More from the harpsichord list on Bach's tuning

Date: Wed, 20 Sep 1995 07:36:43 -0500
Sender: Harpsichords and Related Topics
From: Paul Hahn
Subject: Re: Temperaments: request for references

On Sat, 16 Sep 1995, mcgeary thomas nelson wrote:
> Regarding reading material appropos temperaments, I would strongly
> suggest an underrecognized and appreciated article by Rudolph Rasch,
> "Does 'Well-Tempered'Mean 'Equal Tempered'?" in "Bach, Handel,
> Scarlatti: Tercentenary Essays, ed.by Peter Williams. In a very
> careful, meticulous manner Rasch looks at many myths, fictions,
> and misconceptions about temperament and Bach.

On your suggestion, I found and read this article. It's interesting,
but there are a few points that I think he doesn't argue as convincingly
as he thinks he does.

> some of his points (I'm
> recalling from memory) include: there is no reason to associate Werckmeister
> III with Bach (W. in fact had other temperaments, including ET);

This is true, and a lot of other writers mention ET as well. (But I do
find a little questionable when Rasch says "hey, look at all these
theorists who recommend ET" when he has obviously just gone through and
selected out the (equally) many who don't.) However, ET is really a
pretty obvious solution once you begin considering the question of the
disposition of the comma. OTOH, the most obvious method isn't always
the best one. ET is probably the hardest temperament of all to set
accurately by ear. Recall that Bach was reputed to be able to tune his
harpsichord in fifteen minutes. I'd like to see anyone who could set a
good ET in that time; even the best tuners I've seen take much longer
than that.

> there is no
> justification or rationale for the Barnes-Bach temperament (Barnes'
> methodology is subjective, his sample too [small]),

Rasch does raise some signficant issues about Barnes' work, but I would
note that Barnes says straight out in his own article that the sample is
too small to be conclusive statistically. But if we required the level
of rigor in musicology that physicists do, I shudder to think how many
(few) articles would get published.

> that all the contemporary
> statements about Bach's tuning practice (for stringed keyboards, of course)
> suggest equal temperament.

With all respect, the evidence is hardly as conclusive as Rasch would
have us believe. There are many possible interpretations even for
some of the evidence he cites. Example: he quotes the following
passage from Forkel's biography:

: Nobody could have any thanks for quilling his harpsichord for him; he
: always did it himself. Also the tuning of his harpsichord and
: clavichord was his own affair, and he was so practised in this work
: that it did not take him more than a quarter of an hour. But then,
: when he improvised, all twenty-four keys were his; he could do with
: them what he wanted. He connected the most remote keys together as
: easily and naturally as the nearest; one could believe he was
: modulating only in the inner circle of a single key.

He then concludes that the last two sentences indicate that all keys
sounded the same in Bach's tuning. However, is it not as plausible that
Forkel is praising Bach's skill in improvising smooth modulations?

> Two quotes Ihave ready-to-hand: "equal temperament
> was becoming the norm for tuning during the second half of the eighteenth
> century"

Too bad Bach died in 1750, huh?

To be fair, Rasch says this in order to argue that if WTK _were_ in fact
for an unequal temperament, those later theorists for whom ET was "the
norm" would have remarked on the fact. Still, those theorists didn't
have any more evidence than we do.

> and "equal temperament has been described and discussed so often
> in eighteenth-century writings as a practical system that it must have
> played an important part in musical performance."

See above. Just because it's an obvious theoretical solution doesn't
mean it was practical, or that there weren't other factors weighing
against it.

[snip the rest]

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."

------------------------------
Date: Thu, 21 Sep 1995 10:53:10 -0400
Sender: Harpsichords and Related Topics
From: John Sankey
Subject: Re: Temperaments: request for references

"Bach's keyboard temperament - Internal evidence from the
Well-Tempered Clavier", John Barnes, Early Music 7:236-49 (1979)
shows that the distribution of intervals even in the 48 is
nowhere near ET - it matches Werckmeister III better than any
other historical temperament.

Bill Sethares & I have submitted a paper to the Journal of the
Acoustical Society of America with an analysis of the temperament
of Domenico Scarlatti, but it hasn't got through the review
stage yet.

--
John Sankey bf250@freenet.carleton.ca
Music is Beauty, Beauty is Truth, Truth is Freedom

Johnny Reinhard wrote:

> Should we really disregard J.P. Kirnberger's assertion that to change the
> key of a composition into a distantly related key is to damage said
> piece? Keep in mind that Kirnberger did more to promote J.S. Bach than
> any of his kids.

We should remember also that Kirnberger was an opponent of equal temperament
and claimed that J. S. Bach did NOT use equal temperament. He even got a
corroborating letter to that effect from Bach's son Emanuel.

See:
Johann Philipp Kirnberger, Die Kunst des reinen Satzes in der Musik, (Berlin
and Koenigsberg: Decker & Hartung, 1774-79), facsimile repr. (Hildesheim:
Georg Olms, 1968), vol. ii, p. 188. This controversy is recounted in: Rita
Steblin. A History of Key Characteristics in the Eighteenth and Early
Nineteenth Centuries (Ann Arbor, MI: UMI Research Press), p. 92.

Bill Alves
alves@hmc.edu
http://www2.hmc.edu/~alves/

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Fri, 22 Sep 1995 22:09 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id NAA20944; Fri, 22 Sep 1995 13:09:22 -0700
Date: Fri, 22 Sep 1995 13:09:22 -0700
Message-Id: <00996CC07217D66C.20A2@ezh.nl>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

Re: Kirnberger's saying to Marpaug that "Bach tune each of his major
thirds sharp." This is true in both equal temperament _and_ Werckmeister
III. The Werckmeister III contains 4 sizes of major third, one of which
is equivilent to 402 cents, one that is Pythagorian at 408 cents,
one at 396 cents, and the smallest one at 390 - all sharper than the just
386 cents.

