Re Ton Koopman's fusing just 3rd C-E 5/4 ~386 Cents-resonance Re:lecture note10/

Hello Andreas,

So, Ton Koopman's personal preference for a 5/4 major third between C and E
now trumps his earlier preference for Werckmeister III (as with his recording
of the Brandenburg Concerti)?

Any modern take is irrelevant to the affect achieved through Bach's
preference, whatever it may be. History gives evidence that ALL the major thirds were
sharp for Bach, even C to E. Alas, Kirnberger made the feint toward the just
third, not Bach.

best, Johnny Reinhard

______________________
Appearently some latecomers overslept that progress, found
already at the turn of the century in in modern "Bach-tunings".

bye
A.S.

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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Hello Andreas,
>
> So, Ton Koopman's personal preference for a 5/4 major third between
> C and E
> now trumps his earlier preference for Werckmeister III (as with his
> recording
> of the Brandenburg Concerti)?

All i can report you from my dispute with Ton is,
that he insisted in precisely JI 5/4 for the C-E,
he demonstrated that on the harpsichord of the:
http://en.wikipedia.org/wiki/Hessischer_Rundfunk
" hr2 is hr's cultural and classical oriented radio."

During all the concert i perceived his C-E on that instrument as pure,
but in an further examination after his performance i found
barely by ears something ~387...~388Cents,
about maximal an schisma sharper than just,
so that the beating in C-E-G vanished by fusing.

> Any modern take is irrelevant to the affect achieved through Bach's
> preference, whatever it may be.
Agreed:
/bach_tunings/topicId_unknown.html#53

> History gives evidence that ALL the major thirds were
> sharp for Bach, even C to E.
Kirnberger reports so to Marpurg,
but C.P.E. vehemently contradicts Kirnberger
by insisting, that nobody was able to tune his fathers
instruments to his satisfaction.
Every thing -concerning tuning-
did his father always himself.

Both can't be right:
Hence nobody knows today anymore how serious
we can take Kirnbergers allegations, in contrast to
his own instructions and C.P.E. that demand some JI 3rds.

> Alas, Kirnberger made the feint toward the just
> third, not Bach.
Sorry but i.m.h.o. in that case:
Nothing secure can be concluded from such
an inconsistent contradictoriness.
Not even that yours alleged "feint"
can properly be traced back to Kirnberger.
>
bye
A.S.

> History gives evidence that ALL the major thirds were
> sharp for Bach, even C to E.
'Kirnberger reports so to Marpurg,
but C.P.E. vehemently contradicts Kirnberger
by insisting, that nobody was able to tune his fathers
instruments to his satisfaction.'

But Andreas, that is not truly vehement, what may be considered "tongue in
cheek" in the sense that C.P.E. did tune for his father, many times, especially
with his brother during the St. Matthew's Passion performances. And besides,
C.P.E. was not addressing Kirnberger or Marpurg. And incidentally, it is
easier to match a just interval than an exactly tempered one.

"Every thing -concerning tuning-
did his father always himself."

Just like Mayor Bloomberg in NYC, only people do have to have to do things
for themselves. ;)
This was a statement largely of family pride.

A.S.: Both can't be right:
Hence nobody knows today anymore how serious
we can take Kirnbergers allegations, in contrast to
his own instructions and C.P.E. that demand some JI 3rds.

JR: Um, C.P.E. demands some JI 3rds? I have never seen that. You may have
misconstrued. If you think I am confused, please show me how.

> Alas, Kirnberger made the feint toward the just
> third, not Bach.
Sorry but i.m.h.o. in that case:
Nothing secure can be concluded from such
an inconsistent contradictoriness.
Not even that yours alleged "feint"
can properly be traced back to Kirnberger.
>
bye
A.S.

JR: I have now a 180 page book on Bach and Tuning. I find that building on
secure information can lead to connections through time. Hence, Kirnberger's
"all major thirds are sharp" differentiates both his own Kirnberger tunings I,
II, and III, from Werckmeister III tuning, with "all major thirds sharp."

