Bach/Lehman Temperment [important]

http://www.goshen.edu/news/pressarchive/04-20-05-bach-temper.html

F. Richard Burt

Thanks, Dick, for sharing this link on Bach's secret well-tempered keyboard.
Vocal tuning was a variant. It was very interesting.

He wrote his tuning method on his Well-tempered music so it made no sense to
others outside his family. And no one till Bradley Lehman very recently in
2005 was able to decipher it! Bach's Well-temperament would play in 12 major and
minor keys. But differently than was supposed. It was neither Meantone (MT),
Werckmeister (WM), nor Equal Temperament (ET). Today it's properly called
Bach/Lehman Temperament (BLT).

0, -1/12 (1.792 cents) and -1/6 (3.584 cents) comma (21.506 cents) subtracted
from equal-tempered intervals were used.

Bach didn't write the cents. Neither did Lehman give them on his page below.
Neither did the pipe organ firm give the numbers which tuned a pipe organ to
Bach/Lehman. I calculated them here to the 3rd decimal point. Since I'm
experimenting with Just Intonation *JI), I'm used to calculating pitches and
intervals.

With Bach's scale each key has its own characteristic sound.

Notes/keys C, C#(Db), D, Eb(D#), E, F,
Cents -3.584 98.208 196.416 298.202 400 496.416
Notes/keys F#(Gb), G, G#(Ab), A, (A#)Bb, B.
600 696.416 798.208 896.416 998.208 1100

Major 3rds vary +/- 400 cents. Minor 7ths are large..

Your link led me to more links on the subject:

Bradley Lehman Feb & May 2005 articles on Bach's temperament
Click here: Early Music -- Search Result
I didn't read these PDFs, as I had to register.

Click here: larips.com Bradley Lehman's page

Click here: Goshen College Music Center: Opus 41 Pipe Organ
Only pipe organ tuned to Bach's tuning.

However interesting Bach's tuning may have been compared to MT, WM, or ET, I
can only say JI is much better, despite the extra notes needed!

Pauline Phillips, Interlude organist
Johannus 2002 Sweelinck 30 AGO
Sunnydale Academy SDA Church
Centralia, MO, USA
Johannus & Makin Organs eSchool

>Dear Pauline,
--- In tuning@yahoogroups.com, prophecyspirit@a... wrote:
>
Goshen College alum solves Bach's temperamental puzzle;
> http://www.goshen.edu/news/pressarchive/04-20-05-bach-temper.html
:...."Then in March 2004, Lehman received an e-mail message from
British harpsichord and clavichord enthusiast David Hitchin who
reported that two German researchers suggested that the drawing might
be a clue to a temperament. But Lehman felt the temperament that the
Germans were proposing didn't make sense"......for himself in
his own mind and private opinion, that i do fully respect.
So he decided to avoid referring to the original source paper
of the year 1998, that he knew, but didn't liked,
availbale on:
http://www.strukturbildung.de/Andreas.Sparschuh/
http://homepages.bw.edu/bachbib/script/bach1.pl?0=Sparschuh,%20Andreas

All other autors before Lehman refer to that initial first work on
Bach squiggels in citeting my paper correctly until in 2005
"Rosetta-stone" as an further reinterpretation appeared,
by neglecting academic citation standards,
that other scientists urgently need in order to identify the primary
sources.

http://lists2.wu-wien.ac.at/pipermail/earlyml/2005December/002271.html
/tuning/topicId_59217.html#59217
the former president of the german clavichord soc.:
Michael Zapf comments such an behaviour adaequate:
"This, and his complete omission of
Andreas Sparschuh's name and discovery in the Early
Music article makes him a plagiarizer, nothing less."
http://clavichord.info/engl/23bre1e.htm

>
> It was very interesting.... too,
how Oxford University Press reacted on that complete flop,
presenting proudly Lehmans remake as theirs world premiere debut
performance as first Bach WTC squiggle discovery interpretation
in theirs "unrivaled" journal Early-Music.
>
> He wrote his tuning method on his Well-tempered music so it made no
sense to
> others outside his family. And no one till Bradley Lehman very
recently in
> 2005 was able to decipher it!

Amazingly:
Alone one single man worldwide alone claims to assert that fiction
in his own individual private point of view still again and again,
that exclusively only he, but nobody else too,
could have been so far able to find his "Rosetta-stone" version
reconstruction, even after centuries,
that Bach one had tuned his WTC just in his strange way.
That person seems to consider evidently that nobody else
would be apt enough to do that too, as he assumes about himself.

Look, to confirm that in:
http://en.wikipedia.org/wiki/Well-Tempered_Clavier
for the historys background.
Sorry, excuse-moi : but i.m.o. there is no cure for that. Pardon!
All we can do here is: regarding his insights respectfully with
demanded carefullness and file his meanwhile obsolete pamphlet for
storing aside ad acta,
in order to get rid -by applying occams razor- from superfluous
versions, that can be evidently excluded as ahistorical neobaroque
fake without any relevance.

