Re: [tuning] Werckmeister vs. Kellner.2

In a message dated 8/13/01 9:47:55 AM Eastern Daylight Time,
ha.kellner@t-online.de writes:

> Dear Johnny Reinhard,
>
> Thank you for your message. The lines below may interest you.
>
> Couldn't it appear then as madness to claim there exists an exact
> mathematical/technological specification of Bach's "wohltemperirt"
> harpsichord temperament???
>
And yes, some do think it madness for us to parcel things out in such fine
amounts. Ironically, that is what the Baroque temperament masters did, often
with beautifully drawn monochords, as was the one drawn for publication for
Werckmeister.

> For the (N+1)/N of 369, then results 370/369. This, as mathematics show,
> is the tempering for Bach's fifth.
> The most simple numbers pertaining to "Werckmeister/Bach/wohltenmperirt"
> are therefore are: 7, 5 the fifths, and 369, etc.
>

I am sorry I still do not understand, why is the number 369 evident from page
75 as the superparticular ratio for "improving" a harmony? This mysterious
harmony would then further mystify the players who were to be in tune with
it. Unless there is a reliable understanding, rather than a Soviet mystery,
the intonation will always be suspect.

> The 4 Duets, before my results impossible to explain, have ***369 *****
> bars; their midpoint being musically distinguished - look it up.
> That midpoint of the entire structure falls into Duetto II, its bar 112.
>
> 369= 185+1+185

In the few music works you have analyzed by J.S. Bach, why did you pick these
4 Duets?

As Duetto I has 73 bars, we have 73+112=185 for that central bar

> of the overall structure.
> Gematria converts CHRISTUS, overall central bar into 112 - the "mediator"!
>
> The Duetto II itself,
> 149 bars, is structured 37+75+37 bars.
> 7 perfect fifths+
> 5 fifths ""wohltemperirt".
>

So we find symmetry in Bach measures, that's to be expected. Can we
interpret by numbers indifferent ways, in myriad ways? Yes, that is done
with statistics for political persons. So what are rules of Gematria? Where
might it be referred to in Bach Documente? And where they find the time to
encrypt so efficiently?

> The 75 central bars are structured 75=31+13+31 - tri-unitary. In baroque
> times the triad was a musico-theological symbol. In particular, by
> Werckmeister's musico-theological speculations.
>
>
> The 37 framing bars are structured, again symmetrically, as 37=9+19+9:
> Therein, 9 is the trias trinitatis per additionem, 9=3+3+3, and
> 19 intervals, 12 fifths and 7 octaves in the reversed sense, close
> the circle.
>
>
I almost wonder if for a religious man like Werckmeister, he would be
"dishonest" by encrypting a true tuning camouflaged by Spam.

> Werckmeister invented "Bach/wohltemperirt":
> **************************************************
>

You may mean "Werckmeister lays hidden instructions for a composer he never
met to one-up his very own published tuning." But I do know what you mean,
that there is an agreement in the use of this mysteriously hidden insight.

> This final application below of Gematria for baroque musicology
> proves beyond doubt that Werckmeister considered by no means
> the "nominal system Werckmeister III" as optimal!

Werckmeister claimed nothing as optimal. He was open to many possibilities.
Once you admit the Werckmeister III tuning, for which he was always suspected
of having favored, is a treasure chest of many different European tunings
(e.g. variants of different meantones, Pythagorean, modes), then there is no
"optimal." It's the same realization Anaximander had when the Ionians put
all numbers together as equals. Discussions here of good and bad are out of
place.

> Could any person of esprit and competent in harpsichord
> tuning take seriously a system having within C-G-D-A-E three
> tempered and one perfect fifth?
> Could anybody explain to me what are the sufficient reasons
> NOT to equalize these four fifths??

This shows a bias to me, but not a true reasoning. What is wrong with a pure
A-E again? I'm not aware of any. A major is rather unused among keys. But
redistributing the comma fraction might not be so bad at B-F#. Might not
their be a melodic advantage, in this music of simultaneous melodies. Isn't
"temperatur" a setting for pitches, but not necessarily more harmonic than
melodic?

> blabla that just serves to push "Das XVIII. Capitel" onto page 75! If no
> really substantial material is available, and you work under the FINALITY
> to
> attain with Cap. 28 the page 75 of 7 perfect and 5 well-tempered fifths,
> haven't you then necessarily to be verbose???
>

Wow, that was a surprise, I never thought you would think of Werckmeister IV,
V, and VI as SPAM!
And Werckmeister's verbosity was intended to be directed at his paranoia of
future attacks, on his brown nosing, on his reputation for poor German, on
his lack of clarity, etc.

> My lifetime is, like of anybody else, limited; and so, at best will and
> intentions, I cannot retype here my thoroughly elaborated text of :
>

Herbert Anton, you have most generous with your information and I do hope to
read all I can on this subject.

> Sometimes, in fact, I eat carotte-tarts.
>
Now, you are making me hungry. ; )

> > Still, there is only "Werckmeister III" for the full
> > circle of keys in his Quedlinburg publication; the others are for a
> > swatch of keys, not intended for full 12-note chromaticism.
>
> For not-full-12-note chromaticism, may I recommend mean-tone!!!
>

Which one and why?

