Dear Anthony,

   Regarding pitching of lutes, we have good historic evidence that this
   is closely related to the tensile strength of gut. Thus whatever the
   pitch one generally tunes the highest course to just under breaking.

   As a rough guide I use the following

                                HIGHEST PITCH OF TREBLE
   String length, cm    @ A392   @ A415    @ A440

   76                               f'            e'            eb'
   72                               f#'          f''             e'
   68                               g'           f#''           f'
   64                               g#'         g'             f#'
   60.5                            a'          g#'            g'
   57                              a#'         a'             g#'
   54                               b'         a#'            a'

   One corollary to this: there's a little evidence that some 17th century
   French solo lute music, especially the earliest, might not pitch
   trebles quite so close to breaking stress, in which case you might
   pitch with the top course one, or even two steps, below those indicated
   above.

   Martyn

   --- On Tue, 23/11/10, Anthony Hind <[email protected]> wrote:

     From: Anthony Hind <[email protected]>
     Subject: [LUTE] Re: tying two strings together (in process of
     changing from 407Hz to 392)?
     To: [email protected]
     Date: Tuesday, 23 November, 2010, 16:06

      Dear All,
            I suppose I should add an explanation for why I need this
   gluing
      technique.
      I have always regretted that my Baroque lute was strung for 415Hz
      rather than for 392 (for which I had actually asked my lute maker,
   but
      he had forgotten this). The main reason for 392 would have been to
      achieve thicker trebles for my 700mm lute, allowing the fingers to
   "dig
      more deeply" into these strings. Diapason 392 could  allow f1:0.46,
      d2:0.54, and A3:0.64 (instead of f1:0.42, d-2:0.50 and A3:0.58 at
      415Hz).
      Historic arguments in favour of this, for the French Baroque lute,
      might be the relatively small diapason of historic French lutes
   (around
      68 according to Martyn, and others), which would imply relatively
   thick
      trebles, unless the diapason pitch was above 415Hz. I rather assume
      this is part of the French aesthetic. What do you think?
      $
      I managed to lower the diapason to 407 (and slightly raise the top
      string tensions); this was the lowest point at which these loaded
      strings would work well (I kept the original tension by
   simulataneously
      raising the tension of the octaves). I believed the original tension
   on
      the basses was 3Kg and on the octaves 2K8 (as indicated by my
      lutemaker). I therefore thought that after lowering to 407 and
   changing
      the octaves to 3K1 for that frequency, I would maintain the
   lutemakers
      suggested tension, but have 2K9 on the basses and 3K1 on the octaves
   (I
      roughly confirmed this with Dan Larson's string calculator).
      However, I did notice that the Venice Octaves were clearly now the
   lead
      voice, which I felt was highly desirable, but which did not quite
   fit
      in with the small difference of tension. Also Martin Shepherd told
   me
      that 2K9 was quite high tension on the basses. However, this was not
   at
      all how they felt, but I just put that down to the flexibility of
   the
      loaded basses.
      $
      Recently, however, I wondered whether I could achieve 392 with
   basses
      close to 2K9 by moving C11 to D10 and D10 to E9, and so forth (in
   other
      words by a simple shift of each string up one). I did fear I might
   get
      a more irregular tension pattern, and also that the tension might be
      too high.
      $
      At this point, I played around with Arto's string calculator, and
      finally understood how it worked (I am a little computer programme
      challenged, and previously gave up when not quite understanding
   which
      field corresponded to what parameter) .
      With Arto's calculator now uderstood, I was  able to set the
   diapason
      explicitly to 407Hz and remove the guess work. I was surprised to
   find
      my basses at 407Hz were actually at a lowish 2K7 (taking account of
      true thickness of the flexible loaded Venices by dividing their
   value
      by 1.07, as explained by Mimmo on the Venice string page).
      Dropping them to diapason 392 (according to "Arto-calc" would bring
      them effectively to around the 2K9, I thought I had originally. I
      believed this would be acceptable, although I could still drop the
      diapason slightly to 380Hz or so to compensate if necessary.
      I would of course have to change most of the other strings, but I
      didn't want to throw out my "expensive" and well worn in loaded
   basses
      (unless they prove already to be a little too old, I have had them 2
      years or more?)
      $
      Anyway I thought I could use these, at least, to check the resulting
      values would work well at 392 with 2K9 tension. I made just one
   check
      by tuning the C11 string D10 at 392Hz, and it seemed acceptable, so
   I
      think I can go ahead with the experiment.
      $
      I then remembered that as my loaded strings had been cut very short
   to
      prevent them rubbing against the decorative panel of the peg-box. I
      might need to "lengthen" some loaded basses and perhaps some Venice
      octaves to reach the peg two above, which is why I have asked for
   your
      knotting advice. Thank you everyone for your help.
      I will of course need at least one new loaded string for C11 to
   carry
      out the experiment.
      $
      I am just wondering whether other loaded gut users have tensions
   around
      my target 2K9, higher or lower? 2K7 did work alright, I must admit.
      Do most of you try to lower your basses by  compensating with higher
      tension octaves (or are they the same, or lower)?
      Do most pure and gimped gut users have basses around 2K5 (Dan
   Larson),
      lower (Satoh), or higher?
      $
      Practical considerations:
              I am aware that pure gut string users will probably consider
      2K9 as a high tension. Dan Larson's standard is 2K5, but this is for
      pure gut, no doubt to compensate for its natural thickness (and
      inharmonicity, or high impedance, at high tension), and also to
