--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> translated:
>...I may also let the fifths be, as described in the
> monochord, some pure and some tempered, which also goes quite well. I
> also wanted to give another such small division [Bruch] so that the
> fifths are all tempered a little one with another on the monochord;
> [I] also wanted to depict the partition but because such divisions are
> tiresome to construct with the compass and the ingratitude much too
> great, so I have misgivings to write any more about it; primarily
> because it requires [a] publisher and expense. But since sensation
> [and] reason are the judges, so [one] has from my monochord or
> ``sensus'' so much information, that he can well find his feet and
> manage for himself, and there is the self-evident proof in it, to see
> and hear what is certain; > ... More when I get round to it!
>
Dear Tom,
alike Zarlino & others bevor him,
W. divided the SC=80:81 regulary into:

2 parts: (160/161)(161:162) alike Kirnberger 3 inbetween D-A-E
3 parts: (242:243)(242:241)(241:240) alike Stanhope inbetw: G-D-A-E
http://groenewald-berlin.de/text/text_T041.html
Groenwald confuses in his reprenstation PC versus SC.
see: Lindley's "Stimmung & Temeratur"
or
http://launch.groups.yahoo.com/group/tuning/message/75760
"it is also possible to read Werckmeister's #3 pattern

C~G~D~A E B~F#...C

in 1/3 SC terms:

C 242/243 G 241/242 D 240/241 A E B 32768/32805 F# C# G# D# Bb F C
"
http://launch.groups.yahoo.com/group/tuning/message/75449
"http://diapason.xentonic.org/ttl/ttl01.html
on p.37, Chap. XVII
when considering some arithmetical subdivisions of
81:81 for tempering:
"Wenn ein Comma in zwey Theile getheilt wird /
so stehen in kleinesten Zahlen 162. 161. 160.
In drey Theile sind die kleinsten Termini 243. 242. 241. 240.
So es in vier Theile gemachet; stehen die kleinsten Termini 324. 323
322. 322. 320. Die äussersten sind das comma...."
tr:
'If a comma is divided into 2 parts,
then arise in the smallest numbers 162. 161. 160.
In 3 parts the smallest termini become 243. 242. 241 240.
when made into 4 parts, the smallest Termini get 324. 323. 322. 320.
the outer ones represent the comma...'"

http://harpsichords.pbwiki.com/f/Kirn_1871.html
"Oder wenn man von C nach e 80 : 81 in vier Quinten vertheilen will,
kann es folgender Art geschehen:

C-G 216 : 323 temperirte Quinte = 2/3 - 1/324
216 : 324 reine Quinte
-------------------------------------
G-d 215 1/3 : 322 temperirte Quinte = 2/3 - 1/323
215 1/3 : 323 reine Quinte
-------------------------------------
A-e 214 2/3 : 321 temperirte Quinte = 2/3 - 1/322
214 2/3 : 322 reine Quinte
-------------------------------------
D-A 214 : 320 temperirte Quinte = 2/3 - 1/321
214 : 321 reine Quinte
-------------------------------------


Analogous
in generalizing W's concept of SC subdivisions Neidhardt obtained:
11 an corresponding epimoric subfactors:
(880:881)(881:882)(882:883)*...*(890:891)
so that:
Werckmeister11/Kirnberger11/Neidhardt11's approx. of 12 ET yiels:

F# 32805:32768 C# 890:891 G# 889:890 Eb 888:889 Bb...
...A 882:883 E 881:882 B 880:881 f#

That makes in modern 20th century TUs = PC(1/720) units:

F#
schisma:
(720TU*ln(32768/32805) / ln((3^12) / (2^19)) = ~-59.9607138...TUs
C#
(720TU * ln(890 / 891)) / ln((3^12) / (2^19)) = ~-59.665901...TUs
G#
(720TU * ln(889 / 890)) / ln((3^12) / (2^19)) = ~-59.732979...TUs
Eb
(720TU * ln(888 / 889)) / ln((3^12) / (2^19)) = ~-59.8002081...TUs
Bb
.
.
.

.
.
A
(720TU * ln(882 / 883)) / ln((3^12) / (2^19)) = ~-60.2067818...TUs
E
(720TU * ln(881 / 882)) / ln((3^12) / (2^19)) = ~-60.2750822...TUs
B
(720TU * ln(880 / 881)) / ln((3^12) / (2^19)) = ~-60.3435377...TUs

Espeically for those in that group here that do claim to be able to
tune 12-EDO stepwise in that precision,
or even an alleged "Squiggle"-reinterpretation
in exactly 60TUs steps, without sligthest error in deviation.

I.m.h.o:
It's an modern absurd oversimplification
to impute that Bach had only tempered barely in 60TU steps.
Completely ahsitorically!

Yours Sincerely
A.S.