Yahoo Tuning Groups Ultimate Backup tuning New Telemann page

Hi Manuel,

> From: <manuel.op.de.coul@eon-benelux.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 09, 2001 6:30 AM
> Subject: [tuning] New Telemann page
>
>
> Thanks to Johnny's attentiveness in a bookshop,
> I could buy a copy of a book about Telemann with
> the article about his tuning system, which he wrote
> at age 86. It has been discussed on the list during
> the past months.
> I've put it on a webpage with some comments:
> http://www.xs4all.nl/~huygensf/doc/telemann.html

Thanks so much for doing this! It's quite amazing:
I was just thinking the other day of sending an email
to Johnny to ask him to copy these pages and send them
to me. I've been researching the "9 commas per whole-tone"
idea for over a month now, and really wanted to see this
Telemann work again, and to translate and understand it.
I've been working on it already since you announced this...

It seems to me too that Telemann intended a 44-tone subset
of 55-EDO, or something similar to it. I wonder why he
settled on a 44-tone subset. ...?

His system is clearly *not* 43-EDO, because as I just showed
yesterday in my "meride" page update, Fbbb and C### are audibly
equivalent in that cycle, and they are clearly two separate
sounds in Telemann's table. Also, the 43-EDO "chromatic semitone"
is 3 commas and not 4.

It's unusual to me because the "chromatic semitone" is
*not* divided into 4 parts using only the pitches Telemann
gives in his table... that requires the other 11 pitches of
55-EDO which he leaves out.

I'm looking forward to spending more time with this.
Thanks!

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:
>
> Thanks to Johnny's attentiveness in a bookshop,
> I could buy a copy of a book about Telemann with
> the article about his tuning system, which he wrote
> at age 86. It has been discussed on the list during
> the past months.
> I've put it on a webpage with some comments:
> http://www.xs4all.nl/~huygensf/doc/telemann.html
>
> Manuel

Let's see . . .

>Telemann divides the chromatic semitone into four commas, and the
>whole tone in nine commas. He explains that sharps and flats are not
>the same and that sharps are lower: C (ces) is lower than D (déb).
>He doesn't say which comma he means, the syntonic or Pythagorean
>comma. This doesn't matter much since they are almost the same, and
>at that time the distinction was often not made. So ces is four
>commas higher than C and cex four commas higher than ces, etc. On
>page 272 he states that the whole tones stride in equal pace, so
>they are all 9 commas wide. What he doesn't specify unfortunately is
>the size of the diatonic semitone (distance of E to F and B to C).
>Is it equal in size to the chromatic semitone, 4 commas or a comma
>larger, 5 commas?

Manuel, the diatonic semitone is equal to the whole tone minus the
chromatic semitone, by definition. So it's 5 commas -- no ambiguity
whatsoever.

>The former possibility leads to a system comparable to 53-tone equal
>temperament in that the tones of his system form a subset of 53-tET
>or something close to it. In 53-tET, there are 9 steps in the whole
>tone and 4 in the diatonic semitone: 5×9+2×4=53 and the fifth is
>virtually pure.

Manuel, Telemann's description is clearly not compatible with 53-tET,
since the chromatic semitone is 5, not 4, in 53-tET.

>So I think we should be cautious to consider Telemann's system as a
>rigid prescription of a 55-tone equal tempered basic scale.

Right -- it could be any tuning with fifths averaging approximately
698 cents.

Looking at the table on page 267 we see 7×6+2=44 different names.

Aha -- I didn't notice that he had left 5 blanks before!

>Telemann says nothing about any equivalences between the tones of
>his system. Putting them in ascending order using the 55-tET step as
>the comma indeed gives no enharmonic equivalences. All the tones
>belong to one long cycle of 43 tempered fifths, 22 from C in the
>downward direction and 21 in the upward direction.

Whoa -- well that's an important finding, Manuel! This certainly
gives further evidence that the tuning is generated as a chain of
(tempered) fifths, and not conceived in some non-meantone way that we
haven't thought to consider.

P.S. A correction: There is no real evidence that Mozart intended 1/6-
comma meantone rather than 1/5-comma or some other meantone system.
It wouldn't make much sense for one to be that specific in regard to
Mozart anyway, since he clearly assumes enharmonic equivalence even
in a few passages for strings unaccompanied by keyboard, which
violates his known violin teaching altogether.

🔗monz <joemonz@yahoo.com>

> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 09, 2001 5:44 PM
> Subject: [tuning] Re: New Telemann page
>
>
> --- In tuning@y..., <manuel.op.de.coul@e...> wrote:
>
> > http://www.xs4all.nl/~huygensf/doc/telemann.html
>
>
> > So I think we should be cautious to consider Telemann's
> > system as a rigid prescription of a 55-tone equal tempered
> > basic scale.
>
> Right -- it could be any tuning with fifths averaging
> approximately 698 cents.

At the bottom of page 269, Telemann clearly explains in a
musical illustration the following:

1 3 1 4 4 = number of commas between pitches
C Dbb C# Db D D#

The 12-EDO "5th" size of 700 cents of course provides only
one semitone-sized step between chromatic pitches, so Telemann's
"5th" must be narrower than this.