> Bach's Well-temperament would play in 12 major and
> minor keys. But differently than was supposed. It was neither
> Meantone (MT),
> Werckmeister (WM), nor Equal Temperament (ET). Today it's properly
> called
> Bach/Lehman Temperament (BLT).
Correct labeld:
Lehmans Reinterpretation Try (LRT) of at least 3 prior other works.

>
> 0, -1/12 (1.792 cents) and -1/6 (3.584 cents) comma (21.506 cents)
subtracted
> from equal-tempered intervals were used.
>
> Bach didn't write the cents.
never!
> Neither did Lehman give them on his page below.
> Neither did the pipe organ firm give the numbers which tuned a pipe
>organ to
> Bach/Lehman.
I asked in an email the organ builders Boody&Talor for that too
futile to get at least some absoulte frequencies or according
relative beating rates, as i tryed already six months ago:
After all my effords: No reply.
All attempts were to no avail.
Has anybody else here the concrete frequencies of T&Bs op.41
avialable?
It seems that they try to hide their values so much secret that
they probably do not anymore know themselfes how they had really
detuned the instrument anyhow in an other way than specified,
as in "Rosetta"

So far as my associctated professional organ tuner colleagues report
from listening about records of the organ op.41:
Many intervals deviate from the "Rosetta" own specification.
The defects actual tuning needs touching up amendmend.

But in any case i do recommend strongly to retune back the instument:
http://www.etruth.com/News/Content.aspx?ID=344215&page=
"Opus 41, the organ in the Rieth Recital Hall at Goshen College, was
originally set to be tuned using the Bach-Kellner system"
because it sounds weak in the actual somehow applied actual PC^(1/6)
sound espeically in the mainly used major 3rds turn out worser than
in the formery intended
superior Kellner PC^(1/5) as formerly planed a priori by the
experts in organ acustics.

May be that aggravation in worsening the 3rds
is one reason among others to refuse us to communicate
any secrete frequenies or arcane beating-ratios.
That looks only vague without knowinh the real
concrete beating rates in practice, like preciesely given in
Silbermanns instructions in counts of pulse-heart-beatings at
of 60 strokes/sec specified each peciesely for the individual
labeld 5ths in the circle, easily to determine from his work-sheet.

> I calculated them here to the 3rd decimal point. Since I'm
> experimenting with Just Intonation *JI), I'm used to calculating
pitches and
> intervals.
>
> With Bach's scale each key has its own characteristic sound.
>
> Notes/keys C, C#(Db), D, Eb(D#),
E, F,
> Cents -3.584 98.208 196.416 298.202 400 496.416
> Notes/keys F#(Gb), G, G#(Ab), A, (A#)
Bb, B.
> 600 696.416 798.208 896.416
998.208 1100
>
> Major 3rds vary +/- 400 cents. Minor 7ths are large..
so far the "Rosetta" theory,
but my best students identified T&B as Kellners PC^(1/5) by ear.
One needs an spectum analyzer to verify that scientifical,
but i found yet nobody conisdering it worth wasting time
to determine the concrete detuning.
>
>
> Bradley Lehman Feb & May 2005 articles on Bach's temperament
> Click here: Early Music -- Search Result
> I didn't read these PDFs, as I had to register.
Because OUP demands money for downloading?
>
> Click here: larips.com Bradley Lehman's page
>
> Click here: Goshen College Music Center: Opus 41 Pipe Organ
> Only pipe organ tuned to Bach's tuning...
....only in Lehmans claim.
How would Bach comment that tiny ~2cents sharp meantonic tamed mini-
wolf, called "Dackel-sousage-dog-5th" A#>F amouning ~704 cents wide?
disposed in Werckmeister #3 in 1681, already 4 years before
Bachs birth in 1685. The documents reports that Bach critizied
Gottfied Silbermann for the dackel-5th G#>Eb in Freiberg chathedral
organ, playin it so long until Silbermann absconded anyoed
out of the the church.
Why should Bach went back again to Arnold Schlicks
1511 obsolete tuning-base tone F ear intstead using the common
A=~410Hz cammerthone on A tuning forks, like for instance
Pascal Taskin, harpsichord builder, Paris opera and chapelle du roi,
and generally applied in Hamburgs contemporary organs.
Does anybody anybody know here about the existence of an baroque F-
tuning fork, where "Rosetta-tuning" starts and ends?
like in Alexander Ellis "History of musical pitch" many A-forks.

