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Gainable accuray in high precision-tuning was:Re: epimoric bisection 81:80

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  • Andreas Sparschuh
    ... Hi Brad, simply short all nominators over denominators by the factor 10 in order to meet scala the convention of integral fractions: !Sparschuh885A5.scl
    Message 1 of 69 , Jul 3, 2008
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      --- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
      >

      Hi Brad,

      simply short all nominators over denominators by the factor 10
      in order to meet scala the convention of integral fractions:

      !Sparschuh885A5.scl
      SC=80:81 inbetween F~C~G~D~A~E & schisma in E~B_F#_C#_G#~Eb~Bb~F
      12
      2790/2643 ! 279.0C#4 / 264.3C4
      2960/2643 ! 296.0D_4 / 264.3C4
      6275/4926 ! 627.5Eb4 / 528.6C5
      6615/4926 ! 661.5E_4 / 264.3C4 = (5:4)(882:881) ~+1.964 Cents sharp
      3524/2643 ! 352.4F_4 / 264.3C4 = (4:3)(882:881) ~+1.964 Cents sharp
      3720/2643 ! 372.0F#4 / 264.3C4
      3960/2643 ! 396.0G_4 / 264.3C4 = (3:2)(880:881) ~-1.966 Cents flat
      4185/2643 ! 418.5G#4 / 264.3C4
      4425/2643 ! 442.5A_4 / 264.3C4 440Hz(+2.5Hz = 150 MetronomeBeats/min)
      4705/2643 ! 470.5Bb4 / 264.3C4
      4960/2643 ! 496.0B_4 / 264.3C4
      2/1
      !

      That results in epimoric beating lowered 5ths, all amounts given
      in rational, ~Cents~ & ~TUs~ for the Syntonic-comma in F~C~G~D~A~E

      F 881:882 C 880:881 G 296:297 D 295:296 A 294:295 E = product 80:81
      F ~-1.963 C ~-1.966 G ~-5.839 D ~-5.859 A ~-5.879 E = sum ~-21.506C
      F ~-60.28 C ~-60.34 G ~-179.2 D ~-179.8 A ~-180.4 E = sum ~660.04TUs

      and the schisma = 2^15/5/3^8 = 32768:32805 ~-1.954Cents ~-59.96TUs
      inbetween E~B_F#_C#_G#~Eb~Bb~F

      E 3968:3969 B_F#_C#_G# 2510:2511 Eb 3764:3765 Bb 4704:4705 F
      E ~-0.43624 B_F#_C#_G# ~-0.68959 Eb ~-0.45988 Bb ~-0.36799 F
      E ~-13.3886 B_F#_C#_G# ~-21.1641 Eb ~-14.1141 Bb ~-11.2940 F

      >
      > With only an A=440 tuning fork in one hand, a harpsichord tuning lever
      > in the other hand, and absolutely NO electronic devices of any kind:
      > how exactly should one proceed to get all twelve of your notes
      > correctly tuned onto a harpsichord, using this scheme?

      The wanted precision of accessible accuracy
      depends on several factors:

      1. Quality of tuneability for the instrument alike
      deviations due to inhamonicty of the strings?

      2. Counting beats barely by own heart-pulse of
      under aid of an clock or even better an adjustable Metronome?

      3. Tuner is rested/relaxed or fatigued/exhausted or
      may be even incompetent?


      > And with no
      > way of measuring integer frequencies, either, or knowing when they've
      > been achieved precisely?

