WTC II

In the course of vorbifying these, I've found that Hafner's rule
doesn't always work for Book II. Prelude 8, for instance, has an F#
minor triad, so we need to go down as far as A. We can't fudge things
on the other end of the chain either, as we have an E# major triad,
so we also need to go up as far as G##.

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

> In the course of vorbifying these, I've found that Hafner's rule
> doesn't always work for Book II. Prelude 8, for instance...

Prelude 13. Prelude and Fugue 8 is Hafner-ready.

>In the course of vorbifying these, I've found that Hafner's rule
>doesn't always work for Book II. Prelude 8, for instance, has an F#
>minor triad, so we need to go down as far as A. We can't fudge things
>on the other end of the chain either, as we have an E# major triad,
>so we also need to go up as far as G##.

Inchresting. I wonder about fugues 12 and 24 from book I.

-Carl

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

Gene, this is a repost to the tuning group, since I munged the
address, or didn't join the group beforehand.

Thank you all for discussing Hafner's idea (the 48 revisited in 31),
which I've been playing around with for some time, but in ignorance
of his prior art. The quotes from Hafner's article, submitted
earlier by Paul Erlich, well explain the concept, although there are
deviations from his rule for finding the best transposition of
meantone for each piece. My notes on testing some of Bach's cycles
of clavier pieces for meanness of intonation are now posted at
www.dslnorthwest.net/~jolliff . The method of rotating the wolf to
accommodate each set holds up in a majority of cases, and where it
does not, still provides insight regarding which orientation of
unequal temperament would work. The Well Tuned Keyboard contains
enough adventurous dissonance aside from issues presented by
meantone, that mistuned intervals can be seen in some cases as
another tonal resource. But yes, it is a tuning lesson, intended to
train the ear, along with the hands and musical imagination.