> However interesting Bach's tuning ... ????
one gets from the 1998 standard interpretation

_____1/1_______ == 1
C#__132/125____ == 1.056
D____28/25_____ == 1.12
Eb__297/250____ == 1.188
E___157/125____ == 1.256
F___667/500____ == 1.334
F#__176/125____ == 1.408
G___187/125____ == 1.496
G#__198/125____ == 1.584
A____42/25_____ == 1.68
Bb___89/50_____ == 1.78
B____47/25_____ == 1.88
C'___ 2/1______ == 2

by a dozen arbitrary chosen transition-factors(in lower case letters)

c#:==2^(11/3)_*3^-2*5^3/11_~= 1.00214... ~+0.21 % ~+3.7C worst-sh.
_d:==2^(4/3)__*3^-2*5^2/7__~= 0.99994... ~-0.006% ~-0.1C best-fl.
eb:==2^(17/6)_*3^-4*5^3/11_~= 0.99989... ~-0.011% ~-0.1C flat
_e:==2^(20/3)_*3^-4*5^3/157~= 0.9986.... ~-0.14 % ~-2.4C flat
_f:==2^(5/6)__*3^+1*5^3/667~= 1.00176... ~+0.17 % ~+3.0C sharp
f#:==2^(11/3)_*3^-2*5^3/11_~= 1.00214... ~+0.21 % ~+3.7C worst-sh.
_g:==2^(13/6)_*3^-1*5^3/187~= 1.00041... ~+0.04 % ~+0.7C best-sh.
g#:==2^(5/4)__*3^-3*5^3/11_~= 1.00101... ~+0.10 % ~+1.7C sharp
_a:==2^(9/2)_ *3^-4*5^2/7__~= 0.99768... ~-0.23 % ~-4.0C worst-fl.
bb:==2^(41/12)*3^-1*5^2/89_~= 0.99988... ~-0.011% ~-0.2C flat
_b:==2^(17/3)_*3^-3*5^2/47_~= 1.000725.. ~+0.07 % ~+1.2C sharp

into Lehmans 2005 "Rosetta-Stone" reinterpretation by mutilying
them simply with the above 1998 original:

C*c__:==2^0_____/3^0 == 1
C#*c#_:==2^(5/3)_/3__ ~= 1.0582...
D*d__:==2^(10/3)/9__ ~= 1.1199...
Eb*eb_:==2^(11/6)/3__ ~= 1.1879...
E*e__:==2^(20/3)_/81_~= 1.2543...
F*f__:==3/2^(7/6)___ ~= 1.3363...
F#*f#_:==2^(11/3)/9__ ~= 1.4110...
G*g__:==2^(13/6)/3__ ~= 1.4966...
G#*g#_:==2^(9/4)_/3__ ~= 1.5856...
A*a__:==2^(11/2)/27_ ~= 1.6761...
Bb*bb_:==2^(28/12)/3_ ~= 1.7798...
B*b__:==2^(17/3)/27_ ~= 1.8813...
C'____:==2^1/3^0_____ == 2

by easy undergaduate maths-level.

In 1998 i assumed by mistake Gottfied Silbermanns Dresden 1725
tuning-fork of 420 Hz guessing its frequency wrongly
as Bachs normal pitch of a' for the 1722 WTC, also
confirmed by Sauveurs 1704 determaination of c"=500 Hz standard.
But meanwhile Bruce Haynes has reconstucted Bachs
intended normal Cammerthone pitch more preciesely:
http://www.goldbergweb.com/fr/magazine/essays/2005/06/31980_8.php
He made an convincing correction down to a'=~410 Hz absoulte, well
agreeing with my recent g'=410 Hz Werckmeister reconstruction at
the respecting cornetthone level at a'=456Hz:

/makemicromusic/topicId_11464.html#11491

C 2173 Hz start absolute begin
G (6561)6560,3280,1640,820,410,205(204,102,51) Cammerthone=410Hz
D 153(152,76,38,19)
A 57 Chorthone 456Hz:=57Hz*8, 3 octaves above 57 Hz
E 171
H 513(512,256Hz,128,..,1)
F# 3
C# 9
G# 27
D# 81
B 243
F 729
C 2173 cycle closed

PC=3^12/2^19=(6561/6560)(205/204)(153/152)(513/512)=531441/528244

so the formerly wrong 420Hz must be excluded now and has
be abandoned and replaced by the lower
Haynes woodwind cammerthone 410 Hz compatible to Werckmeister:
in the now actual valid 2005 version:

A3 = 205,410 Hz :=a' or A4 absolute begin
E4 = 307,614(615:=A3*3)
H2 = 115,230,460,920(921:=307*3)
F#1= 43,86,172,344(345)
C#3= 129
G#4= 387
D#6= (145,290,580,1160)1161:=387*3
B4 = (217,434)435
F5 = (325,650)651
C6 = (487,974)975
G6 = (365,730,1460)1461
D6 = (547,1094)1095
A4 = 410,820,1640(1641)

the last concluding 5th D>A
flatness amounts (1095/1094)*(1641/1640)=657/656
hence the PC is subdivided into 9 superparticular factors:
3^12/2^19=531441/524288=
(615/614)(921/920)(345/344)(1161/1160)(435/434)(651/650)(975/974)
(1461/1460)(657/656)

have a lot of fun with that tunings
A.S.