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    <p>Hi again,</p>
    <p>I failed to say this... a benefit of using a PI-loop is that the
      DC-component out of the ring-modulator is servo-steered to zero,
      so no DC-blocking would be needed for the audio output part of the
      loop once locked.</p>
    <p>So, if one has a ring-mod one wants to dedicate to this, fairly
      simple mods can be done. Just some care that not large DC-shifts
      is not DC-blocked away. Unlocked the offset should be fairly close
      to zero.<br>
    </p>
    <p>Cheers,<br>
      Magnus<br>
    </p>
    <div class="moz-cite-prefix">On 2020-02-13 16:58, Magnus Danielson
      wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:9309283a-278e-df24-6a3e-b5cd2129f4dd@rubidium.se">
      <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
      <p>Hi,<br>
      </p>
      <p>As you where doing BBD, and care about BBD output noise, why
        not try to feed it a 1 kHz or better yet 3 kHz tone from a ...
        you know... synthesizer. Then use another oscillator as
        measurement lock-up oscillator, this one you want a DC-coupled
        linear FM input if you can get it, but otherwise you have to go
        with the normal CV input.</p>
      <p>As phase-detector you can use a ring-modulator, but here you
        want a DC output of the signal, which most does not do as they
        have DC-blockers. You could use an XOR-gate if you have
        square-waves into it.</p>
      <p>Out of the phase-detector, you have two signal paths, one is
        the loop filter for the PLL. Here I prefer to build a PI-loop,
        which is essentially an integrator. The minimum build-up is an
        op-amp with a input resistor and then a capacitor and resistor
        in series in the negative feedback path. The minimum setup is
        however a bit difficult to dimension things correctly on, as it
        get good result when all the parameters is fixed so it's own
        values can be fixed. A gain-pot may be needed to scale loop-gain
        properly, that helps part of the PLL design problem. The second
        path from the phase-detector should have a fixed gain stage
        typically. So, a TL-072 with a handful of passives and a
        XOR-gate of your choosing. Maybe another op-amp pair to square
        signals up if needed.</p>
      <p>Then, finally, a spectrum analyzer over the audio frequency
        range. Nothing exotic, but good dynamics come into use. I would
        maybe use a DN60 because it's lying around, but even the phone
        with an app would work. If your oscilloscope can pull a FFT off,
        fine.<br>
      </p>
      <p>If one can insert a signal from an offset oscillator (for a 1
        kHz carrier signal, consider a 1,1 kHz tone to measure to
        produce the 100 Hz offset) with a known relationship in
        amplitude relative the carrier signal, say -30 dB, then one can
        calibrate the scale for improved knowledge of noise levels, as
        phase-noise is reported in dBc/sqrt(Hz), decibels relative
        carrier, and corrected with the filter bandwidth.</p>
      <p>It's not that this is very exotic things, it's just that since
        you do not use these things like this, they may not be very well
        prepared for it, so it's more that which causes you problems.
        Some oscillators have PLL capability, I have a pair of JLC Moog
        921 clones lying around, which has the PLL in them so it becomes
        more the effort of pulling the right signal.</p>
      <p>As you getto this, the cleanness of the oscillators etc. may
        become a problem, but if you clearly can hear problems, then
        maybe you have good enough stuff.</p>
      <p>Phase-noise measurements like these isn't all that hard, and if
        you work a little more with it, you will find slopes of noise as
        well as spikes. The slopes is due to the white and flicker
        noise, and as shaped by the resonator bandwidth, as modeled by
        Dr. David Leeson in an article in Feb 1966. That and his 2016 50
        year lookback is good reads, while just a scratch on the
        surface. For long-term stability we use the time-stability
        measure called Allan Deviation, of Dr. David Allan, as published
        in the same Feb 1966 special issue. For Allan deviation, read
        the Wikipedia article on Allan Variance, which I wrote.</p>
      <p>One can home-brew quite sensitive phase-noise measurement tools
        for very low cost, even for higher frequencies. I have a couple
        of more extensive rigs that I use to measure high stability
        quartz oscillators and atomic clocks. My basement lab grew
        slightly out of hand from measure and perfect the ASM-1 VCOs,
        which is where I started.<br>
      </p>
      <p>Cheers,<br>
        Magnus<br>
      </p>
      <div class="moz-cite-prefix">On 2020-02-13 15:21, Tom Wiltshire
        wrote:<br>
      </div>
      <blockquote type="cite"
        cite="mid:5695A29F-585E-46DF-9200-D31806E74704@electricdruid.net">
        <meta http-equiv="Content-Type" content="text/html;
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        Thanks Magnus.
