Thanks Daniel - this is really interesting because It's something I'm
struggling with. I've noticed when attempting Gerle's fret positions
that using an electronic tuner to tune the open strings doesn't work
- basically because I don't know what temperament I'm trying to tune
to. The box has a pre-set 1/6 comma setting but the results
definitely don't sound right. So my process is to set the (first 8)
frets exactly as Gerle says, then tune the open strings to suit using
the box to help set a standard pitch and check some equivalent
pitches. Then the frets need a tweak, then the strings need a tweak,
and so on. Sounds nice in the end but I'm guessing this isn't the
best way to do it.
Another thing I don't really understand is why Gerle's (and
Dowland's) system doesn't require a tastino. To me, the appeal of
Gerle is that I'm really reluctant to use tastini. Looking at your
numbers below I can see a 1st fret position that seems quite narrow?
- do you use another first fret below that?
Any more advice would be much appreciated - though I appreciate it's
a big subject...
Cheers
Andrew
On 21 May 2008, at 14:12, Daniel F Heiman wrote:
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
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