   account
      for the relative stiffness of Dan's gimped strings.
      With loaded Venice strings the flexibility, especially for the lower
      basses, is even greater than that of a Venice (as the core is
      relatively thin, the weight determined more by the loading).
      Therefore the impedance at the bridge, even with highish tensions,
      remains low.
      $
      Theoretical consoderations:
      Of course, low tension as a hypothesis of historical stringing is
      mainly advanced to account for the tiny historic bridge holes
      contrasting with the naturally thick pure gut string (and the poor
      harmonicity of such strings when at higher tension); but also to
   relate
      to the relatively thin bass strings represented in the iconography
   (see
      for example the Charles Mouton lute).
      Further arguments for low tension are that most iconography and lute
      marks (see Mimmo Lute news NADEG 94) indicate an RH position near
   the
      bridge, which could indicate an attempt to compensate low tension by
      finding a string point with greater tension (see T. Satoh).
      $
      If one adopts the loaded string hypothesis, however, higher tensions
      can be achieved, while maintaining thin string diameter compatible
   with
      small bridge holes and the iconography; while the RH position could
      indicate an attempt to achieve a point of higher resistance with low
      impedance strings.
      (An alternative high tension theory is put forward by Charles
   Besnainou
      involving a special low impedance spring bass string, more of this
      later. Perhaps, George Stoppani's lang lay ropes might  have a
   similar
      but less low impedance potential).
      Regards
      Anthony
        __________________________________________________________________
      De : Guy Smith <[1][email protected]>
      A : Anthony Hind <[2][email protected]>
      EnvoyA(c) le : Lun 22 novembre 2010, 18h 33min 07s
      Objet : RE: [LUTE] Re: tying two strings of different thickness
      together?
      I agree. The grapevine knot works best when the sizes are roughly
      equal. Fortunately, I've never had to extend a loaded string.
      ____________________________________________________________________
   ___
      From: Anthony Hind [mailto:[3][email protected]]
      Sent: Monday, November 22, 2010 8:58 AM
      To: Guy Smith
      Subject: Re : [LUTE] Re: tying two strings of different thickness
      together?
      Thanks Guy
             One of the two ropes could be a loaded one, and so probably
   not
      supple enough to participate in a double knot. The sheet bend knot
      might be all I can manage, but for other strings I will try your
      suggestion.
      Regards
      Anthony
      PS I see there animated knot examples, that make things fairly
      foolproof.
      ____________________________________________________________________
   ___
      De : Guy Smith <[4][email protected]>
      A : [5][email protected]; Anthony Hind <[6][email protected]>
      EnvoyA(c) le : Lun 22 novembre 2010, 17h 18min 57s
      Objet : RE: [LUTE] Re: tying two strings of different thickness
      together?
      I use a grapevine knot. I learned that in my rock-climbing days as a
      bombproof way to tie into a rope. Probably overkill, but if it can
   hold
      a
      twenty foot leader fall, it should be able to handle a lute
   string:-)
      FWIW, the traditional knot for joining two lengths of fishing line
   is a
      blood knot, which would be another possibility. I tend to avoid
   square
      knots. They can easily be turned into a cats paw knot, which isn't
      secure at
      all.
      Here's a good reference for all sorts of knots:
      [1][7]http://www.layhands.com/Knots/Knots_KnotsIndex.htm
      Guy
      -----Original Message-----
      From: [2][8][email protected]
      [mailto:[3][9][email protected]] On Behalf
      Of Martyn Hodgson
      Sent: Monday, November 22, 2010 8:05 AM
      To: [4][10][email protected]; Anthony Hind
      Subject: [LUTE] Re: tying two strings of different thickness
   together?
          I use a reef knot - but secured with a drop of super glue....
        --- On Mon, 22/11/10, Anthony Hind <[5][11][email protected]>
   wrote:
          From: Anthony Hind <[6][12][email protected]>
          Subject: [LUTE] tying two strings of different thickness
   together?
          To: [7][13][email protected]
          Date: Monday, 22 November, 2010, 15:28
            Dear All
                  I may need to lengthen a string which does not quite
   reach
        the
            peg, but goes well beyond the nut. I would like to attach it
   to a
            slightly thinner short piece of gut to reach the peg in
   question.
      I
            remember that Stephen Gottlieb had done that for several
   strings
      on
        my
            lute; but I can no longer remember the type of knot he used.
   Can
        anyone
            advise me, or tell me of a page where this knot is described.
            Regards
            Anthony
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References

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   3. http://de.mc263.mail.yahoo.com/mc/[email protected]
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   5. http://de.mc263.mail.yahoo.com/mc/[email protected]
   6. http://de.mc263.mail.yahoo.com/mc/[email protected]
   7. http://www.layhands.com/Knots/Knots_KnotsIndex.htm
   8. http://de.mc263.mail.yahoo.com/mc/[email protected]
   9. http://de.mc263.mail.yahoo.com/mc/[email protected]
  10. http://de.mc263.mail.yahoo.com/mc/[email protected]
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  12. http://de.mc263.mail.yahoo.com/mc/[email protected]
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  14. http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
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  16. http://www.layhands.com/Knots/Knots_KnotsIndex.htm
  17. http://de.mc263.mail.yahoo.com/mc/[email protected]
  18. http://de.mc263.mail.yahoo.com/mc/[email protected]
  19. http://de.mc263.mail.yahoo.com/mc/[email protected]
  20. http://de.mc263.mail.yahoo.com/mc/[email protected]
  21. http://de.mc263.mail.yahoo.com/mc/[email protected]
  22. http://de.mc263.mail.yahoo.com/mc/[email protected]
  23. http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
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