new Werckmeister webpage

to all:

i've made a webpage that i've been wanting to create for
years, with a detailed analysis of Werckmeister III
("Correct Tuning #1") and a list of pitches in his
"Correct Tuning #2" :

http://www.ixpres.com/interval/dict/werckmeister.htm

to Johnny,

thanks for the quick reply. ... however, it's still
not entirely clear. i think you made a typo here:
wouldn't "quarter-comma meantone with split keys"
be Werckmeister II?

i've been looking thru Barbour's book but can't find
any references to Werckmeister I or II. Barbour discusses
Werckmeister's "Correct Temperaments" Nos. 1, 2, and 3,
and also Werckmeister's "Septenarium" tuning. numbers
1 and 3 temper some 5ths by 1/4 of a Pythagorean comma,
#2 by 1/3 of a comma, and the Septenarium by 1/7 of a comma.

i'd appreciate some more about this from you, or anyone else
who has a copy of "Musicalische Temperatur".

Johnny, what do you mean by "...in Werckmeister III there
are no leading tones. It muddies the tuning fabric." ...?

here's a list of the 12 possible "leading tones" in
Werckmeister III (taken from my webpage); because
Werckmeister III is a closed 12-tone tuning, "black-key"
notes can be taken as either sharps or flats -- i'm using
the conventional naming here:

minor 2nd / augmented prime

107.820 B:C, A:Bb, E:F, F#:G
101.955 D:Eb, C#:D
96.090 G:Ab, Eb:E, Ab:A, Bb:B
90.225 C:C#, F:F#

the minor-2nds on the bottom row, which are the smallest
"leading tones" in Werckmeister III, are exactly the same
as the Pythagorean minor-2nd (3^-5) or _limma_, and more
than 14 cents larger than the 1/4-comma meantone augmented
unison (chromatic semitone).

the largest ones, those in the top row here, are
nearly 4 cents smaller than the JI 16:15 ratio and
more than 9 cents smaller than the 1/4-comma meantone
minor-2nd (diatonic semitone).

-monz
"all roads lead to n^0"

----- Original Message -----
From: <Afmmjr@aol.com>
To: <tuning@yahoogroups.com>
Sent: Saturday, September 07, 2002 8:51 AM
Subject: [tuning] New Werckmeister Tidbits

> In a message dated 9/7/02 11:40:42 AM Eastern Daylight Time,
> monz@attglobal.net writes:
>
>
> >
> > one question for Werckmeister experts: his most
> > famous tuning is continuously referred to as
> > "Werckmeister III", but Barbour lists it as
> > "Correct Temperament #1". ...????
> >
> >
>
> Hey Joe,
>
> Werckmeister considered JI too perfect (Werckmeister I)
> and thought that quarter-comma meantone with split keys
> incorrect (Werckmeister III). So, Werckmeister III is
> the first "correct" temperament in Barbour-language.
>
> Most interesting to me is that when playing in
> Werckmeister III there are no leading tones. It
> muddies the tuning fabric.
>
> Best, Johnny Reinhard
>

> From: "monz" <monz@attglobal.net>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, September 08, 2002 9:13 AM
> Subject: [tuning] new Werckmeister webpage
>

> http://www.ixpres.com/interval/dict/werckmeister.htm
>
> <snip> ...
>
> here's a list of the 12 possible "leading tones" in
> Werckmeister III (taken from my webpage); because
> Werckmeister III is a closed 12-tone tuning, "black-key"
> notes can be taken as either sharps or flats -- i'm using
> the conventional naming here:
>
> minor 2nd / augmented prime
>
> 107.820 B:C, A:Bb, E:F, F#:G
> 101.955 D:Eb, C#:D
> 96.090 G:Ab, Eb:E, Ab:A, Bb:B
> 90.225 C:C#, F:F#

oops ... that table should look like this
(G# instead of Ab):

minor 2nd / augmented prime
107.820 B:C, A:Bb, E:F, F#:G
101.955 D:Eb, C#:D
96.090 G:G#, Eb:E, G#:A, Bb:B
90.225 C:C#, F:F#

-monz
"all roads lead to n^0"