        <div class=""><br class="">
        </div>
        <div class="">What’s the “ghetto” way of doing such a test?!</div>
        <div class=""><br class="">
        </div>
        <div class="">I don’t have either a reference source of
          frequencies that high (25-600KHz) or a spectrum analyser. The
          scope does an FFT, but that’s as close as it gets. I don’t
          even have a very accurate way to measure frequencies, much
          less while they’re jumping about.</div>
        <div class=""><br class="">
        </div>
        <div class="">Tom</div>
        <div class=""><br class="">
          <div class="">
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                word-spacing: 0px; -webkit-text-stroke-width: 0px;">==================<br
                  class="">
                       Electric Druid<br class="">
                Synth & Stompbox DIY<br class="">
                ==================</div>
            </div>
          </div>
          <div><br class="">
            <blockquote type="cite" class="">
              <div class="">On 13 Feb 2020, at 14:15, Magnus Danielson
                <<a href="mailto:magnus@rubidium.se" class=""
                  moz-do-not-send="true">magnus@rubidium.se</a>>
                wrote:</div>
              <br class="Apple-interchange-newline">
              <div class="">
                <meta http-equiv="Content-Type" content="text/html;
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                <div class="">
                  <p class="">Hi,</p>
                  <p class="">The classical wow and flutter test is to
                    use a reference signal and then measure side-band
                    noise.</p>
                  <p class="">One way is to phase-lock an oscillator, as
                    the phase-lock locks up, the lock forces the output
                    of the phase-detector to produce side-band. Measure
                    the noise out of the phase-detector, preferably with
                    spectrum analyzer. With a separate oscillator being
                    inserted offset from the carrier, with known
                    amplitude and offset relative the carrier, the scale
                    can be calibrated.<br class="">
                  </p>
                  <p class="">Report noise amplitude in reference to the
                    amplitude of the carrier wave. This phase-noise
                    measurement is essentially what is described in IEEE
                    Std 1139.</p>
                  <p class="">Cheers,<br class="">
                    Magnus<br class="">
                  </p>
                  <div class="moz-cite-prefix">On 2020-02-11 13:06, Tom
                    Wiltshire wrote:<br class="">
                  </div>
                  <blockquote type="cite"
                    cite="mid:5123C853-5DF1-4B57-84D4-664DCA74BD1D@electricdruid.net"
                    class="">
                    <meta http-equiv="Content-Type" content="text/html;
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                    Hi All,
                    <div class=""><br class="">
                    </div>
                    <div class="">I thought I’d give you an update on
                      this.</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">I’ve been able implement some of the
                      ideas you all provided, although it wasn’t
                      straightforward (is it ever?).</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">Moving to the new chip allowed me to
                      double the NCO clock to 32MHz (idea 1). I also
                      doubled the frequency increment to use more
                      resolution in the NCO (idea2). This means that the
                      NCO output is four times higher than I need it, so
                      I then have to implement /4 somehow (idea 3).