Further, Kirnberger himself gave directions for the tempered fifth whose
ratio (10935:16384) is almost exactly 1/12 of a comma smaller than the
pure fifth in several publications, including his *Von der Temperatur*.
The method by which he arrived was to take seven pure fifths in
succession plus one pure major third. This gives the tempered fourth
8192:10935, which is larger than the pure fourth by 1/12 of a comma, its
inversion is the tempered fifth 10935:16384.

According to Kirnberger he
showed this discovery to Leonhard Euler in 1766 and remarked to him that
this fifth could be used to determine all ratios of equal temperament,
an idea subsequently developed by Johann Heinrich Lambert and published
in the *Memoires de l'academie royale des sciences et belle lettres*
(Berlin 1774) and used by Marpaug against Kirnberger. (see p. 20 of the
*Art of Strict Musical Composition* by Kirnberger, Yale University Press)

There is great bitterness against Kirnberger, chief violinist and
keyboardist at the court in Berlin by Marpaug, the Lottery King Of Berlin.

Clearly, this argument of fifths over thirds is an aesthetic battle of
historic proportions. Politics enters at every level and success is oft
measured by clout. What intrigues me most about Prof. Rasch's
perspective is that the Netherlands has been a leader in performing
"early music" in historic intonation and as its main musical intellectual
in this area, Rasch bucked the trend. Perhaps if he were in any one of
the other countries that had been resistant to historic intonation
systems, he might have headed the other way.

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com


p.s. Manuel please forward as appropriate. Thank you.

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Mon, 25 Sep 1995 23:48 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id OAA25337; Mon, 25 Sep 1995 14:48:01 -0700
Date: Mon, 25 Sep 1995 14:48:01 -0700
Message-Id:
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

Bach was known for tuning everything himself and well within 15 minutes.
Though absolute pitch as evidenced by the gene for "perfect pitch" would
be quite ignored in the era before pitch standards, Bach could well have
worked out the finest distinctions of pitch differentiation. Most likely
on his favored clavichords.

Perhaps well temperament, with its myriad of tuning relationships, is
a prototype for the polymicrotonality I am composing. From German city to
German city there were different German tuning preferences in the
baroque period (e.g. Matheson-12ET-Hamburg, Handel-extended
meantone-cosmpolita, Silbermann-sixth-comma meantone-Dresden). Telemann
proposed a theoretical 5ET so that a circular sixth-comma meantone could
be obtained.

Essentially, Werckmeister III is an archetype for all future well
temperaments. When Werckmeister wrote in 1691 _Musical Temperament_ he
provided the first description of a "correct" tuning that played in a full
cycle of keys. Werckmeister first describes a divine just intonation
relationship between tones which is basically unreachable due to the
keyboard manual's arrangement. Werckmeister I is simple ratio just
intonation.

The second description of a temperament in "incorrect" ("unrichtige")
because it did not allow unrestricted modulation. Werckmeister
particularly frowns on the technology of split black (or sometime
inversely white) chromatic keys. Werckmeister II is quarter-comma
meantone.

The largest discussion in _Musical Temperament_ centers on what has come
to be known as "Werckmeister III". The author didn't name the "good
temperament" but merely described a popular tuning of the middle baroque
in Thuringia and throughout German lands (definitiely including
Danish-speaking Lubeck where Dietrich Buxtehude was an ardant Werckmeister
fan.) (And of course Bach almost lost employment for just taking off to
Lubeck to see Buxtehude play in person.)

Werckmeister embarrassingly met the charge that 12ET was nowhere to be
found in his privately-produced publication by claiming that the
"engraver" of his monochord drawings refused to draw it! (This is
described in the New Grove article "temperament." Though there are
alternate well-temperament arrangements outlined that might now be called
Werckmeister IV, V, and VI, these are given relative short shrift by the
author. Werckmeister III is the prominent well temperament tuning current
in Bach's Thuringia and is more than half the monograph.

J.S. Bach lived for a number of years with his cousin Johann Walter (an
organist, composer, author of the first major German language music
encyclopedia, and former student of Werckmeister). Walter would receive
letters and music from his older friend Werckmeister. Do you think Bach
could ignore the famous Werckmeister? He couldn't help but tune only to
his own satisfaction, clearly accepting on some level the pronouncements
of Thuringia's leading organ designer and organist of an earlier
generation. If Bach had been equal-tempered he would have
said so. If he was well-tempered, likewise he would say so, and he did.

Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM


SMTPOriginator: tuning@eartha.mills.edu
From: mr88cet@texas.net (Gary Morrison)
Subject: Re: Bach and lutes
PostedDate: 07-12-97 19:18:46
SendTo: CN=coul1358/OU=AT/O=EZH
ReplyTo: tuning@eartha.mills.edu
$MessageStorage: 0
$UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH
RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH
RouteTimes: 07-12-97 19:16:54-07-12-97 19:16:55,07-12-97 19:16:43-07-12-97 19:16:44
DeliveredDate: 07-12-97 19:16:44
Categories:
$Revisions:

Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2
9-3-1997)) with SMTP id C1256566.00646AF6; Sun, 7 Dec 1997 19:16:49 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA08678; Sun, 7 Dec 1997 19:18:46 +0100
Date: Sun, 7 Dec 1997 19:18:46 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA08677
Received: (qmail 9486 invoked from network); 7 Dec 1997 10:18:42 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 7 Dec 1997 10:18:42 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu