Andrew: This whole thread has been fascinating to me. Sorry I have not had the time to participate earlier.
Since I created the spreadsheet, one might logically ask which fret placement system I use. The answer is, none of the above. I have set my frets empirically, according to what sounds good to me. I just measured my 55 cm 7-course, the instrument I play most frequently, and got the following numbers (nearest half mm), with indications in parentheses as to which historical temperament most closely matches that value: 1st, 2.85 cm (Kepler tastino) 2nd, 5.75 (Aron meantone) 3rd, 8.7 (Equal temperament!) 4th, 10.95 (Aron meantone/both Mersenne) 5th, 13.7 (both Mersenne/Werckmeister) 6th, 15.85 (Silbermann 1/6th comma) 7th, 18.1 (Aron meantone) 8th 20.05 (Silbermann 1/6th comma) Keep in mind that the fret placement interacts strongly with how you set the piteh intervals between the strings in determining the frequency generated by any given string/fret combination, so that you cannot just tune each string off an equal-tempered electronic box and expect any historical temperament to sound good. For example, I take a reference pitch for the 6th course and tune the 4th course/2nd fret to an exact octave above that, so the 2nd fret placement determines the 6th/4th course interval. I then tune the 2nd course 3rd fret from the open 4th course (maybe not quite so exactly), so the 6th/2nd course interval is determined by the placement of both the 2nd and 3rd frets. I am kind of out of time, but I will try to continue this evening. Daniel On Wed, 21 May 2008 10:08:58 +0100 Andrew Gibbs <[EMAIL PROTECTED]> writes: > Thanks Sean - that is helpful. > > I've yet to experiment with tastini. Apart from ET, the only other > > fret positioning system I use is Gerle's (as given in the handy > Excel > sheet on the American Lute Society web site). I have to say I'm not > > sure exactly what this is - some kind of mean-tone other than > quarter- > comma? or an irregular system like the much later Mersenne and > Werckmeister 'well temperaments'? > > Andrew > > > On 13 May 2008, at 17:46, Sean Smith wrote: > > > > > Dear Andrew, > > > > Yes, theoretically. But meantone's saving grace on the ren lute is > > > that the "keys" of G, C, and their minors use much of the same > > keyboard so you don't really have to change any fret positions > > (mostly white keys on the piano w/ a few Bb's and Cb's). So you're > > > essentially safe in 85% of the music --w/ a few exceptions of > course. > > > > But. When you move to a key in A or Amin, E and Emin, Fmin and > > Bbmin, then things start to get wonky (ie, a lot of flats or > sharps). > > > > Think about that 1st course, 1st fret. If you're playing an Ab on > > > it you're ok for most of the rep. If you need to play a G# that > > means the fret has to be in the other position (closer to the nut: > > > the tastini position). Same goes for 2nd course, 1st fret: if > > you're playing an Eb, that's fine usually but if it needs to be a > > > D# you have to put the fret in the tastini position again. > > > > I know this is a generalized way of looking at only one small > > aspect of meanton on the lute. And I don't mean this at all to be > > > applicable to the baroque lute whatsoever. I hope this helps in > > some small way. > > > > Sean > > > > > > On May 13, 2008, at 8:13 AM, Andrew Gibbs wrote: > > > >> The whole idea of moveable frets allowed relatively easy shifts > > >> between temperaments? e.g. mid-concert between a suite of pieces > > >> in one key and the next suite in another? > >> > >> Andrew > > > -- > > To get on or off this list see list information at > http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html > >