There is no alleging Kirnberger's surprise use of a pure major third from C
to E in his own publication, new to Bach.

best, Johnny Reinhard

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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
Hi Johnny & all others,
>
>... C.P.E. did tune for his father, many times, especially
> with his brother during the St. Matthew's Passion performances.
later C.P.E. wrote 1753 in his
http://www.koelnklavier.de/quellen/versuch/_titel1.html
http://www.koelnklavier.de/quellen/versuch/kap1-0b-3.html
The paragraph §.14 about tuning:

"§. 14. Beyde Arten von Instrumenten müssen gut temperirt seyn, indem
man durch die Stimmung der Quinten, Quarten, Probirung der kleinen und
grossen Tertien und gantzer Accorde, den meisten Quinten besonders so
viel von ihrer größten Reinigkeit abnimmt, daß es das Gehör kaum
mercket und man alle vier und zwantzig Ton=Arten gut bracuhen kan.
Durch Probirung der Quarten hat man den Vortheil, daß man die nöthige
Schwebung der Quinten deutlicher hören kan, weil die Quarten ihrem
Grund=Tone näher liegen als die Quinten. Sind die Claviere so
gestimmt, so kan man sie wegen der Ausübung mit Recht für die reinste
Instrumente unter allen ausgeben, indem zwar einige reiner gestimmt
aber nicht gespielet werden. Auf dem Claviere spielet man aus allen
vier und zwantzig Ton=Arten gleich rein und welches wohl zu mercken
vollstimmig, ohngeachtet die Harmonie wegen der Verhätnisse die
geringste Unreinigkeit sogleich entdecket. Durch diese neue Art zu
temperiren sind wir weiter gekommen als vor dem, obschon die alte
Temperatur so beschaffen war, daß einige Ton=Arten reiner waren als
man noch jetzo bey vielen Instrumenten antrift. Bey manchem andern
Musico würde man vielleicht die Unreinigkeit eher vermercken, ohne
einen Klang=Messer dabey nöthig zu haben, wenn man die
hervorgebrachten melodischen Töne harmonisch hören sollte. Diese
Melodie betrügt uns oft und läßt uns nicht eher ihre unreinen Töne
verspüren, bis diese Unreinigkeit so groß ist, als kaum bey manchem
schlecht gestimmten Claviere."

Translation: William J Mitchell,
"Essay on the True Art of Playing Keyboard Instruments"
New York: Norton, 1949

"§. 14. Both types of instrument must be tempered as follows:
In tuning the fifths and fourths, testing minor and major thirds and
chords, take away from most of the fifths a barely noticeable amount
of their absolute purity.
All twenty-four tonalities will thus become usable.
The beats of fifths can be more easily heard by probing fourths,
an advantage that stems from the fact that the tones of the latter lie
closer together than fifths.
In practice, a keyboard so tuned is the purest of all instruments,
for others may be more purely tuned but they cannot be purely played.
The keyboard plays equally in tune in all twenty-four tonalities and,
mark well, with full chords, notwithstanding that these, because of
their ratios, reveal a very slight impurity.
The new method of tuning marks a great advance over the old,
even though the latter was of such a nature that a few tonalities were
purer than those of many present non-keyboard instruments,
the impurity of which would be easier to detect (and without a
monochord) by listening harmonically to each melodic tone. Their
melodies often deceive us and do not expose their impurity until it is
greater than that of a badly tuned keyboard...."

But C.P.E. left open whether his father
tuned according the "old" or the here presented "new" method?

The "old" versus "new" controversy refers back to:
http://felbick.de/werckmeister.html
"/ also müste der exces in die 12. Theile vertheilet werden/ welches
dann eine gleiche und richtige temperatur geben würde: Bissher habe
ich dieser Meinung nicht können Beyfall geben/ weil ich lieber die
Diatonischen claves reiner halten wollen/ damit dasselbe genus/
welches am meisten gebrauchet wird/ desto reiner behalten würde:
Andere meinen/ dass die temperatur da alle consonantien in der
Gleichheit stehen/ endlich würde den Preis behalten/ und die Music
würde künfftig durchaus so excoliret werden/ dass ieden gleichviel
seyn würde/ ein Lied aus dem c. oder cis zu spielen/ u.s.w. Den Gott
würde unsern Nachkommenden viel Wunder erzeigen: Ich lasse auch diese
Meinung in ihrem Werth/ es kan sich viel ändern/ denn viel Dinge so
vor hundert Jahren denen Musicis ein Eckel gewesen/ sind jetziger Zeit
am angenehmsten. Et sic mundus regitur opinionibus oder wie andere
wollen/ Homo astris. Da nun die alten in denen tertiis maj. ein gantz
comma haben ertragen können ..." (aus: Hypomnemata musica, oder
Musicalisches Memorial, p. 35-36)"

