Try this- Pp. 29 - 32:

http://dspace.mit.edu/bitstream/handle/1721.1/61924/707340180.pdf?sequence=1

Also of some interest-
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/cavity.html#c4
http://newt.phys.unsw.edu.au/jw/Helmholtz.html

On 11/30/2014 11:55 PM, Martyn Hodgson wrote:
    In his interesting response, I had understood Martin was asking for a
    measured scientific explanation rather than a list of anecdotal (and
    necessarily subjective) observations:    "I invite all you proper
    physicists out there to explain why!".  I'd be interested to read
    anything you have along these lines.
    MH
      __________________________________________________________________

    From: David Tayler <vidan...@sbcglobal.net>
    To: BENJAMIN NARVEY <luthi...@gmail.com>
    Cc: "lute@cs.dartmouth.edu" <lute@cs.dartmouth.edu>
    Sent: Sunday, 30 November 2014, 19:13
    Subject: [LUTE] Re: Single versus triple roses
      This is a very interesting question, and also one that has been
    debated
      in the construction of harpsichords.
      I have a few, very simple observations.
      First of all, and most importantly, Andy is absolutely correct that
    if
      you use a measurement micaI recommend the DPA 4007aand analyze the
      sound coming out of the sound hole (or holes), the sound is vastly
      different. The classic mistake when recording lute, guitar, cello,
      harpsichord, etc, is to place the mic too close to the soundhole,
      because of the extreme difference in the sound. You can also make a
      tube out of paper, roll it up and listen like a coelenterate. Using
    the
      same mic, you will also see that the bridge is the other hot spot.
      Let's take a little detour here and mention that in almost all
      recordings of lute, the frequency pattern is skewed so the left
    channel
      sounds different than the right, and that's because the sound is
      fundamentally different from the rose and the bridge, causing big
      imaging problems (which can be fixed using the lute centering trick,
      subject of another post).
      I can also go on record as saying that if you take a cheap lute and
      remove the rose and put a different one in, it will change the sound.
      Also, the surface area of the actual holes (not the size of the rose
      but the amount of space in the rose) makes a difference. If you add a
      vent hole to the bass, well, it changes the sound. They knew this
    back
      whenever.
      Lastly, the rose and the lute form a strategic sound system. You
    can't
      teak one without tweaking the other. And that's because the size of
    the
      rose affects the resonance and flexibility of the soundboard on the
      rose bar amplification nodeaa sub-hotspot that runs usually through
    the
      middle of the rose, edge to edge but mainly in the middle (the center
      of the rose or rose pattern, in most cases).
      If you make a BIG single rose that has the same open surface area as
    a
      triple, generally speaking it will sound more open, and if too big
    will
      make the lute yawn. But it all depends on the way the sound board
      interacts with the tension resulting from the roseaa really big rose
      bends easier, unless heavily barred (another factor).
      My feeling is that the most open sound comes from a large, single
    rose
      with narrower weaving, but you can achieve almost the same sound with
    a
      triple. And, again speaking very generally, if you want a more open
      sound, have the rose made a bit larger, bearing in mind that the lute
      may yawn. A lute that has a naturally stiff top may benefit from the
      added flexibility of a single rose, because the top of the triple is
      inherently stifferamore soundboard, less rose. Obviously, the shape
    of
      the bowl comes into play as the sound board may be wider at the top
    of
      the rose with a more barge-like bowl. It could also be that players
    in
      the renaissance and baroque preferred a more covered sound. After
    all,
      there are no recorders made nowadays with historical windways, the
      builders just widen them.
      It's up to the builder to find the sweet spot for an instrument, and
      it's up to the player to work with the builder to push the limits.
      dt

    _______________________________________________________________________
      From: BENJAMIN NARVEY <[1]luthi...@gmail.com>
      To: Martin Shepherd <[2]mar...@luteshop.co.uk>
      Cc: "[3]lute@cs.dartmouth.edu" <[4]lute@cs.dartmouth.edu>
      Sent: Sunday, November 30, 2014 4:45 AM
      Subject: [LUTE] Re: Single versus triple roses
        Dear All,
        Thanks so much for all your thoughts into the single/triple rose
        conundrum. It is obviously so hard to know just how this aspect
      changes
        the tonal colours of lutes. It is also very difficult to test just
      how
        this one aspect alters things given that every lute is different,
      even
        if it is the same model from the same maker.
        I will continue to do some intuitive and highly unscientific tests!
        Best wishes,
        Benjamin
        On Sunday, 23 November 2014, Martin Shepherd
      <[1][1][5]mar...@luteshop.co.uk>
        wrote:
          I fear there is a natural tendency to think of the rose as the
    hole
          that "lets the sound out", but I think this is a case where
          intuitive physics lets us down.A  The size of the opening affects
          the natural resonant frequency of the body, with a smaller
    opening
          giving a lower frequency.
          But I invite all you proper physicists out there to explain why!
          A more complex issue, but one which is related in that it also
          involves a mismatch between intuitive physics and the real thing:
          many people seem to believe that the lute soundboard should be
          flexible to "allow it to vibrate", and that the more flexible it
    is
          the better the bass response.A  In fact I think - please
    contradict
          me if I'm wrong - that the frequencies which we are interested in
          are far too high to be aided by a floppy soundboard, which is
    more
          likely to have a damping effect.A  As far as I can see, a
      relatively
          rigid soundboard is going to produce a more sustained sound.A
    The
          most important factor is the mass, which must be kept as small as
          possible so it can be activated by a small input of energy -
    hence
          the rather thin soundboards (supported by many bars to retain
          sufficient rigidity) required by lutes.
          Martin
          On 23/11/2014 16:07, BENJAMIN NARVEY wrote:
          A  A  Dear All,
          A  A  Just wondering if any of you (especially the makers out
      there)
          have
          A  A  thoughts about the projection of single versus triple
    roses.
          A  A  I have had many lutes/theorboes with both single and triple
          roses over
          A  A  the years, and I have always felt that triple roses helped
          make more
          A  A  sound, and that single roses made possibly more focussed,
    but
          more
          A  A  "woody", interior, sounds. Perhaps I am wrong?A
          A  A  All thoughts welcome.
          A  A  All best,
          A  A  And thanks,
          A  A  Benjamin



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