                      Luckily there are two “Configurable Logic Cells”
                      on the chip that can be set up as divide-by-two
                      flip-flops. Unfortunately they don’t accept the
                      output from the NCO as an input, so I had to route
                      the NCO via another module (the “Digital Signal
                      Modulator”) set-up to pass the NCO straight
                      through. The final divided NCO output goes to the
                      “Complementary Waveform Generator” module that
                      makes the final biphase-output-with-deadband that
                      I need.</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">In summary, the final “BBD Clock” uses
                      five different hardware modules on the 16F18313
                      chip! It looks like this:</div>
                    <div class=""> </div>
                    <div class="">NCO -> DSM -> CLC1 -> CLC2
                      -> CWG</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">Ok, so in theory I should see some
                      improvement in performance. Now I come to my new
                      question! -</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">How can I evaluate the performance of
                      this version against the old version?</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">Currently the only real metric I have
                      is “does it sound noisy?” when it’s put in the
                      final circuit. This isn’t great since the noise
                      level depends very heavily on the exact
                      relationship between the frequency increment and
                      the NCO length, so it can vary markedly for quite
                      small changes.</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">Thanks,</div>
                    <div class="">Tom</div>
                    <div class=""><br class="">
                      <div class="">
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                              class="">
                                   Electric Druid<br class="">
                            Synth & Stompbox DIY<br class="">
                            ==================</div>
                        </div>
                      </div>
                      <div class=""><br class="">
                        <blockquote type="cite" class="">
                          <div class="">On 31 Jan 2020, at 12:07, Tom
                            Wiltshire <<a
                              href="mailto:tom@electricdruid.net"
                              class="" moz-do-not-send="true">tom@electricdruid.net</a>>
                            wrote:</div>
                          <br class="Apple-interchange-newline">
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                            <div style="word-wrap: break-word;
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                              after-white-space;" class="">Ok, so the
                              advice would be:
                              <div class=""><br class="">
                              </div>
                              <div class="">1) Use the highest NCO clock
                                I can to minimise jitter</div>
                              <div class="">2) Increase the frequency
                                increments as much as possible to use as
                                much of the available increment
                                resolution as I can</div>
                              <div class="">3) Divide the resulting
                                frequency down if it’s too much high</div>
                              <div class="">4) Add a little bit of
                                dither to break up audible cycles/tones</div>
                              <div class="">5) Sample the LFO at as high
                                a frequency as possible</div>
                              <div class=""><br class="">
                              </div>
                              <div class="">Is that a fair summary?
                                Anything I’ve missed? (Noise shaping the
                                dither, I suppose)</div>
                              <div class=""><br class="">
                              </div>
                              <div class="">For (1) I can move the clock
                                from 16MHz to 32MHz, so there’s a small
                                improvement.</div>
                              <div class="">For (2) we can increase the
                                frequency increment, assuming I can work
                                out a way to get the chip to provide the
                                division for (3). If I could run the NCO
                                at (say) x8 of the frequency I need,
                                that might offer some real benefit.</div>
                              <div class="">The dither (4) doesn’t
                                really depend on anything else, so that
                                should be do-able.</div>
                              <div class="">The LFO sample frequency
                                should also be able to increase since
                                the whole chip is running twice as fast
                                as the previous generation (32 vs 16MHz
                                again). So everything else being equal,
                                I might be able to up the LFO sample
                                rate to 50KHz or so. However, that seems
                                a bit crazy (audio-rate sampling for an
                                LFO with a max of 20Hz) and instead I
                                might do better to add some
                                interpolation of the frequency increment
                                at the end of each cycle. E.g. We’re
                                aiming for an increment of X, and we’ve
                                got an increment of Y, so next cycle
                                uses X+x to get a bit closer. The
                                difficulty there is that we need to know
                                how many NCO cycles there will be before
                                our next LFO sample, and that sounds
                                horribly like division! So maybe just
                                whacking the LFO sample rate up is in
                                fact the best you can do for that after
                                all.</div>
                              <div class=""><br class="">
                              </div>
                              <div class="">Thanks,</div>
                              <div class="">Tom</div>
                              <div class=""><br class="">
                                <div class="">
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                                        class="">
                                             Electric Druid<br class="">
                                      Synth & Stompbox DIY<br
                                        class="">
                                      ==================</div>
                                  </div>
                                </div>