tr:
/hence the exceeding comma(PC) should be divided into 12 parts/
that would yield an equal and correct temperature: Until now I
disagree with that view (of Simon Stevin)/ because I prefer to keep
the diatonic keys more pure/ in order to keep the most used keys/
the purest. Others deem ET would win the price in the future/
with the result that playing a song from c. ore c# would make
no difference/ &.ct..../ I leave up the value of that opinion/
...because the ancients tolerated in the major 3rds even
when detuned an whole comma sharp... (loc. situs.)

W's own practice:
"...da ich nun die Tertien in dem genere Diatonico
etwa 1/2 oder 2/3 Commatis nachschweben laßen /... "

'because I left beat the 3rds in the diatonic genre
about 1/2 or 2/3 comma sharper beating...'

In contrast to his own preference W. refers to Neidhardt's ET
approximation, which he considers as more problematic:

"und allen Quinten nur 1/12 Commatis, u. s. w. könte abgenommen werden
/ ich auch diese Stimmung / in Theoria auf meinen Monochordo und in
Praxi, versucht und gut befunden / denn wie hätte ich sonst wißen /
und schreiben können / daß die Tert. maj 2/3 und die minores 3/4 Comm.
schweben müsten / so kan ich nicht umhin / die Wahrheit länger
zuverhelen / insonderheit / da Gott nun noch andere rechtschaffne
Leute erwekket / die diese Temperatur vor richtig erkennen / und
dieselbe an den Tag / und öffentlich in den Druck gehen laßen / wie
hierinnen insonderheit Herr Joh. Georg Neidhardt S.S. Theolog:
Studiosus, sich löblich erzeiget / und den Proces gantz deutlich
vorgestellet hat. Auf meinem heraus gegebenen Monochordo könte
dieselbe Temperatur wenn es länger ware / auch gar leichte mechanicè
aufgetragen werden / denn die darauf schon aufgerissenen Commata, die
da in 3. oder 4. Theil getheilet sind / könten in 12. Theil getheilet
werden / da man immer von einer reinen Quinta zur andern 1/12theil
eines Commatis, wie mit den Viertheln geschehen / abnehmen könte /
darnach könte man auch erfahren / wie viel die Tertien, Sexten,
Quarten schweben. Welche dann alle gantz erleidlich seyn werden / da
keine Tertia ein gantz Comma, sondern wie oben erwehnet / schweben
wird. Ich hätte auch solche Temperatur durch die 12. Theile Commatis
laßen aufreißen / weil aber der Kupfferstecher sich beschwerete (und
derselbe auch nicht recht perfectioniret war) die engen Spatia der
Commatum in 12. Theile zutheilen / muste ich daßelbe anstehen laßen.
Denn mein gantzes Monochordum ist von C. biß nur 2 Fuß lang."

In a nutshell:
Here W. describes in detail how to generalize his own division of
the comma into 4 subparts into 12 subparts
and excuses lack of that ET-approximation
in his earlier specifications by 2 reasons:

1. The engraver's incompetence and complaints.
2. The small seize of his private only 2-foot long string monochord.

Then W. argues more en detail against ET....
"...hätte ich also bald allen Tertien im genere Diatonico ihre
Schwebung so starck gegeben /wie in der 12theiligen Eintheilung der
Commatum geschehen muß/ so wäre ich von den Wölffen der Ignoranz gar
zerrißen worden."

'..if I had charged all diatonic 3rds as much as in 12-ET/
I would got roasted in an slating review by the wolfs of ignorance.'

....as inacceptable among coeval tuners.

