Claudio simply dismissed this as 'idiocy', and while I don't blame him,
I think it wouldn't hurt to show what's wrong with this idea, for those
new to figuring out temperaments and fractions of commas.
From the instructions, you have a pure C-E third. If you tempered the 4
fifths in between evenly, you'd have 1/4-comma meantone. Instead, this
temperament has two pure fifths, meaning the comma has to be divided
between just two fifths (D-A, A-E)! These end up unbearably narrow.
Really quite unusable. Then all the others are pure fifths, so you have
a lot of really wide thirds.
Essentially that's the same as Kirnberger II. Not a usable temperament
for anything, really.
Jonathan
On 05/12/16 10:48 AM, Shields, Michael wrote:
> Hi Claudio and Andrew,
>
> Yes, one can also tune the keyboard to the string players. It depends who's playing, and this may be the best method for those musicians and tuners who are not the best. For what it's worth, here's a practical compromise from 1771, a just keyboard tuning with open fifths designed for accompanying strings, recommended by J.A.P. Schulz (regarded by music historians as one of the most important 18th-century music teachers in Scandinavia). Schulz explicitly says it's an ultra-easy method to use, has good key character, and is especially good for accompanying strings. He wrote many of the encyclopedia articles on music, but as far as I remember Kirnberger was overseer and took the credit (and presumably payment too). I think this tuning (or Schulz' article?) is also recommended in Diderot's encyclopedia, but forget where.
>
> 1. Tune pure 5ths and 4th c-g-d.
> 2. Tune e a pure third above c.
> 3. From e tune pure fifths and fourths e-b-f#.
> 4. Tune pure fifths/fourths c-f-bflat [-eflat-aflat-dflat].
> 5. Tune a equally out with d (partial on a) and with c (partial on e).
> 6.
> Recommended for harpsichord/piano to accompany strings. Source: Johann Georg Sulzer, Allgemeine Theorie der schönen Künste, vol.4, entry "Stimmung". 2nd enlarged edition, Leipzig 1794, p.465. (Author: Schulz). This edition available on archive.org, in 18th-century German. As a tuning scheme it has similarities with the so-called "Erlangen" clavichord tuning (mid 15th century: may have grown out of 14th-century adjustments to Pythagorean tuning). Annette Otterstedt advocated its use for organs when accompanying viols in 17th-century music, in Chelys vol.25, p.32-52 (with high scepticism ratings among reviewers because of the lack of 17th-c. evidence). I'd be interested if anyone knows similar (admittedly low-brow) tuning schemes, other than those which I have already found discussed in Claudio's book on unequal temperaments and the literature before it. Maybe a good tuning for Christmas carols.
>
> Greetings from a cold & clammy Ireland,
>
> Michael
>
>
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--
Jonathan Addleman - http://www.redowl.ca
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Note: opinions expressed on HPSCHD-L are those of the individual con-
tributors and not necessarily those of the list owners nor of the Uni-
versity of Iowa. For a brief summary of list commands, send mail to
[log in to unmask] saying HELP .
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