The Keyboard Temperament of J. S. Bach

For those interested in this topic, new findings are available at:
http://www.eunomios.org/contrib/francis1/francis1.html

Regards
Charles

--- In tuning@yahoogroups.com, "Charles" <Francis@d...> wrote:
> For those interested in this topic, new findings are available at:
> http://www.eunomios.org/contrib/francis1/francis1.html
>
>
> Regards
> Charles

I find these conclusions insupportable. That C-A would be a
Pythagorean major sixth (27:16), while A-F# would be a just (5:3) or
near-just major sixth, goes against the key-gradation pattern that
all well-temperaments of the time exhibit. C-A and G-E were the major
sixths closest to just (or very nearly so) in all of the 17th and
early 18th century keyboard temperaments, since they occur most
frequently in the keys with the fewest accidentals in their key
signatures. Meanwhile, A-F# and E-C# were typically closer to the 12-
equal major sixth.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Charles" <Francis@d...> wrote:
>
> I find these conclusions insupportable. That C-A would be a
> Pythagorean major sixth (27:16), while A-F# would be a just (5:3) or
> near-just major sixth, goes against the key-gradation pattern that
> all well-temperaments of the time exhibit. C-A and G-E were the
> major sixths closest to just (or very nearly so) in all of the 17th
> and early 18th century keyboard temperaments, since they occur most
> frequently in the keys with the fewest accidentals in their key
> signatures. Meanwhile, A-F# and E-C# were typically closer to the
> 12-equal major sixth.

Thanks for your feedback, Paul. My observation would be that the historical record indicates Bach always tuned his own instrument, so any objection that he did not follow historical precedent appears somewhat mute. The proof of the pudding is how Bach's music sounds in this temperament (forgive the mixed metaphor), and this is something everyone can find out for themselves.

I would argue Bach certainly had the necessary background to create his own keyboard temperament. His cousin Nikolaus was well-known as an instrument builder, and in 1706 beat Neidhardt in a tuning contest: Nikolaus tuned a section of an organ by ear, while Neidhardt did another section; that of Nikolaus being judged superior to Neidhardt. Then consider Bach's role as a consultant for the commissioning of organs; his critique of Silbermann's temperament as reported by Andreas Sorge and Edward John Hopkins. Last, but not least, the two books of "Well Tempered Clavier" attest to Bach's personal interest in tuning. That Bach's temperament breaks with tradition has precedents, moreover: consider, for example, his innovations with regard to keyboard fingering or his adaptation of concertos to the organ. One would not expect, a priori, Bach's contemporaries to use his temperament, which may well have been a professional secret; but the same observation is not true for Bach's son's, and it is likely they maintained the tuning methods they were taught.

Regards
Charles

How often we've heard these exact words, with regard to this or that
exact temperament!

Good luck,
Paul

--- In tuning@yahoogroups.com, "Charles" <Francis@d...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Charles" <Francis@d...> wrote:
> >
> > I find these conclusions insupportable. That C-A would be a
> > Pythagorean major sixth (27:16), while A-F# would be a just (5:3)
or
> > near-just major sixth, goes against the key-gradation pattern that
> > all well-temperaments of the time exhibit. C-A and G-E were the
> > major sixths closest to just (or very nearly so) in all of the
17th
> > and early 18th century keyboard temperaments, since they occur
most
> > frequently in the keys with the fewest accidentals in their key
> > signatures. Meanwhile, A-F# and E-C# were typically closer to the
> > 12-equal major sixth.
>
>
> Thanks for your feedback, Paul. My observation would be that the
historical record indicates Bach always tuned his own instrument, so
any objection that he did not follow historical precedent appears
somewhat mute. The proof of the pudding is how Bach's music sounds
in this temperament (forgive the mixed metaphor), and this is
something everyone can find out for themselves.
>
> I would argue Bach certainly had the necessary background to create
his own keyboard temperament. His cousin Nikolaus was well-known as
an instrument builder, and in 1706 beat Neidhardt in a tuning
contest: Nikolaus tuned a section of an organ by ear, while
Neidhardt did another section; that of Nikolaus being judged superior
to Neidhardt. Then consider Bach's role as a consultant for the
commissioning of organs; his critique of Silbermann's temperament as
reported by Andreas Sorge and Edward John Hopkins. Last, but not
least, the two books of "Well Tempered Clavier" attest to Bach's
personal interest in tuning. That Bach's temperament breaks with
tradition has precedents, moreover: consider, for example, his
innovations with regard to keyboard fingering or his adaptation of
concertos to the organ. One would not expect, a priori, Bach's
contemporaries to use his temperament, which may well have been a
professional secret; but the same observation is not true for Bach's
son's, and it is likely they maintained the tuning methods they were
taught.
>
>
> Regards
> Charles