Finally W. concludes his personal refuse of 12-ET
and approximations of that:

"Indeßen bin ich doch nicht ungeneigt / und bleibe dabey / daß man die
diatoni schen Tertien etwas reiner laße / als die andern so man selten
gebrauchet / es giebet auch gute Veränderung / und sind die in meinen
Monochordo enthaltene Temperaturen zu erdulden / aber ein jeder weiß
sie nicht ins Gehör zubringen. Denn da der Faber Stapul: und Glareanus
die ordinaren Tertien welchen ein Comma in genere Diatonico zu groß
waren /vor gut und angenehm in dem Gehör gehalten / so werde ich ja
auch entschuldiget seyn können / wenn ich etlicher Tertien als cis,
und f. gis, und c Welche doch gar selten / selten gebrauchet werden /
ein Comma oder nur 3/4 Commat: über sich schweben laßen / damit
dieselben / welche stets vorkommen / desto angenehmer bleiben möchten."

'Nevertheless / i do persist remaining /
/in leaving the diatonic 3rds slightly purer/
/than the only rare used ones in the remote keys /
/that results also in an good variation (away from pureness)/
/as shown in the(diverse) temperings in my own monochord/
/but only a few (experts) are able to apply them properly by ear.
/Because
http://en.wikipedia.org/wiki/Jacques_Lef%C3%A8vre_d%27%C3%89taples
"...name Jacobus Faber Stapulensis"
and
http://en.wikipedia.org/wiki/Heinrich_Glarean
's ditones (81:64) were once even one comma (81:80) to much sharp/
but they considered the ditone as pleasant sounding in thier ears/
hence that may excuse my own 3rds /
that deviate an comma or barely 3/4 commatis sharp /
in the remote keys alike: c#, f, g#.../
that are only seldom used/
in contrast to the always occuring 3rds /
that might remain the more pleasant sounding.'

> And besides,
> C.P.E. was not addressing Kirnberger or Marpurg.
corret,
he was wise enough to refrain
from that fruitless controversy.

> And incidentally, it is
> easier to match a just interval than an exactly tempered one.
Natch.
>
> Just like Mayor Bloomberg in NYC,
> only people do have to have to do things
> for themselves. ;)
> This was a statement largely of family pride.
Probably.
>
>
> JR: Um, C.P.E. demands some JI 3rds?
in the above §14 he,...
>I have never seen that.
...allows finally even for 3rds:

"...impurity until it is greater than that of a badly tuned keyboard"

Whatever C.P.E. had in mind when he wrote that lax statement?

At least C.P.E. avoids to foist an inept ~704Cents broade
"diminished-6th" inbetween "A#-F" on his own fahter's practice,
when he assessed that JSB took that secret within his grave.

> You may have
> misconstrued.
Sorry, if i talked here at cross-purposes.

> If you think I am confused, please show me how.
In deed, i never intended to cause confusion.
>
>
> JR: I have now a 180 page book on Bach and Tuning.
It's really about time
to adjust the proliferation of insustainable specuations
over the last years in the field of modern so called 'Bach-tunings'.
You are welcome to debunk the recent pseudoscience in that topic.
Im looking forward to learn there more about yours results.
When may i have a look on that?

> I find that building on
> secure information can lead to connections through time.
In order to come from reviewing the facts again to
new conclusions to better insigts.

> Hence, Kirnberger's
> "all major thirds are sharp" differentiates both his own Kirnberger
> tunings I,
> II, and III, from Werckmeister III tuning, with

Remember:
Werckmeister repeats his demand
>"all major thirds sharp."
in his works again and again.

That old practical advise can be traced back at least to
http://en.wikipedia.org/wiki/Arnolt_Schlick
's recommendations in his:
http://upload.wikimedia.org/wikipedia/commons/a/a1/Schlick_spiegel.jpg
chapter 8, 'tuning of the organ'

> There is no alleging Kirnberger's
> surprise use of a pure major third
> from C
> to E in his own publication, new to Bach.

No surprise if you study him in print:
http://de.wikipedia.org/wiki/Bild:Tabelle_der_diatonischen_und_chromatischen_Intervalle_f%C3%BCr_jeden_Grundton_grand.jpg
http://upload.wikimedia.org/wikipedia/de/c/c5/Tabelle_der_diatonischen_und_chromatischen_Intervalle_f%C3%BCr_jeden_Grundton_grand.jpg
http://de.wikipedia.org/wiki/Bild:Die_Kunst_des_reinen_Satzes_(auszugII).jpg

Presumably K. seeked intentionally to maximise
the desired effects of different key beahveiour
http://www.wmich.edu/mus-theo/courses/keys.html

The contrast turns out to be
even more aspired and pronounced than
in the cases of his predecessors:
Schlick & Werckmeister.

