Dear Anthony,
I think you can really only appreciate the whole temperament issue by
practical experience, not mathematics. I came to it by learning to
tune a harpsichord, though I found that I had been using an "unequal"
fretting on my lutes for years, having found (empirically) that the
theoretical (equal tempered) fret positions didn't work. Interestingly,
once I knew the theory, I found that one of my lutes was pretty close to
1/6 comma, as are Gerle's instructions (repeated, with a few errors, by
John Dowland 70-odd years later).
One of the really useful things about meantone temperaments on the lute
is that they make achieving a satisfactory tuning so much easier. The
thing about ET is that the thirds are already so wide that if there is
even the slightest error in the direction of being wider they go easily
beyond our tolerance. Whereas in MT, the size of the third is always
narrower than an ET third (Dank sei Gott) but exactly how much narrower
is not so crucial. You might end up with something closer to 1/7 comma
than 1/6 comma, but it still sounds OK.
Fret positions can be calculated, of course, and this is what I usually
do, at least to get started. But it is illuminating to use a tuner to
tune the frets as well as the strings. It doesn't even matter whether
your open string is in tune - if you have a Korg or some other tuner set
to the temperament you want, set it to "listen", play the open string
and note how sharp or flat it is. The next note (first fret) should be
the same amount sharp or flat, and so on. Maybe the needle says they're
all 5 cents sharp, that's OK it means the frets are in the right
places. Using this method, what you do find is that different courses
may require slightly different fret positions, sometimes leading to
slightly slanted frets - usually nearer the nut in on the bass side,
especially as you get higher up the fingerboard.
I hope this helps.
Best wishes,
Martin
Anthony Hind wrote:
Daniel
This is all very interesting, but I admit that I was hoping to be
able to set-up my lute in some sort of meantone, avoiding too much
fiddling about, by using a preprogrammed Turbo tuner. David v O., in
a recent posting, does seem to consider that it is possible to use
this to tune to meantone temperaments, although he also gives a
method of calculation, on his site using ear, paper and pencil.
I admit that I am maths challenged, and can rarely manage to measure
anything, or draw a straight-line, and my ear is probably not above
average, either.
However, I recently went to hear and see the very unusual toroidal
diapasons made by Charles Besnainou of the CNRS, and I was not only
surprised by how he makes those strings (but I'll keep that to
another day), but also by the extraordinary fretting on his Baroque
lute. All the frets were oblique (difficult to tweak that with a
tuner), and at different intervals, and of course there was the usual
sprinkling of Tastinis. Now he is capable of any type of acoustic
analysis, but tells me he sets up his lute entirely by ear not even
using paper and pencil. I wish I had made a photo of his lute.
Another French Baroque lute player, Vincent Siess, who is very
competent mathematician tells me he sets his lute by the paper,
pencil and ear method.
These photos are of "The other" Stepen Stubb's lute in 1/4 comma.
Stephen uses David's exact instructions on how to tune with minimal
use of a tuner, at
http://home.planet.nl/~d.v.ooijen/david/writings/meantone_f.html
This gives the following result, with an additional top fret instead
of a Tastini:
http://tinyurl.com/63ewuj
http://tinyurl.com/69w65e
http://tinyurl.com/6fnrt4
Nevertheless, David does seem to consider that it is possible to use
the Turbo tuner at least as a help to tune in unequal temperament.
For example, David gives the following chart for programming 6th comma
http://home.planet.nl/~d.v.ooijen/david/writings/meantone_p_bestanden/
silbermann.JPG
We see David's use of Tastini, here:
http://tinyurl.com/5mzblr
He says the Tastinis can be relaced by using half a double fret. I
have therefore ordered double frets, on my future Baroque lute.
Petersen does give two charts showing how their tuner is
preprogrammed for 1/6th comma
Petersen Chart:
Here are the offsets for 1/6th Comma Meantone where A=440Hz:
[b][i]Note_____Offset[/i][/b]
C________+04.9
C#_______-06.4
D________+01.7
Eb_______+09.8
E________-01.6
F________+06.5
F#_______-04.9
G________+03.3
Ab_______-08.2
A________-00.0
Bb_______+08.1
B________-03.2
1/6th Comma Meantone with an Equally Tempered Root of C:
[i][b]Note_____Offset[/b][/i]
C________+00.0
C#_______-11.3
D________-03.2
Eb_______+04.9
E________-06.5
F________+01.6
F#_______-09.8
G________-01.6
Ab_______-13.1
A________-04.9
Bb_______+03.2
B________-08.1
Petersen says, "1/6th Comma Meantone is included as a preset in our
new [url="www.strobosoft.com"]StroboSoft[/url] tuning software."
I suppose this should mean that they offer more than one preset, and
a G lute might, perhaps, be preset as follows. Just how many presets
might you need, and how exactly do you determine when you need a
particular one?
G = 0
Ab = -11,5
A = -3,3
Bb = +4,8
B = -5,5
C-=+1,6
D=-1,6
Eb=+6,5
E=-4,9
F=+3,2
F#=-8,2
G=0
The paper and ear method, begins to seem inviting. I am no
mathematician, and I do regret that there seems to be no easy way out.
I hope you understand that I am crying out for help over this issue.
Anthony
Le 21 mai 08 =E0 15:12, Daniel F Heiman a ecrit :
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
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