Schweben

Just doing a drive-by posting after Thomas Dent alerted me to the fact
that there was some discussion of my translation of Werckmeister and
the problem of the word "Schweben", postings which I have now read in
the meantime.

All I can say is that if you read Neidhardt - the treatises Thomas has
posted on the tuning wiki - there can be absolutely no doubt
whatsoever that, at least for him, Schweben meant the amount of
tempering an interval bears, NOT the beating. He talks about adding up
the "Schweben" of various fifths and if the sum is such and so the
result is so and so. It all ONLY makes sense when the things you are
adding up are the comma fractions. So Schweben meant "degree of
tempering" - punkt schluß!

Modern Germans think it means beating, but that is only because they
have been confusing the issue for a century or so. So don't go ask a
modern German what he thinks. Just read Neidhardt.

I don't like the suggestion "suspended" because it doesn't work very
well with fifths larger than pure. Suspended things are hanging, which
means down only.

Frankly, I don't see the problem with just a good literal translation
- hovering. Why cast about for anything else? The helicopter can hover
over the crime scene or under the bridge. What's the problem?

OK, back into hibernation to finish writing my book on my newly
discovered ultimate method of tempering by ear. As I already told
Thomas, it can be found be reading between the lines of Werckmeister
and Neidhardt, and has the following characteristics:

(1) It does not use any absolute beat rates, and therefore works at
any pitch level: French opera tone, Kammerton, Chorton, Hoch Chorton,
even the "exotic Venetian" pitch.

(2) It does not require the tempering of any major or minor third,
even to do things like 1/5 or 1/6 or 2/7 comma meantone.

(3) It does not rely on the comparison of beat speeds of any two
intervals, neither fifths nor thirds (nor their inversions), adjacent
or disjunct. None of that 3 beats of G-D for ever 2 beats of C-G and
that sort of nasty complicated mucking about.

(4) The individual steps of the tempering process are not octave
specific, that is, at any point within the tempering procedure, you
can go up or down an octave if the beating is too slow or too fast to
manipulate; the specific instruction for that step in the process and
the exact procedure remains exactly the same no matter which octave
you are in.

(5) It doesn't mater which pair of beating harmonics you are listening
to when tempering a fifth; 3 against 2, 6 against 4, 9 against 6,
whatever you can hear best can be used, and in all cases by following
exactly the same instruction.

(6) Devising a recipe for any temperament is significantly easier than
solving your average sudoku puzzle - even for the Neidhardts and
Sorges, or Young's 3/16 S. comma, or Werckmeister's +/- 1/4 P. comma.
No complicated math of any kind is required - no computer, no
calculator, no slide rule, no abacus. Your average 8 year old could do
it with pencil and paper in a couple minutes.

(7) It requires no technological assistance of any kind, not even a
monochord, though the most ancient and simple time marking device is a
handy method for honing your skills.

Anybody guess how it works? Write me off-list if so.

Happy Trails!

Ciao,

P

Paul wrote: "Just read Neidhardt."

Thanks for the drive by. But I have been trying to find a copy of Neidhardt
for years, now. Any help would be most appreciated. Rudolph Rasch never
got to his plan to make it available, and I have not found it in any NYC
libraries.

I make it my habit to own the great writings on tunings, and I have most all
of them, except for the Neidhardt writings.

all best, Johnny

p.s. Anyone?

************************************** See what's new at http://www.aol.com

Hi Paul, thanks for dropping in. I'm with you on
literal translations.

> OK, back into hibernation to finish writing my book on my newly
> discovered ultimate method of tempering by ear.

Not an effective way to disengage from conversation around here!!

-Carl

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Paul wrote: "Just read Neidhardt."
>
> Thanks for the drive by. But I have been trying to find a copy of
Neidhardt
> for years, now. Any help would be most appreciated. Rudolph
Rasch never
> got to his plan to make it available, and I have not found it in
any NYC
> libraries.

Well, the major excerpts have been available freely on the web since
December 2005, when somebody kindly put up both a scan and a
transcription here:
http://harpsichords.pbwiki.com/Tuning

And I've had them linked from my page
http://www-personal.umich.edu/~bpl/larips/errata.html
since about the week after that, along with a bunch of other
clarifications, plus some detailed corrections of both the Barbour
book and Lindley's _New Grove_ article about the Neidhardt temps.

As for all the Neidhardt 1732 temps, working from that online
facsimile and transcription, I've had a document of all of them here
since October 2006:
http://harpsichords.pbwiki.com/f/Neidhardt_1732_Charts.pdf

I've done almost all of them myself on harpsichords, by now across
the past couple of years, without bothering to count any beats
anymore but rather taking them as simply knowing what a sensation of
single/double/triple "twang" sounds like in quality.
http://www-personal.umich.edu/~bpl/larips/twang.html

This stuff is not hard. I demonstrated it last Thursday to a
freshman music theory class at St Olaf College, and they could hear
what I was talking about immediately on the harpsichord sitting
there. The 5ths/4ths are either noticeably tempered (i.e. double),
scarcely tempered (i.e. single), or none. No need to *count*
anything, but only to have a musical skill. It's an analog skill,
not a digital one. Counting beats down to the Nth is pretty much
worthless anyway, since the harpsichord's intonation is going to move
around a bit within the hour or two after it's tuned, or day to day
or week to week. Measuring any frequencies numerically is even more
worthless (an exercise in futility), from this practical point of
view. Tune the whole instrument in 10-15 minutes by ear, be done,
and spend the rest of the time playing music!

I too would like to get a copy of Neidhardt's whole document...but
those several chapters at the pbwiki site are an excellent start.

Brad Lehman

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> Just doing a drive-by posting after Thomas Dent alerted me to the
fact
> that there was some discussion of my translation of Werckmeister and
> the problem of the word "Schweben", postings which I have now read
in
> the meantime.
>
> All I can say is that if you read Neidhardt - the treatises Thomas
has
> posted on the tuning wiki - there can be absolutely no doubt
> whatsoever that, at least for him, Schweben meant the amount of
> tempering an interval bears, NOT the beating. He talks about adding
up
> the "Schweben" of various fifths and if the sum is such and so the
> result is so and so. It all ONLY makes sense when the things you are
> adding up are the comma fractions. So Schweben meant "degree of
> tempering" - punkt schluß!
>
> Modern Germans think it means beating, but that is only because they
> have been confusing the issue for a century or so. So don't go ask a
> modern German what he thinks. Just read Neidhardt.
>
> I don't like the suggestion "suspended" because it doesn't work very
> well with fifths larger than pure. Suspended things are hanging,
which
> means down only.
>
> Frankly, I don't see the problem with just a good literal
translation
> - hovering. Why cast about for anything else? The helicopter can
hover
> over the crime scene or under the bridge. What's the problem?
>

Paul --

The problem with using a progressive verb like "hovering" (or
"floating" which was the choice of my wife and son, both native
bilinguals) is that it suggests motion; the tempered tuning clearly
stops at some point and we clearly wish it to be distinct from the
periodic and motive qualities of "beating".

"Suspension" is not only hanging from above: in chemistry or
topology, it's from both sides, and in a legal context, it's a
halting or a delay in time. Even the musical voice-leading usage is
normally a suspension above (the retardation ^7-^8 excepted).

djw

Dr. Daniel Wolf
Komponist
Frankfurt, Germany