In concrete numbers:
http://harpsichords.pbwiki.com/f/Kirn_1871.html
http://harpsichords.pbwiki.com/f/K_III.html

bye
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> "§. 14. Both types of instrument must be tempered as follows:
> In tuning the fifths and fourths, testing minor and major thirds and
> chords, take away from most of the fifths a barely noticeable amount
> of their absolute purity.

So, this method cannot really be related to Kirnberger, since K.
leaves most of the fifths pure but tempers the others by 1/4 comma or
more, which is *very* noticeable.

> The new method of tuning marks a great advance over the old,
> even though the latter was of such a nature that a few tonalities were
> purer than those of many present non-keyboard instruments,

I think the 'old' method must be either: meantone with a wolf, or
modified meantone with several sharp fifths. Meantone in a few
tonalities is purer than almost anything, certainly purer than any
Werckmeister!

> the impurity of which would be easier to detect (and without a
> monochord) by listening harmonically to each melodic tone.

The significance of this remark has not really been noticed. It
implies: To tell whether a melodic note is in tune, compare it with
the harmony, with the relevant chord. Essentially: Harmony, chords,
are the judge of tuning and temperament, both in keyboards and other
instruments.

Any supposed 'melodically effective temperament' receives no support
here. Tuning is done to produce good chords.

> Their melodies often deceive us and do not expose their impurity
> until it is greater than that of a badly tuned keyboard...."

This corresponds simply to the fact that the tolerance or sensitivity
of the ear to mistuned/tempered melodic intervals (successive tones)
is much greater than to mistuned harmonies (simultaneous tones).

> "...impurity until it is greater than that of a badly tuned keyboard"
>
> Whatever C.P.E. had in mind when he wrote that lax statement?

- Flutes, maybe, Baroque flutes give a very irregular scale unless the
player takes a lot of care.

> Presumably K. seeked intentionally to maximise
> the desired effects of different key behaviour
> http://www.wmich.edu/mus-theo/courses/keys.html
>
> The contrast turns out to be
> even more aspired and pronounced than
> in the cases of his predecessors:
> Schlick & Werckmeister.

But less than 'French' tunings like Rameau etc. with several wide
fifths...
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> > C.P.E.:
> >... take away from most of the fifths a barely noticeable
> > amount of their absolute purity.
>
> So, this method cannot really be related to Kirnberger, since K.
> leaves most of the fifths pure but tempers the others by 1/4 comma
> or more, which is *very* noticeable.

Nobody knows any more C.P.E.'s concept of "noticable",
alike JSB's lost art of tuning.

>
> > The new method of tuning marks a great advance over the old,
> > even though the latter was of such a nature that a few tonalities
> > were purer than those of many present non-keyboard instruments,
>
> I think the 'old' method must be either: meantone with a wolf, or
> modified meantone with several sharp fifths.

The result depends on:
To what "non-keyboard instruments did C.P.E. refer in that comparison?

> Meantone in a few
> tonalities is purer than almost anything, certainly purer than any
> Werckmeister!

Where inbetween 'meantone' and C.P.E.
would you locate Werckmeister, not to mention JSB?

>
> > the impurity of which would be easier to detect (and without a
> > monochord) by listening harmonically to each melodic tone.
>
> The significance of this remark has not really been noticed.
It's in deed often overlooked:
In contrast to Neidhardt, C.P.E. abstains from the monochord.

> It
> implies: To tell whether a melodic note is in tune, compare it with
> the harmony, with the relevant chord. Essentially: Harmony, chords,
> are the judge of tuning and temperament, both in keyboards and other
> instruments.

Done by counting beats of the deviation from the 'relevant chord'.

>
> Any supposed 'melodically effective temperament' receives no support
> here.

'melodically' means 3-limit Phythagorean intervals alike:
32/27 or 81/64,

>Tuning is done to produce good chords

'harmonically' corresponds to 5-limit syntonic intervals alike:
6/5 or 5/4, that differ both from Pythagorean by 81:80.