The 55-EDO "5th" size of ~698.1818182 cents is the only one
which gives exactly equal step sizes which fit Telemann's
descriptions.

At the 43-EDO "5th" size of ~697.6744186 cents (= 2^(25/43) ),
there are no longer 4 commas between chromatic pitches but
only 3.

The 31-EDO "5th" size of ~696.7741935 cents (= 2^(18/31) )
provides only 2 steps between chromatic pitches.

Depending on how far one takes the cycles, various sizes of "5th"
less than 700 and greater than ~696.7741935 cents, except the
one of 43-EDO, will give 4 commas per chromatic semitone.
Between 43- and 31-EDO, the pitches at the more extreme ends
of the cycle switch position (bbb become higher than ###, etc.).

> > Telemann says nothing about any equivalences between the tones of
> > his system. Putting them in ascending order using the 55-tET step as
> > the comma indeed gives no enharmonic equivalences. All the tones
> > belong to one long cycle of 43 tempered fifths, 22 from C in the
> > downward direction and 21 in the upward direction.
>
> Whoa -- well that's an important finding, Manuel! This certainly
> gives further evidence that the tuning is generated as a chain of
> (tempered) fifths, and not conceived in some non-meantone way that we
> haven't thought to consider.

Based on what I've gotten out of the Telemann article so far, it
seems pretty clear to me that he intended a meantone cycle based
on either 55-EDO or 1/6-comma.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

🔗manuel.op.de.coul@eon-benelux.com

I wrote that Telemann didn't mention in the article that
the dimished fourth is different from the major third.
I found this in another place in the book, in a letter to
Carl Heinrich Graun from 15 December 1751, page 248.
He says D#-Fx is a major third, and D#-G a diminished fourth
(or "smallest fourth" in his terminology). And that "just
because from these keys, in both cases, in the present-day
temperament, a healthy harmony originates, I don't see why
one should make the remaining ones into invalids".

Paul wrote,
>Manuel, Telemann's description is clearly not compatible with 53-tET,
>since the chromatic semitone is 5, not 4, in 53-tET.

I know, but I was being careful, after all the paper's title
was "Neuen musikalischen Systems".

>P.S. A correction: There is no real evidence that Mozart intended 1/6-
>comma meantone rather than 1/5-comma or some other meantone system.

Thanks, I'll update the page.

Manuel

🔗manuel.op.de.coul@eon-benelux.com

🔗Paul Erlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

Hi Paul,

> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, November 12, 2001 5:40 PM
> Subject: [tuning] Re: New Telemann page
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > From: Paul Erlich <paul@s...>
>
> > > Right -- it could be any tuning with fifths averaging
> > > approximately 698 cents.
> >
> >
> >
> > At the bottom of page 269, Telemann clearly explains in a
> > musical illustration the following:
> >
> > 1 3 1 4 4 = number of commas between pitches
> > C Dbb C# Db D D#
> >
> > The 55-EDO "5th" size of ~698.1818182 cents is the only one
> > which gives exactly equal step sizes which fit Telemann's
> > descriptions.
>
> But the "commas" need not have been exactly equal.

Yep... I noted several possibilities in the original post:
/tuning/topicId_30057.html#30091

I was expecting *you* to make a comment (and hoped that you
would), but wanted your comments to be based on the additional
info in *that* post.

As I said, I'm pretty much in agreement with both you and
Manuel that Telemann is clearly examining a meantone system
here, and one which closely approximates 1/6-comma or 55-EDO
if it is not exactly either one of those. But my guess is
that for the sake of simplicity 55-EDO is what he had in mind.

The curious thing for me is that he stopped at a 44-note cycle,
instead of exploring the whole 55-tone set, which is the main
reason that I grant the possibility that he may have had some
other tuning in mind; but even then, I think it was probably
1/6-comma (since that cycle *doesn't* close at either 44 or 55,
but *does* give the proper commatic differences between the
notes in his examples).

And this is the post giving details about the Telemann musical
examples of which I've made mp3's:
/tuning/topicId_30093.html#30093

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗Afmmjr@aol.com

🔗manuel.op.de.coul@eon-benelux.com

🔗BobWendell@technet-inc.com

Paul:
P.S. A correction: There is no real evidence that Mozart intended 1/6-
comma meantone rather than 1/5-comma or some other meantone system.
It wouldn't make much sense for one to be that specific in regard to
Mozart anyway, since he clearly assumes enharmonic equivalence even
in a few passages for strings unaccompanied by keyboard, which
violates his known violin teaching altogether.

Bob:
Thank you for bringing this to light, Paul. I believe it illustrates
a crucial point regarding the "over-interpretation" of historical
clues that I've tried to make a number of times before. I especially
refer to Johnny Reinhard and Bach's allegedly exclusive use of
Werckmeister's well-temperament even in non-keyboard contexts simply
because a modern interpreter's researches have indicated that Bach
favored it and because that same interpreter has also become enamored
of its harmonic/melodic properties and colors as they shift from key
to key.

