      176/131 ! f3/ c3 =(4/3)*(132/131) some scholars prefer 175 instead 176
      186/131 ! f#3/c3
      196/131 ! g3 /c3 = (3/2)*(392/393)
      208/131 ! g#3/c3
      220/131 ! a3 /c3 in order to meet Scheibler's absolute preference
      234/131 ! bb3/c3
      246/131 ! b3 /c3
      2/1
      !


      get rid of the 2 wide-5ths ib that
      in order to obtain a real 'well-temerature' "Wohl-Temperatur"
      by the modified chain of 5ths:

      C 392:393 G D 440:441 A E 494:495 B 740:741 F# C# 1664:1665 G#
      Ab Eb Bb 350:351 F 524:525 C

      !rev_Sept_Well_mod.scl
      !
      without the wide 5ths in Werckmeister's original ratios
      12
      !
      555/524 ! c#5/c5
      147/131 ! d3 /c3
      156/131 ! eb3/c3
      165/131 ! e3 /c3 =(5/4)*(132/131)
      175/131 ! f3/ c3 =(4/3)*(525/524) some scholars prefer 175 instead 176
      185/131 ! f#3/c3
      196/131 ! g3 /c3 = (3/2)*(392/393)
      208/131 ! g#3/c3
      220/131 ! a3 /c3 Scheibler's fork a4=440cps
      234/131 ! bb3/c3
      247/131 ! b3 /c3
      2/1
      !

      but that sounds
      -at least in my ears-
      all to much alike 12-EDO.

      > There is one small revision that might appeal to me, and I would be
      > very curious as to your opinion on what I might propose.
      >
      > Looking at the sizes of fifths, I noticed that at D-A there is a fifth
      > considerably narrower than any other, at only about 694.1 cents, or
      > almost 8 cents smaller than pure, with a ratio of 884/592. This is a
      > bit more than 1/3 Pythagorean comma of tempering, and I wondered if
      > the step A (Scala step 9) might be raised slightly to make this fifth
      > a bit closer to pure without seriously compromising any other
      > interval.
      >
      > In this proposed variation on your tuning, A is raised to 885/529 with
      > respect to C, or 885/592 with respect to D, forming a fifth D-A which
      > is narrow by almost exactly 1/4 Pythagorean comma -- indeed, the
      > accuracy of 885/592 in approximating this common degree of temperament
      > is amazing! The main complication I would see, if you like the result,
      > is that your pitch standard would then become a4 = 442.5.

      fully agreed!
      that's an good idea,
      as already mentioned in:
      http://launch.groups.yahoo.com/group/tuning/message/76113
      "!well_Violin2Piano.scl
      ...
      885/523 ! A = 442.5Hz*2 absolute a4
      "
      >
      hence i do accept yours improvement as welcome:
      > ! ProposedVariationOnSparschuh442wideFrench5th.scl
      > !
      > Proposed revision: step 9 (A) at 885/529, 890.9 cents -- Margo Schulter
      ...
      > 885/529
      ...
      meanwhile i do consider
      264.5C4 as to harsh for the middle-C4,
      a better choice -in my ears, at least on my piano- would be:
      264.3


      Perhaps you also like an further "septenarian" refinement too:
      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) through all 8 Bs on the piano-keys
      F#; 93F#2 := B0*3
      C#; 279C#4 := F#2*3
      G#; 209G#3 418G#4 836G#5 (< 887 = C#4*3)
      Eb; 627Eb5 := G#3*3
      Bb; 235Bb3 470Bb4 940Bb5 1880Bb6 (< 1881 = Eb5*3)
      F; (C4:3=88.1 C5:3=176.2 C6:3=352.4 <) 352.5F4 705F5 := Bb3*3
      C; (G1:3=33 ... G4:3=264 <) 264.3C4
      G; 99G2 = 33*3

      Chromatically on the keys in frequencies as absolute-pitchs:

      264.3_C4
      279___C#4
      296___D4
      313.5_Eb4
      330.75E4
      352.5_F4
      372___F#4
      396___G4
      418___G#4
      442.5_A4
      470___Bb4
      528.6_C5

      !sparschuh885A5.scl
      !
      c880:881g296:297d295:296a3968:3969bf#c#836:837g#eb1880:1881bbf3524:3525c
      !
      12
      !
      2790/2463
      2960/2463
      3135/2463
      6615/4926 ! (5:4)(882:881)
      3525/2463 ! (4:3)(3525:3524)
      3720/2463
      3960/2463 ! (3:2)(880:881)
      4180/2463
      4425/2463
      4700/2463
      4960/2463
      2/1
      !

      What do you think about that now?

      Yours Sincerely
      A.S.
    • 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:

        http://launch.groups.yahoo.com/group/tuning/message/62904

        http://launch.groups.yahoo.com/group/tuning/message/62039

        http://launch.groups.yahoo.com/group/tuning/message/56664

        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:

        http://en.wikipedia.org/wiki/Kudsi_Erguner

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

        http://www.neyzenim.com/neyzenler.htm

        Oz.


        http://launch.groups.yahoo.com/group/tuning/message/36343

        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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