> > Their melodies often deceive us and do not expose their impurity
> > until it is greater than that of a badly tuned keyboard...."

Because here C.P.E. considers the 'harmonic' sound-check
as more essential than barely the 'melodic' estimation.
>
> This corresponds simply to the fact that the tolerance or
> sensitivity
> of the ear to mistuned/tempered melodic intervals (successive tones)
> is much greater than to mistuned harmonies (simultaneous tones).
>
Confirmed by the psychoacoustical result, that for JNDs
http://en.wikipedia.org/wiki/Just_noticeable_difference
the human ear possesses
for 'simultane' intervals an higher precision in accuracy
than for the same 'successive' steps,
when presented sequential in time.
>
> > > "...impurity until it is greater than that of a badly tuned
> > > keyboard"
> >
> > Whatever C.P.E. had in mind when he wrote that lax statement?
>
> - Flutes, maybe, Baroque flutes give a very irregular scale unless
> the player takes a lot of care.

When flutes got blown inept,
even todays modern recorders do often yawl broadly laymanish
widish (~704Cents) out of tune ;-)
alike
http://en.wikipedia.org/wiki/P._D._Q._Bach
's "esotheric" 'rosetta-stone'd tuning in:
http://en.wikipedia.org/wiki/Grand_Serenade_for_an_Awful_Lot_of_Winds_and_Percussion
http://www.bach-cantatas.com/Topics/Manuscripts.htm
"Arthur wrote (July 29, 2002):
I have not been in the Brtish Library for many, many years. In fact
when I was there it was called the British Museum, and to get to the
Music Room, one had to walk past the Rosetta Stone.

In those days one could see almost anything. But even then, the Handel
manuscripts would not be brought out unless the reader had a valid
reason to examine the originals. One was expected to use a microfilm
instead. More and more libaries are refusing permission to view the
origibnals, since so many manuscripts are deteriorating due to
pollution...."
>
but back to:
>
> > ....different key-characteristics...

> > as... in the cases of his predecessors:
> > Schlick & Werckmeister.
>
> But less than 'French' tunings like Rameau etc.
Later Rameau abandoned from that practice in favour of ET.

> with several wide fifths...
Surely that's correct for coeval "french" ordinaire tunings, but

John O'Donnell critized
questionable wild "wide 5th" speculations as 'problematic':
http://em.oxfordjournals.org/cgi/content/full/34/4/625
http://muse.jhu.edu/journals/early_music/v034/34.4odonnell.html

" 6.
If Bach's temperament included a wide 5th, and if this was indeed the
temperament that C. P. E. Bach used, it is strange that the latter
failed to mention this component. Wide 5ths are perfectly acceptable
in themselves, but Emanuel Bach mentions only a majority of narrow
5ths, surely leaving us to understand that the remaining 5ths are to
be tuned pure."

O'D's own interpretation also tries to refer to C.P.E.'s "Versuch...":

"Perhaps it is simply to ensure that the intervals of the 4th and 5th
are visually distinct, and perhaps there is something in what C. P. E.
Bach advises about tuning: ‘The beats of 5ths can be more easily heard
by probing 4ths, an advantage that stems from the fact that the tones
of the latter lie closer together than 5ths.’12 Hence clear single
coils for the 4ths, convoluted double coils for the 5ths."

and doubts about Brad's insutainable allegations:

"And if he (JSB) did have a single system for tuning his harpsichord,
it seems that Emanuel Bach and Kirnberger were not aware of it, the
former's instructions being very general, the latter mentioning only
the sharpening of all major 3rds."

In opposition to Ton Koopman's just 5/4 C-E 3rd,
i do prefer to sharpen C-E about ~1...~2 Cents,
in order to meet the above criterion,
more precisely in:

/tuning/topicId_78659.html#78677

"
!Mietke.scl

304/243 ! ~387.74... E (5/4)*(1216/1215)
"

with C-E wide about an
http://www.xs4all.nl/~huygensf/doc/intervals.html
"1216/1215 Eratosthenes' comma"
of
1200Cents * ln(1216/1215)/ln(2) = ~1.42429794....Cents

bye
A.S.