🔗Afmmjr@aol.com

In a message dated 11/13/01 1:19:52 PM Eastern Standard Time,
BobWendell@technet-inc.com writes:

> Bob:
> Thank you for bringing this to light, Paul. I believe it illustrates
> a crucial point regarding the "over-interpretation" of historical
> clues that I've tried to make a number of times before. I especially
> refer to Johnny Reinhard and Bach's allegedly exclusive use of
> Werckmeister's well-temperament even in non-keyboard contexts simply
> because a modern interpreter's researches have indicated that Bach
> favored it and because that same interpreter has also become enamored
> of its harmonic/melodic properties and colors as they shift from key
> to key.
>

Dear Bob,

Sorry, Bob, though nice try. Running to generalizations does not make great
music. Bach is Bach and should not be confused with Mozart, or even
Telemann. Someday, very soon, I hope to present the evidence for Bach in a
book form. At this time, check the archives for lots of detail. As to your
surmise that I find the tuning of Werckmeister particularly seductive to my
modern ear and mind...I suspect you project your sensibilities on to me. I
am interested in the truth for Bach because it adds new dimensions to this
icon of music, and his performance aesthetic.

Johnny Reinhard

🔗BobWendell@technet-inc.com

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 11/13/01 1:19:52 PM Eastern Standard Time,
> BobWendell@t... writes:
>
>
> > Bob:
> > Thank you for bringing this to light, Paul. I believe it
illustrates
> > a crucial point regarding the "over-interpretation" of historical
> > clues that I've tried to make a number of times before. I
especially
> > refer to Johnny Reinhard and Bach's allegedly exclusive use of
> > Werckmeister's well-temperament even in non-keyboard contexts
simply
> > because a modern interpreter's researches have indicated that
Bach
> > favored it and because that same interpreter has also become
enamored
> > of its harmonic/melodic properties and colors as they shift from
key
> > to key.
> >
>
> Dear Bob,
>
> Sorry, Bob, though nice try. Running to generalizations does not
make great
> music. Bach is Bach and should not be confused with Mozart, or
even
> Telemann. Someday, very soon, I hope to present the evidence for
Bach in a
> book form. At this time, check the archives for lots of detail. As
to your
> surmise that I find the tuning of Werckmeister particularly
seductive to my
> modern ear and mind...I suspect you project your sensibilities on
to me. I
> am interested in the truth for Bach because it adds new dimensions
to this
> icon of music, and his performance aesthetic.
>
> Johnny Reinhard

Bob answers:
Hi, Johnny! Nice to hear from you. Been awhile. I suspected that this
might flush you out, although I was sincere in my "nice try"
(giggle). I truly don't think I'm guilty of "confusing" Bach with
Mozart or Telemann. I do think he ranks far above them, even above
Wolfgang Amadeus, and that's saying a lot.

It is clear that I am in some sense generalizing when I imply that
Leopold Mozart's apparent inconsistency might apply to Bach as well
as to everyone else. However, in my defense, I do not believe this to
to be an entirely rash or unthinking generalization, but rather that
it approaches something like what people mean when they talk about
common
sense.

In that regard, no one ever addressed a necessarily well-prefaced
question I posed quite some time ago in a post, but liberally
paraphrased here (since I don't feel like bothering to look it up):

I still have the impression that Bach wrote the Well-Tempered Clavier
to showcase the special properties of the Werckmeister temperament he
favored. His two- and three-part inventions never venture into the
remote keys that this work does. Instead the key signatures look
suspiciously like they accomodate some kind of regular, open meantone
temperament.

Admittedly, he could have done this out of deference to tuning
practice in the wider musical world around him, but I wonder why
you're so adamant about the exclusivity of his commitment to
Werckmeister? Your book will likely explain this in detail, but I
hope you'll forgive my impatience.

Incidentally, I'm quite sure that Bach would have written much that
exploits in exquisite detail the nature of Werckmeister's
temperament. This, however, does not constitute a convincing argument
for its exclusive use by Bach, especially in non-keyboard contexts.
Yes, you may be able to point out some of his non-keyboard music with
characteristics that sound idiomatic to Werckmeister. Nonetheless,
could not certain compositional habits sneak into it from having
composed so much with Werckmeister in mind?

I do not feel that this conjecture somehow demeans Bach's abilities,
in case you wish to argue that. He was human and subject to subtle
musical habits that reflected in his style, and I don't see how that
would denigrate his genius in any way whatsoever.

🔗Afmmjr@aol.com

In a message dated 11/13/01 4:36:49 PM Eastern Standard Time,
BobWendell@technet-inc.com writes:

> Incidentally, I'm quite sure that Bach would have written much that
> exploits in exquisite detail the nature of Werckmeister's
>

I just found a copy of "Bach Werke Verzichnis" in paperback in Amsterdam. It
has every motif Bach composed and I can indeed see how he exploits "in
exquisite detail the nature of Werckmeister's temperament." Glad to hear you
are curious to see the details to be unraveled.

Oh, and I never doubted the respect you have for Bach. However, common sense
often does give way to good sense.

:) Well, off to Toronto tomorrow. Hope I can read a bit while on the road.

Best, Johnny Reinhard