> Idem: Did Werckmeister already know the tuning of J.S. Bach for the "48"?
> English Harpsichord Magazine, Vol. 4, No. 1,1985, page 7-11
>
>

The is an oxymoron in lieu of the dates, but I do think that Werckmeister
picked up tuning specifics in Nordhausen, just south of his birth place, and
which has a nice respect for books. It is where Werckmeister studied Latin.
There he applied a CIRCUL of keys to his own music (as he was a composer),
and to the music of others. He was a well know player on keyboard, an organ
diagnostician, theologian, and mathematician. He married the daughter of the
mayor of the city he was working in.

Werckmeister IV, V and VI is nothing more and else than SPAM. And
> even more surely, if compared to the qualities of W. III, filling up by
> Werckmeister IV, V and VI the pages unto 75.
>

Thank you for being clear here. Though, why did not Werckmeister not offer
more prose Spam? Why NOT tell the truth, as we was sworn to as a Theologian?

> > Counting the letters at 11 and 11 for the title does not interest me much
> > either, I'm afraid.
>
> I respect your personal opinion - although this is not a very
> constructive one and, above all, - IMPO leads you to miss the essential
> point - assures to render yourself blindfolded!
>

Perhaps it will help to figure out how you assign numbers to letters. Could
you send this?

> > The final letter "e" of "Musicalisch eTemperatur" looks
> > wrong as a code.
>
> *This remark I do not understand at all. What could it possibly mean??
> *Where is there any "code"; what, explicitly, is wrong or looks wrong
> *here??**********************************************************
>

The title is only 11 and 11 if you count the last letter of the first word
with the second word. This looks wrong to my eye, especially as you have
deduced an equality. What is the code for each letter as to its number? Or
is it only the sum of the letters on a line, to be divided as best divined?

> Under the hypothesis, Werckmeister intended to encode at an unique
> opportunity his preferred system (ref. my EHM-articles above on
> Werckmeister), I would waste my lifetime to check into titles of his
> other treatises. I suggest you do it yourself and report here your
> observations and any results that you deem significant.
> Or do you really expect he would have encoded a second time something as
> interesting as the system "Werckmeister/Bach/wohltemperirt"? Could it
> possibly be an everyday' event to encode such features this subtle way
> into a title?
>

No, once would be enough. If he encoded, it would always be referred back
to. But to superimpose Werckmeister's titles with a modern slant would
surely show up at least a second one, and I don't think there is one. I've
seen all his titles and they are most imaginative, usually. He was a most
practical man, admired for his mathematical abilities. He came from a family
of musicians and ministers of the Church. Unless there is some hard evidence
that he would entertain something as drawn out of his plates by you as
SUPERIOR to what he invested his entire reputation on, still seems unlikely.
I wonder, do you think that the fact there is no visual image of
Werckmeister was intentional on his part?

> You do certainly know "QUAERENDO INVENIETIS" and thus, are familiar with
> baroque mentality. Also, Kuhnau's riddle in Gematria, from the preface
> of his Biblische Historien Sonaten has now been common lore for some time.
> Isn't it? Kuhnau utilizes, incidentally, the same gematria as Werckmeister
> or J. S. Bach.
>

No, no, and no. Anyone on List know these? What I do know is that Kuhnau
was friends with Werckmeister who lived not far away, and that J.S. Bach
succeeded Kuhnau in Leipzig.

> *The system "wohltemperirt" is the authentic one for "Das wohltemperirte
> *Clavier". You claim, it is indistinguishable from Werckmeister III.
> *Don't you realize that you are in CONTRADICTION with yourself, when
> *you "prefer" Werckmeister III - didn't you just claim, they are
> "INDISTINGUISHABLE"?

You misunderstand me.  Werckmeister III is superior from a contrapuntal point
of view, but perhaps not from a harmonic point of view.  From the melodic
view, the stretched 504 cents is more pronounced than the various in your
suggested tuning.

> And, in view of the properties of Bach's title,
> "Das wohltemperirte Clavier," seen together with its unexpected
> properties, parallel to Werckmeister's title - as a predecessor -
> "Musicalische Temperatur", it would be a vain effort to expect here any
> "technological" or specialized-jargon-experession.

Regarding the title, I would suggest Bach was in homage to Werckmeister
because he used his predecessor's term. The title, itself, is technical and
specialized, actually. And its usage makes manifest an historic recognition.
IMHO

> *It may take other 257 years for the general understanding and
> *acceptance that W. III wasn't taken seriously by Werckmeister himself.
> *As I describe in my publications, Werckmeister was an
> *amateur-mathematician in his leisure-time.
>
I heard that he was a mathematician, and highly respected, when researching
last year in Central Germany. Many of his writings are mathematical in
basis. And this workaholic could hardly of had much leisure time, certainly
as much as you and I seem to have this fine August.

> *Do not base yourself upon hearsay! Thereafter do then criticize
> *specifically any one of my writings in detail.
> It is, finally, amusing that Lenin said "utchitcyia, utchitcyia,
> *utchitcyia", which means "learning, learning, learning"!!!
>
> Kind regards,
>
> Herbert Anton Kellner
>

I'm all ears. Please, don't be so sure you have all the answers, either. As
a recorder player I will stay with WIII for the September 29th concert, but
for a later excursion on a keyboard work tuned to Kellner I, it is most
likely.

Kind regards, Johnny Reinhard