                                <div class=""><br class="">
                                  <blockquote type="cite" class="">
                                    <div class="">On 28 Jan 2020, at
                                      13:07, René Schmitz <<a
                                        href="mailto:synth@schmitzbits.de"
                                        class="" moz-do-not-send="true">synth@schmitzbits.de</a>>
                                      wrote:</div>
                                    <br
                                      class="Apple-interchange-newline">
                                    <div class=""><span
                                        style="caret-color: rgb(0, 0,
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                                        !important;" class="">Hi Richie,</span><br
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                                      <br style="caret-color: rgb(0, 0,
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                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
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                                        normal; font-weight: normal;
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                                        white-space: normal;
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                                        !important;" class="">On
                                        28.01.2020 13:23,<span
                                          class="Apple-converted-space"> </span></span><a
href="mailto:rburnett@richieburnett.co.uk" style="font-family:
                                        Helvetica; font-size: 12px;
                                        font-style: normal;
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                                        class="" moz-do-not-send="true">rburnett@richieburnett.co.uk</a><span
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
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                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class=""><span
                                          class="Apple-converted-space"> </span>wrote:</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
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                                        normal; font-variant-caps:
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                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>>
                                        What I don’t understand though
                                        is how this helps. Increasing
                                        the</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
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                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>>
                                        output frequency is going to
                                        increase aliasing too, and
                                        dividing it</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>>
                                        down again afterwards doesn’t
                                        seem to remove that to me. How
                                        does</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>>
                                        this work please, René?</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
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                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>></span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>
                                         It's a standard trick. With
                                        higher DDS clock you get smaller</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>
                                        time-errors, and then the divide
                                        down just removes transitions
                                        between</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>
                                        the transitions. Higher
                                        synthesized frequency allows you
                                        to use more</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>
                                        of the upper bits of the DDS, to
                                        achieve more effective bits
                                        useable</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>>
                                        in the DDS.</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">></span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">> Ok,
                                        so this allows you to make
                                        better use of the available DDS
                                        frequency</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">> bit
                                        resolution, by synthesising a
                                        higher output frequency and then</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>
                                        dividing it down.  But it
                                        doesn't do anything to help with</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">>
                                        jitter/aliasing at the top end.</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <br style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">Here are
                                        your original points:</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">1)
                                        Resampling of the LFO output by
                                        the NCO reset</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">2)
                                        Frequency stepping caused by the
                                        NCO minimum frequency step</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">3) Jitter
                                        cycles caused by the NCO</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <br style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">Well it
                                        helps updating your NCO more
                                        frequently, because each cycle
                                        is shorter now. I.e. higher
                                        sampling rate of your LFO.</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <br style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">The NCOs
                                        minimum frequency step is
                                        reduced. Because the tuning word
                                        effectively shifts right,
                                        bringing in room for more LSBs.</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <br style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">The cycle
                                        to cycle time variation (aka
                                        jitter) is still 1/f(clock) of
                                        your NCO. Not really an
                                        improvement there by the
                                        division, if you run the NCO at
                                        the same frequency as before.
