The Working Index, that is the product between the frequency of the strings and 
the vibrating string lenght in mt,  can predict when a string start to be 'not 
good enought'.
I am considering here the case of a plain gut string, not the denser versions 
(wound, loaded, gimped etc etc).

Now, generally speacking, we know that, more or less, the 6th course of a 
renaissance lute can be considered the limit for the sound quality and the 
octave is indispensable (and what about the Vihuela? Well  in my opinion it had 
octaves on the 5 and 6 courses because the bass strings were those in use on 
Lutes). The Working Index of the  6th course is around 59 Hz/mt.
 So, if the last bass string of the extended neck exceed the value of  59 Hz/mt 
of Working Index  an octave is necessary like (same working index of the 6th 
course) .
At the modern  'baroque' pitch of 415  the last bass note is a GG of 46.25 Hz 
so:
59/46.25= 1.27 mt
In practice we can say that, generally speacking (generally speacking, ok?) 
when the extended neck start to be less than 1.20-1.30 mt and one uses plain 
gut  start to be necessary  the use of octaves. 
Of course, it is question of taste: some find that a dull sound is still 
welcome, other hate that. If one switch to roped catline gut strings the  
extended neck can be even  a bit shorter than that.
What it is important here is not to have a black or white vision,  we are 
indeed in a sort of grey area were to define if a sound is good or bad is 
matter of taste, which kind of strings and if the proportion of the lutei s the 
right one (the 1st string is working close to the breakage or not?) .  I have  
considered a pactical 'rule of thumb' having seen that  the 6th course had 
octaves  while the 5th is still matter of taste.
Mimmo


-----Messaggio originale-----
Da: lute-...@cs.dartmouth.edu [mailto:lute-...@cs.dartmouth.edu] Per conto di 
sterling price
Inviato: lunedì 11 dicembre 2017 22:27
A: Martin Shepherd <mar...@luteshop.co.uk>; Magnus Andersson 
<magnusl...@gmail.com>; lute@cs.dartmouth.edu
Oggetto: [LUTE] Re: A stringing question for Sellas E. 545

   Question--what is the longest a neck extension can be and still be able
   to have octave strings? I'm making a pegbox for a baroque lute based on
   the 14 course Hoffman pegbox--the original is 115.7cm and I might make
   it a bit longer. I wont bore you with the reason I want it longer--but
   probably 120cm will do it.
   Thanks,
   Sterling
     __________________________________________________________________

   From: Martin Shepherd <mar...@luteshop.co.uk>
   To: Magnus Andersson <magnusl...@gmail.com>; "lute@cs.dartmouth.edu"
   <lute@cs.dartmouth.edu>
   Sent: Monday, December 11, 2017 11:32 AM
   Subject: [LUTE] Re: A stringing question for Sellas E. 545
   Dear Magnus and All,
   A few thoughts:
   I only recently realised that this instrument existed and immediately
   found it puzzling.  Matthew's conjecture that the neck has been
   shortened removes some, but not all, of the puzzle.
   In terms of the string length for the petit jeu of c.90cm, I have
   recent
   experience that (with double strings, as was normal on Italian
   instruments) there begins to be a problem of getting a thin enough
   string for the 3rd course.  I wonder if that tells us something about
   the pitch (nominal or absolute) at which these instruments might have
   been played (I mean theorboes of 90+ cm as opposed to 80+cm).
   If the neck of E545 has been shortened, perhaps that was the point at
   which the basses were made double.  Can anyone enlighten us as to
   whether the bridge is original or has been redrilled?
   The fact that there are only 6 courses on the petit jeu is entirely
   consistent with all known Italian theorboes (and what little is known
   from iconography about French ones, which in this case are surely
   irrelevant anyway).  There is no reason to hypothesise an original
   state
   in which there were more than 6 courses.
   If the neck has been shortened, one might guess an original length for
   the grand jeu of 160-170cm, based on the proportions of extant
   theorboes.  It's hard to imagine double-strung bass courses of this
   length - it's hard enough to imagine at 130cm - so my initial puzzle
   remains.
   Whatever kind of stringing one imagines (even single throughout) there
   is always going to be a big transition from the lowest of the petit jeu
   strings to the first of the long basses - that's just the nature of the
   beast.
   Best wishes,
   Martin
   On 11/12/2017 17:23, Magnus Andersson wrote:
   >    Dear collective wisdom,
   >    I wonder if you might be able to help me with finding
   >    proper strings for a theorbo I ´ve commissioned.
   >    The instrument is a theorbo by Sellas, 1640,
   >    today housed in Paris with the label E. 545.
   >
   [1][1]http://collectionsdumusee.philharmoniedeparis.fr/doc/MUSEE/016179
   9
   >    It ´s quite a spectacular instrument with
   >    six double strings on the fretboard, at 890 mm,
   >    and then 8 double strings for the diapasons, at 1300 mm.
   >    It was probably shortened sometime from its original length
   >    into this present condition.
   >    The problem that arises is when one wants to string the upper
   courses
   >    of the diapasons. Here one needs very thin strings beginning with
   >    0.40-0.42
   >    for the high string of the 7th course Gg, at the string length of
   ca.
   >    1500 mm...
   >    Any ideas would be highly appreciated.
   >    Best wishes,
   >    Magnus Andersson
   >
   >    --
   >
   > References
   >
   >    1.
   [2]http://collectionsdumusee.philharmoniedeparis.fr/doc/MUSEE/0161799
   >
   >
   > To get on or off this list see list information at
   > [3]http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
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References

   1. http://collectionsdumusee.philharmoniedeparis.fr/doc/MUSEE/0161799
   2. http://collectionsdumusee.philharmoniedeparis.fr/doc/MUSEE/0161799
   3. http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
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