Silbermann-Sorge temperament

Just saw the following entry in Wikipedia - it exists only in the german (and the esperanto) version, which probably explains why I never saw it mentioned here:

http://de.wikipedia.org/wiki/Silbermann-Sorge-Temperatur

It is a kind of meantone - actually nearly identical to 1/6 comma meantone, except that a fifth is not tempered down 1/6 of a syntonic comma but a pythagorean comma. I am now wondering how much this difference matters, since the two commas are only 2 cents apart - or if the mention of the pythagorean instead of the syntonic comma is even a mistake in the Wikipedia entry?

Any thoughts/opinions/knowledge here?
--
Hans Straub

Hans,
I don't have any in-depth knowledge, but from my reading on the internet over a few years it seems as though this type of temperament is often defined in terms of PC not SC.
* It does not seem to make much difference in the case of Silbermann-Sorge with 11 small and one (very) large 5th.
* In the case of Vallotti, with 6 small and 6 larger, it makes sense to use 1/6 PC for the small ones, then the larger ones are pure 3/2. If one uses 1/6 SC for the small ones, then the larger ones cannot all be pure.
* I think that Young's original definition for his first temperament used 1/6 SC for the smallest 5ths and pure 3/2 for the largest; this leaves the remaining 5ths with a difficult to describe intermediate value. It is now usually re-defined with 1/6 PC for the smallest, pure for the largest and then the intermediates are exactly 700c.
* Apparently, Bradley Lehman first intended to use 1/6 SC for the smallest 5ths in his Bach temperament, but then decided that 1/6 PC was more historically likely ... but I don't know enough about that.

Steve M.

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> Just saw the following entry in Wikipedia - it exists only in the german (and the esperanto) version, which probably explains why I never saw it mentioned here:
>
> http://de.wikipedia.org/wiki/Silbermann-Sorge-Temperatur
>
> It is a kind of meantone - actually nearly identical to 1/6 comma meantone, except that a fifth is not tempered down 1/6 of a syntonic comma but a pythagorean comma. I am now wondering how much this difference matters, since the two commas are only 2 cents apart - or if the mention of the pythagorean instead of the syntonic comma is even a mistake in the Wikipedia entry?
>
> Any thoughts/opinions/knowledge here?
> --
> Hans Straub
>

On 5/13/2013 1:48 PM, hstraub64 wrote:
> Just saw the following entry in Wikipedia - it exists only in the
> german (and the esperanto) version, which probably explains why I
> never saw it mentioned here:
>
> http://de.wikipedia.org/wiki/Silbermann-Sorge-Temperatur
>
> It is a kind of meantone - actually nearly identical to 1/6 comma
> meantone, except that a fifth is not tempered down 1/6 of a syntonic
> comma but a pythagorean comma. I am now wondering how much this
> difference matters, since the two commas are only 2 cents apart - or
> if the mention of the pythagorean instead of the syntonic comma is
> even a mistake in the Wikipedia entry?
>
> Any thoughts/opinions/knowledge here?

It's closest to "silbermann2.scl" in the Scala archive, which is identified as "Gottfried Silbermann's temperament nr. 2, 1/6 Pyth. comma meantone". So, a confirmation on the Pythagorean part at least.

I'd guess the difference from 1/6-comma meantone isn't enough to be significant. With fifths tempered by 1/6 of a syntonic comma, 45/32 is just, but that's a dissonance in traditional music theory, so it doesn't matter if it's near just.

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> Hans,
> I don't have any in-depth knowledge, but from my reading on the internet over a few years it seems as though this type of temperament is often defined in terms of PC not SC.
> * It does not seem to make much difference in the case of Silbermann-Sorge with 11 small and one (very) large 5th.
> * In the case of Vallotti, with 6 small and 6 larger, it makes sense to use 1/6 PC for the small ones, then the larger ones are pure 3/2. If one uses 1/6 SC for the small ones, then the larger ones cannot all be pure.
> * I think that Young's original definition for his first temperament used 1/6 SC for the smallest 5ths and pure 3/2 for the largest; this leaves the remaining 5ths with a difficult to describe intermediate value. It is now usually re-defined with 1/6 PC for the smallest, pure for the largest and then the intermediates are exactly 700c.
> * Apparently, Bradley Lehman first intended to use 1/6 SC for the smallest 5ths in his Bach temperament, but then decided that 1/6 PC was more historically likely ... but I don't know enough about that.
>
> Steve M.
>

I think I am starting to see the point. It won't make much of a difference to listen - just for "circularity", if you have 12 pitches and want to close the circle of fifths. For that, pythagorean comma is apparently better suited. Thanks for the answers!
--
Hans Straub