      In yours personal "squiggle" impreciseness
      of barely PC^(1/12)= 60TUs
      probable the following rouding would be sufficient
      for yours personal taste?:

      F -1 C -1 G -3 D -3 A -3 E for approximation of about an ~SC
      F -60 C -60 G -180 D -180 A -180 E for exaclty 660TUs~=~SC
      and
      E -0.25 B_F#_C#_G# -0.25 Eb -0.25 Bb -0.25 F in PC^(1/12) units
      E -~15~ B_F#_C#_G# -~15~ Eb -~15~ Bb -~15~ F with sum=60TUs=~schisma

      >
      > To what precision are errors acceptable? And why?
      That approximation in yours personal style
      -if you would achive 15TUs = PC^(1/48) = ~0.5 Cents
      would deviate maximal even less than 6 TUs = PC^(1/120) ~0.2 Cents.
      >
      > Does one first have
      > to agree with your goal of proportional beating, and your constraint
      > of integer frequencies?
      Never at all, due to the possibilty to translate into
      your's terms within an error of less than ~1/5 Cents.

      > All this stuff just looks like
      > nearly-meaningless tables of numerals to me, sorry;
      No problem.
      Maybe
      How about that "squiggle"-type notation with 4 different grades of
      5ths with the cycle:

      F'C'G'''D'''A'''E.B_F#_C#_G#.Eb.Bb.F

      with extended legend that has additional an dot "." for PC(-1/48)

      ' = PC(-1/12)
      ''' = PC^(-1/4) as in W#3 on the average C'''G'''D'''A_E_B'''F#_..._C
      . = PC^(-1/48) that 1/4 of yours usual unit '
      _ = an JI 5th of exactly 3/2=1.5

      If you don't accept PC^(1/48) = ~schisma^(1/4) as smallest unit
      then try intead that modifiaction
      without any subschismatic refinements:

      F'C'G'''D'''A'''E'B_F#_C#_G#_Eb_Bb_F

      > the only way I
      > know to assess its quality is to see if it agrees with *your own*
      > goals...

      I.m.h.o. ~0.2 Cents on the average in precision will suffice enough.

      > which doesn't tell us one way or another about the usefulness
      > for anything else *but* your own goal of proportional beating (or
      > whatever it is).

      Meanwhile I'm more tolerant in that aspect:
      Never mind if you persist in inprecise tuning-methods
      without counting beats exactly.
      >
      > If I'd somehow take the time and get this temperament set up on my
      > harpsichord,
      Simply try it out!

      > within some acceptable error tolerance but without using
      > any electronic devices:

      Surely with yours ability and daily practice
      in hearing you should achieve at least for:

      F'C'G'''D'''A'''E'B_F#_C#_G#_Eb_Bb_F

      an exactness of
      even less than about PC(-1/24)accuracy
      or equivalent ~1 Cents precision an the average.

      > how would the resulting temperament sound in
      > playing (say) some late Couperin?
      Works fine, due to the pronouced Baroque key-characteristics.

      > What does it do for the music,
      > harmonically and melodically?

      C-major deviates the least from JI.

      > That's the kind of thing I personally
      > care about: a temperament that sounds great in the music, and that
      > can
      > be done entirely by ear in less than 10 minutes without having to
      > calculate (or even refer to) a page of numbers.

      even my modern 3-fold stringed piano with 88keys over 7 octaves
      needs only a few minutes retuning when the weather changes.
      >
      > And, what happens if I'd want to start on A=430 or something else
      Transposing is no problem for scala.

      442.5 / 430 = 177/172 = 35.4/34.4 = ~1.02906977... or ~2.9 %

      (1 200 * ln(430 / 442.5)) / ln(2) = -49.6089545...Cents

      that's about an half of an 12-EDO semitone = 50Cents lower than 442.5.

      Where's the problem there,
      except that for A4=430Hz the string tension becomes to loose in an
      modern standard piano?

      > (maybe not having anything to do with integers!), or on some C?
      > Does
      > it all need to be recalculated?

      Scala does that job quite well.

      > Help out the practical musicians who
      > just want to listen to the sounds of intervallic relationships,

      Please let me know your's opinion
      after you have tryed out some of the above versions.


      I do agree with you, that without:
      > calculating
      the corresponding acustical ratios, there is almost
      >nothing....
      understood in tempering key-instruments in an properly way.

      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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