re What?

Hello Mario,

As a point of departure, there is nothing that connects J.S. Bach with equal
temperament. Nothing.

all best, Johnny Reinhard

> Mike takes again the reference of the failed equal tempered scale where ALL
> the tones are flat, it was criticized by its own adopter J. S. Bach and he
> also states that some of the Piagui flat fifths will be MORE out of tune
> than equal temperament and not less.

What?

I suppose that your interrogation (What?) is in conexion with "it was
criticized by its
own adopter J. S. Bach" because the rest is part of your message.
J. S. Bach´s son declared that his father was not satisfied with the equal
tempered scale; somewhere I have this information.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

> The above relations conclude that the frequencies and quotients that define
> the needed flat fifths that are criticized by Mike are not common numbers,
> otherwise the triad chord wave peaks would not have been aesthetic
> responses.

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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
Hi Johnny & Brad,
> As a point of departure, there is nothing that connects J.S. Bach
with equal
> temperament. Nothing...
...except of incompetent ET claims in the late 19.th-centrury in
an early edition of the Grove-Dictionary.
Only heaven knows how long some scholars will continue
persist in referring to that crackbrained nonsene.

But back to the earlier 18.th century:
Even J.G.Neidhard's attempts in approximating Simon Stevin's ET,
/tuning/topicId_68023.html#68755
had no chance against JSB's uncle:

http://www.oxfordmusiconline.com/subscriber/article/grove/music/
Quote:"
Neidhardt, Johann Georg
(b Bernstadt, c1685; d Königsberg, 1739). German theorist and
composer. After early training at Altdorf and Wittenberg, Neidhardt
matriculated as a theology student at Jena, where he produced his
first treatise on temperament and apparently continued his musical
training. It is likely that he studied with the university organist,
J.N. Bach, who knew him well enough to allow him to try one of his
temperaments on the new organ at the city's central church; Bach's
tuning, however, was found more singable."

JSB called him "senoir" of the Bach-family-clan:
http://de.wikipedia.org/wiki/Johann_Nikolaus_Bach_%28Komponist%29
"Johann Nikolaus Bach (* 10. Oktober 1669 in Eisenach, † 4. November
1753 in Jena)" even suvived his nephew JSB over 9 years.
As instrument builder in the clan he was also
authority in questions of tuning:

>
http://www.bestii.com/~mschulter/Lehman_Bach_Neidhardt.txt
"In his article (_Early Music_, February 2005, p. 15), Lehman
tells the story of a contest to tune an organ in "absolutely
equal temperament" in which Neidhardt, using a mathematically
prepared monochord, was bested by his young colleague Nikolaus
Bach "setting his set of 8' flutes entirely by ear." He suspects
that Neidhardt "did achieve equal temperament or something
indistinguishably close to it," while Bach sought and attained a
temperament that "'_seems_ equal'" (Lehman's emphasis) to "all but
the most finicky keyboard geeks, but is more musically pleasing."

Sorry Brad,
but that was completely wrong `suspceted`!,
because the term more 'singable' meant in the coeval Baroque
period still an clear distiction inbetween the JI ratios of:

C 10:9 D 9:8 E 16:15 F 9:8 G 10:9 A 9:8 Bb 16:15 C'

That contains 2 clearly discernabele whole-tone steps:

1. Pythagorean 'major-tone' of ratio: 9:8 ~204Cents
2. Syntonic 'minor-tone' of ratio: 10:9 ~182Cents

hence coeval singer expected in C-major related keys
for C-E and G-A even less than an meantone-step: ~193Cents,
when singing in keys near C-major.

That discerning of the both versions of an tone survied
even the classical period in terms of Kirnberger2,
with D-E & G-A even exactly matching 10:9.
That quality was lost not until the romantic-period,
when the formerly strings in the instruments became stonger and
stronger. That change in arising the diameter of strings,
followed an fit in tuning nearer to somehow ET approximations,
as we do have still in todays intruments.

Werckmeister III satisfies
J.N. Bachs's 'singable'-condition
of having for C-D & G-A whole-tones
less than an meantone step of: ~193Cents.

but Neidhard approximates in all his proposals barely
his own preference:
Pythagorean 'major-tone's of 9:8 everywhere allover the scale,
so that the members of Jena's choir-singers had no orientation,
when expecting Syntonic minor-tones at the usual positions.

Neidhardt's oversimlification simply
neglects the demanded difference inbetween
major(9:8)- versus minor(10:9)-tones in JI.
as awaited by the Jena-singers inbetween C-D & G-A,
even lower than in old meantonics.

Hence -no wonder- Neidhardt lost the tuning-competition vs. JNB
so embarassing in an disappointing fiasco at his Jena-debacle.

He got simply to near to ET in order to pass the examination
of the singer's jury, which anticipated something nearer to JI.

Cnclusion for modern HIPerformance for music of the Bach-family:

It's no good idea to follow the inferior Neidhardt in his attempts,
when speculating about new remakes again of
so called alleged modern "Bach-tunings".

Sorry Brad, concerning yours wishful-thinking
you simply choosed an inapt candidate,
when betting on the wrong horse
in matters of "squiggles" allegations.

Recommendation:
Plaese rethink that matter once more over again,
before republishing such "wishful-thinking" anew.

Yours regretfully
A.S.