Devie's mysterious Werckmeister-Vallotti

... This will not be of interest to most people - who can stop reading
immediately - but there was an old debate about where the following
statements came from:

"VALLOTTI" (...)
This simple 17th century Venetian temperament was known to
Werckmeister in the 1680s, and resurfaced at various times later. It
gets its name from mid-18th-century use by Vallotti and Tartini.
(...)
"Werckmeister III" is really a 1/6 comma temperament (!) disguised as
a 1/4 Pyth comma temperament. It was Werckmeister's attempt to improve
upon this particular Venetian scheme, and on the regular 1/6 comma
meantone behind it.

(from larips.com)

and

"Werckmeister himself had already remarked about the circulating
temperament shape we know as 'Vallotti' (...), referring to it as an
ordinary Venetian temperament, in 1681: long before Vallotti, Tartini
or Barca did."

(from Lehman, Early Music May 2005)

These are referred back to Devie p.136 - a subhead called 'De
Werckmeister a Bach' (From Werckmeister to Bach).
We have (please excuse lack of accents) :

"Notons en passant que Werckmeister a decrit en 1681 un temperament
prefigurant le temperament venetien, elabore beaucoup plus tard par
Vallotti et Barca. Cette decouverte est due a Jean Bosquet. J'en ai
fait mention, plus explicitement, dans le chapitre traitant des
speculation sur le temperament de Bach."

This says - 1) in 1681 Werckmeister described a temperament
*anticipating* the Venetian temperament developed much later by
Vallotti/Barca. Or to put things another way: Vallotti/Barca
reinvented a Thuringian temperament that was described much earlier by
Werckmeister. - 2) This (extra temperament of Werckmeister) was
discovered by Jean Bosquet.

It does not say Werckmeister described or remarked on or referred to a
Venetian temperament in 1681.

There is more detail in the chapter on Bach-temperament-speculations.
So we should look at p.166 as well. There we get:

"Di Veroli (...) propose d'utiliser le temperament de Vallotti-Barca
ou celui de Young. Il ne semble pas s'etre rendu compte qu'une formule
de ce genre avait deja ete decrite par Werckmeister (Orgelprobe,
1681). On doit cette decouverte a Jean Bosquet. Elle figure dans un
texte intitule 'Histoire et representation synthetique des
temperaments', encore inedit lorsqu'il me fut communique.

[Quotation from Bosquet]: Il (Werckmeister) propose un temperament que
l'on peut considerer comme issu du mesotonique mais, d'emblee, il va
tres loin en faisant litteralement eclater la quinte du loup qui se
repartit sur 6 quintes de 703 cents (a partir de Mi) justes a 1 cent
pres. Les 6 autres quintes sont egales (697c). [End quotation]

Ainsi, les 6 quintes de Fa a Si sont alterees. Les autres sont pures.
Les meilleures tierces sont celles de Fa, Do et Sol ; les plus
mauvaises (pythagoriciennes), sur Fa#, Do# et Sol#."

This gives more details, but appears internally inconsistent. It
quotes Bosquet (a manuscript that is still unpublished) to the effect
that Werckmeister put forward in Orgelprobe (1681) a temperament with
6 wide fifths [!] of 703 cents each, within 1 cent of pure, starting
from E ('a partir de Mi'), with the other 6 being equal to 697c.

Then Devie says that 'the 6 fifths from F to B (de Fa a Si) are
altered, the others are pure'. This is precisely Vallotti/Barca.
However it differs from Bosquet's description. First,
Bosquet/Werckmeister's 6 non-flat fifths are not pure, they are 1 cent
wide. Second, Bosquet says that the wide fifths begin from E.

Bosquet's claim will be news to anyone who has studied the 1681
Orgelprobe. It seems to me unlikely that Werckmeister could have
described fifths that were 1 cent wide in any clear or unambiguous
way. According to other sources the smallest amount of temperament he
was considering then, or at least writing about, was 1/4 comma - even
then he did not give any method to achieve the tempering accurately.

Let's suppose for a moment Bosquet was correct. He says Werckmeister
in 1681 put forward a certain temperament with 6 flat fifths and 6
very slightly sharp ones. He does not say anything about 'Venetian
temperament', although it is a reasonable observation (made by Devie)
that this mysterious extra Werckmeister temperament is similar in
structure to Vallotti's.

In the end nothing in Devie's text says or suggests that Werckmeister
wrote on the subject of a Venetian temperament in 1681. The whole
thing was a simple misreading of a fairly simple sentence in French.

The same seems to be true of the pleasing claim that 'Vallotti with 6
pure fifths is like a bad haircut' attributed to Devie. What he
actually said was (after giving the 'simplified' 1770 version with 6
pure fifths):

"La version Barca de 1802 avec schisma partage figure a la page
suivante. On notera on passant la tendance abusive des acousticiens a
<< couper les cheveux en quatre >>."

The phrase at the end doesn't mean haircut, it means hair-splitting.
http://fr.wiktionary.org/wiki/couper_les_cheveux_en_quatre
Devie is saying that Barca's version dividing the schisma into 6
amounts amounts to hair-splitting, typical of acousticians. Or perhaps
that the difference between the two versions is hair-splitting...
~~~T~~