Fwd: Bach Tunings.

--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:

http://www.larips.com/

A controversial topic. Lots of info here.

--- End forwarded message ---

--- In tuning@yahoogroups.com, "robert thomas martin" <robertthomasmartin@...> wrote:
>
> A controversial topic.
>
So it is in deed, dear Thomas,

an other author published an new so called "Bach-Tuning" claim
http://www.groenewald-berlin.de/Mikro-Diff_bei%20_Bach-Stimmungen.html
(in German) in the prestigious journal:
http://www.gdo.de/veroeffentlichungen/ars_organi/
"Heft 2009/1, März

Grönewald, Jürgen:
Hat Johann Sebastian Bach gleichschwebend gestimmt?
(Tuned J.S.Bach in equal-beating ?)
Ars Organi Volume#57, Issue 1, March(2009), pp.38-41

Here his specification in absoulte-pitch frequencies
as found on p.39 :

"Gleich-schwebende Quinten-Kette"
'Equal-beating chain of 5ths'

"Vereinfachte Version"
'simplified version'

c' 263.555 Hz middle C_4
#' 277.655
d' 294
#' 312.362
e' 329.5
f' 351.407
#' 370.207
g' 393.333
#' 416.483
a' 440
#' 468.543
b' 493.75

!Groenewald_simplified_Bach.scl
!
Journal: Ars Organi Volume#57, Issue 1, March(2009) p.39
!
12
!
90.225 ! C#
189.25 ! D
294.135 ! Eb
386.606 ! E
498.045 ! F
588.270 ! F#
693.175 ! G
792.180 ! G#
887.275 ! A
996.090 ! Bb
1086.808 ! B
2/1
!
!

...later, then on p.40 follows finally his:

"Exakte Version"
'exact version'

obtained by an "Probier-Verfahren" 'trial-and-error-method' when
'distributing the Pythagorean-Comma (23.460 cent)'
over the dozen 4ths in counter-clockwise direction:

F -0.092 C
Bb -0.137 F
Eb -0.207 Eb
G# -0.309 Eb
C# -0.464 G#
F# -0.696 C#
B -1.044 F#
E -1.564 B
A -2.343 E
D -3.509 A
G -5.250 D
C -7.845 G

Sum: -23.460 = -PC

as frequencies in absolute-pitch:

c' 263.253 Hz middle C_4
#' 277.531
d' 292.928
#' 312.083
e' 329.554
f' 351.023
#' 370.190
g' 393.095
#' 416.185
a' 440
#' 468.068
b' 493.884

!Groenewald_exact_Bach.scl
!
Journal: Ars Organi Volume#57, Issue 1, March(2009) p.41
!
12
!
91.434 ! C#
190.815 ! D
294.571 ! Eb
388.873 ! E
498.137 ! F
590.175 ! F#
694.110 ! G
792.925 ! G#
889.261 ! A
996.319 ! Bb
2/1
!
!

in reference to the controversial discussions of the topic in:
http://www.gdo.de/veroeffentlichungen/ars_organi/
"
Heft 2008/1:
Billeter, Bernhard: Zur "Wohltemperierten" Stimmung von Johann Sebastian Bach. Wie hat Bach seine Cembali gestimmt? Ars Organi 56, 2008, 18-21. - Hierzu: Martin Blanz, 120; Hubert Holzapfel, 120 f.; B. Billeter, 121. Heinz Hilscher, 190. Thomas Dent, 262 f. B. Billeter, 57, 2009, 53.
http://www.amazon.de/Anweisung-Stimmen-Tasteninstrumenten-verschiedenen-Temperaturen/dp/3875371607
(in German)

English sources:
http://books.google.de/books?id=4t9mtZTLzjQC&pg=PA91&lpg=PA91&dq=bernhard-billeter+tuning&source=bl&ots=YwrJMajCKE&sig=J1hTPLQUbpxS44sAXD8_d9Nor34&hl=en&ei=2ZcASujUN5nv_Aacqr31Bg&sa=X&oi=book_result&ct=result&resnum=1
http://www-personal.umich.edu/~bpl/larips/bachtemps.html#billeter2008

bye
A.S.

bye
A.S.

Hello Andreas,

!Groenewald_simplified_Bach.scl
> !
> Journal: Ars Organi Volume#57, Issue 1, March(2009) p.39
> !
> 12
> !
> 90.225 ! C#
> 189.25 ! D
> 294.135 ! Eb
> 386.606 ! E
> 498.045 ! F
> 588.270 ! F#
> 693.175 ! G
> 792.180 ! G#
> 887.275 ! A
> 996.090 ! Bb
> 1086.808 ! B
> 2/1
> !
> !
>

This is a partly JI scale?
C# - 243/128 - exact 90.225
D - 10/9 ?? - 182.404 is ~7cents off (tempered interval?)
Eb - 32/27 - exact
E - 5/4 - 386.314 is ~0.3cents off (so it's 5/4, nobody can ever tell
the difference)
F - 4/3 -exact
F# - 1024/729 - exact
G - tempering of 40/27 and 3/2??
G# - 128/81 - exact
A - 5/3 ? - 884.359 is ~3cents off
Bb - 16/9 - exact
B - 15/8 or 4096/2187 ?? ~1cent off each

Doesn't look like a normal distribution of a pythagorean comma to me.

>
> ...later, then on p.40 follows finally his:
>
> "Exakte Version"
> 'exact version'
>
> obtained by an "Probier-Verfahren" 'trial-and-error-method' when
> 'distributing the Pythagorean-Comma (23.460 cent)'
> over the dozen 4ths in counter-clockwise direction:
>
> !Groenewald_exact_Bach.scl
> !
> Journal: Ars Organi Volume#57, Issue 1, March(2009) p.41
> !
> 12
> !
>

> 91.434 ! C#
> 190.815 ! D
> 294.571 ! Eb
> 388.873 ! E
> 498.137 ! F
> 590.175 ! F#
> 694.110 ! G
> 792.925 ! G#
> 889.261 ! A
> 996.319 ! Bb
> 2/1
> !
> !
>
The B is missing in the above version?And it still looks to me like the
above scale wants to be a JI scale.
Wouldn't call it distribution of the pythagorean comma.

Marcel

Thanks Andreas for the communication on YET ANOTHER Bach proposal.

> Groenewald_simplified_Bach.scl
> (and the later Exakte Version" )

I performed a full spreadsheet analysis of both.

Major thirds circles: virtually identical to Kirnberger III. It shows
"waste" in making C-E almost pure, with the well-known consequence: while 4
major thirds are better than ET, 6 of them are worse, of which 4 almost
exactly Pythagorean. A system thus fit for music with very few accidentals,
certainly not for Bach.

Fifths: if Bach found meantone fifths too narrow at -5.4 Cents, he would
certainly object to a horrendous C-G narrow by 8.8 Cents(7.8 in Exakte),
also to the poor G-D, narrow by 5.9 Cents.(5.3 in the Exakte).

Cheers,

Claudio

http://temper.braybaroque.ie/

>
> I performed a full spreadsheet analysis of both.
>
> Major thirds circles: virtually identical to Kirnberger III. It shows
> "waste" in making C-E almost pure, with the well-known consequence: while 4
> major thirds are better than ET, 6 of them are worse, of which 4 almost
> exactly Pythagorean. A system thus fit for music with very few accidentals,
> certainly not for Bach.
>

Hmm I don't know.
Just like minor thirds are often 32/27 and should not be 6/5 (sounds wrong)
depending on the key / tonic (sorry don't have better words to explain),
major thirds should often be 81/64, not 5/4. depends on the music.
I don't think there's anybody in the world that can say how something even
moderately complex should be played in JI, so I think nobody can say with a
fair degree of certainty that this tuning is not well suited for Bach's
music.
What I can allready see is that for instance the Beethoven Drei Equali piece
I've been obsessing about this is a very good tempering to play it in (much
better than valotti etc) if you only allow 12tones per octave.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
Hi Marcel,

> This is a partly JI scale?
At least something near JI..

> C# - 243/128 - exact 90.225
> D - 10/9 ?? - 182.404 is ~7cents off (tempered interval?)
> Eb - 32/27 - exact
> E - 5/4 - 386.314 is ~0.3cents off (so it's 5/4, nobody can ever tell
> the difference)
Acustically (con-)fusing with 5/4.

> F - 4/3 -exact
> F# - 1024/729 - exact
> G - tempering of 40/27 and 3/2??
> G# - 128/81 - exact
> A - 5/3 ? - 884.359 is ~3cents off
> Bb - 16/9 - exact
> B - 15/8 or 4096/2187 ?? ~1cent off each
>
> Doesn't look like a normal distribution of a pythagorean comma to me.
What do you understand by an "normal" distritibution of the PC?

> >
> > !Groenewald_exact_Bach.scl
> > !
> > Journal: Ars Organi Volume#57, Issue 1, March(2009) p.41
> > !
> > 12
> > !
> >
>
> > 91.434 ! C#
> > 190.815 ! D
> > 294.571 ! Eb
> > 388.873 ! E
> > 498.137 ! F
> > 590.175 ! F#
> > 694.110 ! G
> > 792.925 ! G#
> > 889.261 ! A
> > 996.319 ! Bb
1089.264 ! B
> > 2/1
> > !
> > !
> >
> The B is missing in the above version?
Sorry, that i had left out the
1089.264 ! B
above in a hurry.

> And it still looks to me like the
> above scale wants to be a JI scale.
> Wouldn't call it distribution of the pythagorean comma.
Why not?

bye
A.S.

Hello Andreas,

What do you understand by an "normal" distritibution of the PC?

I know very little about temperings.
But the minute I saw the cents valeus it made me think of a 5-limit JI scale
except for the D, G and A.
So where I'd expect for a tempering of a Pythagorean scale to try to be as
Pythagorean as possible. (leading to something close to 12tet, or just
equally distribute the PC across a few notes for instance)
This scale looks to me like it doesn't want to be a Pythagorean scale, it
looks to me like it wishes to be a 12-tone 5-limit JI scale where the D, G
and A are tempered in order to make certain comma pumps sound good or
something like that.

I didn't read into how this scale came to be but I got the impression it was
derived from the tuning of one or several old organs where the intent of the
tuner was unknown and is somehow related to Bach?
Or atleast something else where the thought behind the tuning is unknown?
If such a thing is the case then I'd see it as more plauble that the intent
of this scale was not to temper a Pythagoran scale, but to temper a JI
scale.
If I'm wrong and this is a modern scale truly ment to be a tempering of the
Pythagorean scale where for reasons unknown to me the tempering has led to
the scale for the most part comming close to 5-limit JI then I'm curious
what led the creator to temper it in this way.

Marcel