--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@>
> wrote:
> > on my proposal:
> > C
> > temper down:(1 200 * ln(565 / 567)) / ln(2) = ~-6.11744117...Cents
> > G
> > temper down:(1 200 * ln(563 / 565)) / ln(2) = ~-6.13913427...Cents
> > D
> > temper down:(1 200 * ln(561 / 563)) / ln(2) = ~-6.16098177...Cents
> > A
> > E
> > B
> >lower(1200*ln((560/561)*(32768/32805)))/ln(2)=~-5.04245318...Cents
> > F#
> (...)
>
> Please state your present position clearly.
I overtook my current point of view about the
wrong PC^(1/4) re-interpretation from:

Johann Mattheson's
"Grosse Generalbass Schule"
'Big thourough basso contiuo school'
2nd. Ed.
Hamburg 1731,
facsimile reprint: Hildesheim 1968
on p. 164, footnote a;
"Seit 1691 stehet dieselbe scala...
...vor Werckmeisters Buch von der Temeratur...
...daß sie nun bey nahe 40. Jahren nichts daran zu tadeln gefunden
hat. Jetzo aber,..,wirft man sie alsbald in den logarthmischen
Schmeltz-Tiegel, wendet sie zu einem Gebrauch an, dazu sie keines
Falles verfertiget worden..."

tr:

'...about W's temperature...
...now there had nothing to citicize about that for almost 40 years.
But now: it had been be thrown in at the deep end of the
logarithmic melting-crucible, abused in a way,
that was never intended at the time of its invention..."


Similar excludes
http://de.wikipedia.org/wiki/Daniel_Gottlob_T%C3%BCrk
PC^(1/4) for Werckmeister by giving and discussing
the following approximative stringlengths in his:

http://dispatch.opac.d-nb.de/DB=4.1/LNG=DU/LRSET=1/SET=1/SID=a43c2c1f-0/TTL=1/SH\
W?FRST=4
ISBN: 3-910019-14-5
pp. 477-482

C 8192
# 7776
D 7331
# 6912
E 6540
F 6144
# 5832
G 5480
# 5184
A 4905
# 4608
C 4096

also given in the edition
http://diapason.xentonic.org/ttl/ttl01.html
on p.40.

that's in 5ths:

C 2048/2055 G 21920/21993 D 14662/14715 A-E-B 2180/2187 F#C#G#D#A#FC
or
C ~-5.91cent ~G~ 5.76cent ~D~ 6.25cent ~AEB~ 5.55cent F#...C

even Kellner disagrees also with PC^(1/4) too:

http://members.pcug.org.au/~apurdam/tempers.html

pseudo- "Werckmeister III"
0
90
192
294
390
498
588
696
792
888
996
1092
1200

vs:
Werckmeister(Kellner)
0
90
195
294
389
498
588
697
792
892
996
1091
1200

or:
C 697 G 698 D 697 AEB 697 F#...C


Does anybody here in that group knows K's original ratios of that?

http://launch.groups.yahoo.com/group/tuning/message/27024
"By COMMA Werckmeister meant
in this context just any MICRO-INTERVAL!!
There exits no neutral comma with Werckmeister, but he utilizes
MICRO-INTERVALS of various sizes, whereever necessary."

> I want to be sure I
> understand this.
read:
Mark Lindley (in his 'Stimmung &Temperatur') on Zarlino's 2/7-SC:
facsimle on p.166

a 567
c 566
f 565
g 564
h 563
i 562
k 561
c 560


> Are you asserting that you now believe Bach's
> drawing at the top of the WTC title page is meaningless as to
> tuning,
Not at all,
as long as JSB's 11-eyes become interpreted as:
C~G~D~AEB~F#...C

> and that Bach simply slammed Werckmeister's most famous layout onto
> his harpsichords
right!

but certainly not
> more or less sloppily
> i.e. with the tempered 5ths logarithmically equal
that can be excluded.


and B-F# noticeably less tempered than the
> other three)?
alike Tuerck did so too.
>
> Or are you saying something else?
C 2/7sc G 2/7sc D 2/7sc AEB 2/sc+schisma F#...C

A.S.