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
>>
>>
>> --
>>
>> To get on or off this list see list information at
>> http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
>>
>>
>
>
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