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Synchronously wohl_temperiert.scl on modern pianos,was Re: harmonic series rwt?

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  • Andreas Sparschuh
    ... that he ... 1. having no fifths intervals wider than 3/2, 2. and no major thirds intervals smaller than 5/4 ... Hi Jaques & all others, Just those 2
    Message 1 of 26 , May 16, 2008
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      --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
      that he
      >...understands absence of harmonic waste in a 12 tones temperament as

      1. > having no fifths intervals wider than 3/2,
      2. > and no major thirds intervals smaller than 5/4

      > Is that right, or can you or someone
      > tell me how we should define it ?

      Hi Jaques & all others,
      Just those 2 conditions define Werckmeister's german term
      "wohl-temperiert" = 'well-tempered'

      http://dict.leo.org/ende?lp=ende&p=wlqAU.&search=wohltemperiert
      http://dict.leo.org/ende?lp=ende&p=wlqAU.&search=wohltemperierte

      as used by J.S.Bach in Werckmeister's sense:
      http://en.wikipedia.org/wiki/Well-Tempered_Clavier

      for example by the following cycle of a dozen 5ths:


      110A_2 220A_3 440HzA_4
      329 E_4 (< 330 = 3*A_2)
      493.5B_4 987B_5 = 3*E_4
      185F#_3 370 F#_4 740F#_5...2960F#_7(<2961=3*B_5)
      277.5C#_4 555C#_5 = 3*F#_3
      104G#_2 208G#_3 416 G#_4 832G#_5 1664G#_6(<1665=3*C#_5)
      156Eb_3 312 Eb_4 = 3*G#_2
      117Bb_2 234Bb_3 468 Bb_4 = 3*Eb_3
      351 F_4 = 3*Bb_2
      (65.7 131.4<)131.5C_3 263middleC_4 526C_5 1052C_6 (<1053 = 3*F_4)
      65.7*3 = 197.1G_3 394.2 G_4
      (441/3=147 294 <) 294.5 D_4 589D_5 (<591.3 = 3*G_3)
      440 A_4 (<441 = 3*147)

      !wohltemperiert.scl
      !for J.S.Bach's WTC invented by Andreas Sparschuh in 2008
      12
      !
      C-major beats C:E:G = 4: 5*(1316/1315): 6*(1314/1315) synchronously
      !
      555/526 ! C# 277.5/263
      589/526 ! D 294.5/263
      312/263 ! Eb
      329/263 ! E (5/4)*(1316/1315) ~1.316...Cents sharper than JI 5:4
      351/263 ! F
      370/263 ! F#
      1971/1315 ! G 394.2/263 (3/2)*(1314/1315) ~-1.317...C lower than 3:2
      416/263 ! G#
      440/263 ! A
      468/263 ! Bb
      987/526 ! B 493.5/263
      2/1
      !

      that's imho my preferred rational temperament,
      that i personally do reccomend for playing in modern HIP
      http://en.wikipedia.org/wiki/Historically_informed_performance
      of J.S.Bach's music in all 24keys
      on modern keyboard instruments with
      http://en.wikipedia.org/wiki/A440
      as choice of absolute pitch.

      It replaces all my older proposals.

      Quests:
      1. Who in that group dares to try out that one on his/hers own piano?
      2. Has anybody suggestions for better ratios in order to improve it?

      asks sincerely
      A.S.
    • robert thomas martin
      ... as ... 3:2 ... piano? ... From Robert. Try tuning-math message 17251 for another angle.
      Message 2 of 26 , May 16, 2008
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        --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
        wrote:
        >
        > --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
        > that he
        > >...understands absence of harmonic waste in a 12 tones temperament
        as
        >
        > 1. > having no fifths intervals wider than 3/2,
        > 2. > and no major thirds intervals smaller than 5/4
        >
        > > Is that right, or can you or someone
        > > tell me how we should define it ?
        >
        > Hi Jaques & all others,
        > Just those 2 conditions define Werckmeister's german term
        > "wohl-temperiert" = 'well-tempered'
        >
        > http://dict.leo.org/ende?lp=ende&p=wlqAU.&search=wohltemperiert
        > http://dict.leo.org/ende?lp=ende&p=wlqAU.&search=wohltemperierte
        >
        > as used by J.S.Bach in Werckmeister's sense:
        > http://en.wikipedia.org/wiki/Well-Tempered_Clavier
        >
        > for example by the following cycle of a dozen 5ths:
        >
        >
        > 110A_2 220A_3 440HzA_4
        > 329 E_4 (< 330 = 3*A_2)
        > 493.5B_4 987B_5 = 3*E_4
        > 185F#_3 370 F#_4 740F#_5...2960F#_7(<2961=3*B_5)
        > 277.5C#_4 555C#_5 = 3*F#_3
        > 104G#_2 208G#_3 416 G#_4 832G#_5 1664G#_6(<1665=3*C#_5)
        > 156Eb_3 312 Eb_4 = 3*G#_2
        > 117Bb_2 234Bb_3 468 Bb_4 = 3*Eb_3
        > 351 F_4 = 3*Bb_2
        > (65.7 131.4<)131.5C_3 263middleC_4 526C_5 1052C_6 (<1053 = 3*F_4)
        > 65.7*3 = 197.1G_3 394.2 G_4
        > (441/3=147 294 <) 294.5 D_4 589D_5 (<591.3 = 3*G_3)
        > 440 A_4 (<441 = 3*147)
        >
        > !wohltemperiert.scl
        > !for J.S.Bach's WTC invented by Andreas Sparschuh in 2008
        > 12
        > !
        > C-major beats C:E:G = 4: 5*(1316/1315): 6*(1314/1315) synchronously
        > !
        > 555/526 ! C# 277.5/263
        > 589/526 ! D 294.5/263
        > 312/263 ! Eb
        > 329/263 ! E (5/4)*(1316/1315) ~1.316...Cents sharper than JI 5:4
        > 351/263 ! F
        > 370/263 ! F#
        > 1971/1315 ! G 394.2/263 (3/2)*(1314/1315) ~-1.317...C lower than
        3:2
        > 416/263 ! G#
        > 440/263 ! A
        > 468/263 ! Bb
        > 987/526 ! B 493.5/263
        > 2/1
        > !
        >
        > that's imho my preferred rational temperament,
        > that i personally do reccomend for playing in modern HIP
        > http://en.wikipedia.org/wiki/Historically_informed_performance
        > of J.S.Bach's music in all 24keys
        > on modern keyboard instruments with
        > http://en.wikipedia.org/wiki/A440
        > as choice of absolute pitch.
        >
        > It replaces all my older proposals.
        >
        > Quests:
        > 1. Who in that group dares to try out that one on his/hers own
        piano?
        > 2. Has anybody suggestions for better ratios in order to improve it?
        >
        > asks sincerely
        > A.S.
        >
        From Robert. Try tuning-math message 17251 for another angle.
      • Herman Miller
        ... I generally use deviation in place of error in that context. For intervals close to ratios of small integers, the amount of this deviation does seem to
        Message 3 of 26 , May 16, 2008
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          Kalle Aho wrote:

          > Hi Kraig,
          >
          > when I have to talk about *error* of an interval, I cringe because I
          > now think that all intervals have their own character. Maybe
          > 'distance' would be a better word because it's value-neutral.

          I generally use "deviation" in place of "error" in that context. For
          intervals close to ratios of small integers, the amount of this
          deviation does seem to have an effect on the character of the interval.
          "Distance" might also work, but "error" could be misinterpreted.
        • Kalle Aho
          ... Yes, it has an effect on the interval s character but I oppose the simple view that larger deviation always means worse sound even if this is often true.
          Message 4 of 26 , May 17, 2008
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            --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
            >
            > Kalle Aho wrote:
            >
            > > Hi Kraig,
            > >
            > > when I have to talk about *error* of an interval, I cringe because I
            > > now think that all intervals have their own character. Maybe
            > > 'distance' would be a better word because it's value-neutral.
            >
            > I generally use "deviation" in place of "error" in that context. For
            > intervals close to ratios of small integers, the amount of this
            > deviation does seem to have an effect on the character of the interval.

            Yes, it has an effect on the interval's character but I oppose the
            simple view that larger deviation always means worse sound even if
            this is often true.

            > "Distance" might also work, but "error" could be misinterpreted.

            Yes.
          • Kraig Grady
            It stuck me this is almost the opposite of the Spectralist in the sense that they imitate the harmonic series with somewhat conventional scales . here we have
            Message 5 of 26 , May 22, 2008
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              It stuck me this is almost the opposite of the Spectralist
              in the sense that they imitate the harmonic series with somewhat
              conventional scales .
              here we have the harmonic series imitating just such a scale :)


              /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
              _'''''''_ ^North/Western Hemisphere:
              North American Embassy of Anaphoria Island <http://anaphoria.com/>

              _'''''''_ ^South/Eastern Hemisphere:
              Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

              ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',




              Kalle Aho wrote:
              >
              > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Carl
              > Lumma" <carl@...> wrote:
              > >
              > > > > Kalle, if you've got your ears on, can you tell us the
              > > > > lowest subset of harmonics without harmonic waste when
              > > > > interpreted as a WT *that has a mode in which all the
              > > > > denominators are base-2 numbers*?
              > > > >
              > > > > I assume it may be possible to do this with 128-256, as
              > > > > your unrestricted result was done with 116-232.
              > > > > Failing that, 256-512 must have enough resources.
              > > > >
              > > > > Thanks!
              > > >
              > > > Hi Carl,
              > > >
              > > > actually there are four of them!
              > > >
              > > > 128:136:144:152:162:171:182:192:203:216:228:243:256
              > > > 128:136:144:152:162:171:182:192:204:216:228:243:256
              > > > 128:136:144:153:162:171:182:192:204:216:228:243:256
              > > > 128:136:144:153:162:171:182:192:204:216:229:243:256
              > >
              > > Thanks!
              > >
              > > > Here are Scala files for these:
              > >
              > > D'oh! Howabout with the constraint that all 3rds
              > > be < 405cents? (Your original scale happened to
              > > meet this.)
              >
              > Well, there are 25 of those in 256-512, the best (largest major third
              > is 402.844 cents) is this:
              >
              > ! ForCarl5.scl
              > !
              >
              > 12
              > !
              > 271/256
              > 287/256
              > 19/16
              > 161/128
              > 171/128
              > 181/128
              > 383/256
              > 203/128
              > 215/128
              > 57/32
              > 483/256
              > 2/1
              >
              >
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