                                        But if you can run the NCO clock
                                        higher then the variation is
                                        reduced.</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <br style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">Best,</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">René</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <br style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">--</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <a
                                        href="mailto:synth@schmitzbits.de"
                                        style="font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal; orphans:
                                        auto; text-align: start;
                                        text-indent: 0px;
                                        text-transform: none;
                                        white-space: normal; widows:
                                        auto; word-spacing: 0px;
                                        -webkit-text-size-adjust: auto;
                                        -webkit-text-stroke-width: 0px;"
                                        class="" moz-do-not-send="true">synth@schmitzbits.de</a><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
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                                        letter-spacing: normal;
                                        text-align: start; text-indent:
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                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <a href="http://schmitzbits.de/"
                                        style="font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal; orphans:
                                        auto; text-align: start;
                                        text-indent: 0px;
                                        text-transform: none;
                                        white-space: normal; widows:
                                        auto; word-spacing: 0px;
                                        -webkit-text-size-adjust: auto;
                                        -webkit-text-stroke-width: 0px;"
                                        class="" moz-do-not-send="true">http://schmitzbits.de</a><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">_______________________________________________</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <span style="caret-color: rgb(0,
                                        0, 0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none; float:
                                        none; display: inline
                                        !important;" class="">Synth-diy
                                        mailing list</span><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
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                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <a
                                        href="mailto:Synth-diy@synth-diy.org"
                                        style="font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal; orphans:
                                        auto; text-align: start;
                                        text-indent: 0px;
                                        text-transform: none;
                                        white-space: normal; widows:
                                        auto; word-spacing: 0px;
                                        -webkit-text-size-adjust: auto;
                                        -webkit-text-stroke-width: 0px;"
                                        class="" moz-do-not-send="true">Synth-diy@synth-diy.org</a><br
                                        style="caret-color: rgb(0, 0,
                                        0); font-family: Helvetica;
                                        font-size: 12px; font-style:
                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal;
                                        text-align: start; text-indent:
                                        0px; text-transform: none;
                                        white-space: normal;
                                        word-spacing: 0px;
                                        -webkit-text-stroke-width: 0px;
                                        text-decoration: none;" class="">
                                      <a
                                        href="http://synth-diy.org/mailman/listinfo/synth-diy"
                                        style="font-family: Helvetica;
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                                        normal; font-variant-caps:
                                        normal; font-weight: normal;
                                        letter-spacing: normal; orphans:
                                        auto; text-align: start;
                                        text-indent: 0px;
                                        text-transform: none;
                                        white-space: normal; widows:
                                        auto; word-spacing: 0px;
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                                        class="" moz-do-not-send="true">http://synth-diy.org/mailman/listinfo/synth-diy</a></div>
                                  </blockquote>
                                </div>
                                <br class="">
                              </div>
                            </div>
_______________________________________________<br class="">
                            Synth-diy mailing list<br class="">
                            <a href="mailto:Synth-diy@synth-diy.org"
                              class="" moz-do-not-send="true">Synth-diy@synth-diy.org</a><br
                              class="">
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                              moz-do-not-send="true">http://synth-diy.org/mailman/listinfo/synth-diy</a><br
                              class="">
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                    <pre class="moz-quote-pre" wrap="">_______________________________________________
Synth-diy mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Synth-diy@synth-diy.org" moz-do-not-send="true">Synth-diy@synth-diy.org</a>
<a class="moz-txt-link-freetext" href="http://synth-diy.org/mailman/listinfo/synth-diy" moz-do-not-send="true">http://synth-diy.org/mailman/listinfo/synth-diy</a>
</pre>
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                _______________________________________________<br
                  class="">
                Synth-diy mailing list<br class="">
                <a href="mailto:Synth-diy@synth-diy.org" class=""
                  moz-do-not-send="true">Synth-diy@synth-diy.org</a><br
                  class="">
                <a class="moz-txt-link-freetext"
                  href="http://synth-diy.org/mailman/listinfo/synth-diy"
                  moz-do-not-send="true">http://synth-diy.org/mailman/listinfo/synth-diy</a><br
                  class="">
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      <br>
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      <pre class="moz-quote-pre" wrap="">_______________________________________________
Synth-diy mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Synth-diy@synth-diy.org">Synth-diy@synth-diy.org</a>
<a class="moz-txt-link-freetext" href="http://synth-diy.org/mailman/listinfo/synth-diy">http://synth-diy.org/mailman/listinfo/synth-diy</a>
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