new recordings in the Bach temperament

I am pleased to announce several new recordings employing Bach's keyboard
temperament.

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*** Frog Music Press, "The New Bach Temperament" 2-CD set,
performed/realized by James Pressler and produced by Noel Jones.

This recording uses pipe organ samples from an instrument in the Czech
Republic, retuned and driven by MIDI sequences. It includes 22 Bach
selections. Most of them are paired with the same sequence in another
temperament, for direct comparison.
http://www.frogmusic.com/temperamentalcds.html

Recordings of additional repertoire are available at James Pressler's web
site, "Virtually Baroque". These other examples emphasize the Bach
temperament's general utility as an all-purpose tuning.
http://www.virtuallybaroque.com/list5gac.htm

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*** LaripS 1002 and 1003, performances by Bradley Lehman. (These are in
production process, to be released in early summer 2005).

Samples:
http://www-personal.umich.edu/~bpl/larips/samples.html

The organ set 1002 includes music by Bach, Brahms, Pachelbel, Sorge,
Fischer, Erbach, Zachow, Böhm, Walther, and others. It demonstrates the
new two-manual Taylor & Boody Opus 41 at Goshen College, with representative music in all keys.
http://www-personal.umich.edu/~bpl/larips/tb41.html

The harpsichord set 1003 includes Bach sinfonias, preludes and fugues, and
selections by other members of the Bach family.

=====

Information about this temperament:
http://www.larips.com/
and in the February and May 2005 issues of _Early Music_, Oxford University
Press.

Bradley Lehman

--- In tuning@yahoogroups.com, Brad Lehman <bpl@u...> wrote:

> I am pleased to announce several new recordings employing Bach's
keyboard
> temperament.

Here's his article on the temperament:

http://tinyurl.com/59spx

The gist of it is in the first sentence: that Bach actually wrote down
a temperament with a circle of fifths consisting of five 1/6 comma
fifths, three pure fifths, and three 1/12 comma fifths. However, Bach
didn't actually write this down, but drew a diagram which needs
interpreting. In any case, the given amount of tempering doesn't add
up. However, Lehman gives an analysis in terms of tuning units, from
which the temperament in his understanding of it can be reconstructed.
In this, the fifths above F-A are lowered 120 tuning units, or 1/6
Pythagoren comma, above C#, G# and Eb are lowered 60 tuning units, or
1/12 comma, and above Bb is *raised* 60 tuning units, or 1/12 comma.
This is now 5*(1/6)+2*(1/12)-1/12 = 11/12 Pythagorean commas of total
tempering, or one syntonic comma. We still actually need a Pythagorean
comma, not a syntonic comma, so it seems 60 TU really needs to be a
little larger. If we take instead of 60 TU a value X=65 5/11 TU, then
5*(2X) + 2*X - X = 11*X = 720 TU, or one Pythagorean comma.

I'm not sure what's going on here, but I'll repeat my recommendation
that the tuning unit be replaced with a system which divides the
octave into 46032 equal parts, with the Pythagorean comma having 900
parts and the syntonic comma 825 parts; the advantage of this is that
we can represent all 5-limit intervals and are not stumbing about in
the murk as to what, precisely, we are doing when it comes to the
larger intervals. They are closely related to TUs, being 4/5 as large.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> In this, the fifths above F-A are lowered 120 tuning units, or 1/6
> Pythagoren comma, above C#, G# and Eb are lowered 60 tuning units, or
> 1/12 comma, and above Bb is *raised* 60 tuning units, or 1/12 comma.
> This is now 5*(1/6)+2*(1/12)-1/12 = 11/12 Pythagorean commas of total
> tempering, or one syntonic comma.

Whups; I was staring at a table cross-eyed again. This should be
*three* fifths flat by 1/12 Pythagorean comma, for a total of
5*(1/6)+3*(1/12)-1/12 = 1 Pythagorean comma. Who cares what
mathematicians think if they look at a table cross-eyed?