Yahoo Tuning Groups Ultimate Backup tuning Well tempered Beethoven,(was enharmonic)

Greetings,
Todd writes;

>>I also haven't heard Ed Foote's CD, and I'd be curious to

know what works appear on it

In the Kirnberger III(also called a Prinz), we recorded Pathetique and Op.14
nr. 1
In the Young, we recorded the Moonlight and Waldstein. This CD is still
available.

>>Two characterstic Beethoven figures lend themselves to ET, in my opinion:

The first would be long, fast chromatic runs, almost like slow glisses. As

Paul pointed out, these would sound smoother on an ET keyboard. <<

The difference between equal and well temperament is very difficult to
discern in a fast chromatic run. Meantone, yes, but a well tempered
keyboard, not usually. The real place to hear the difference is in the
texture of the harmony.

>>I would also bet that any relationship between Beethoven and ET would show

up much more in his piano works than in his symphonic pieces, simply because

intonation is completely fixed on the piano, and much more fluid in an

orchestra. <<

The relationship between Beethoven and ET doesn't exist to those that
have become familiar with Beethoven and the key character of a well
temperament. The concept of the "Character of the Keys" was extensively
debated and written about before and during LVB's lifetime. Schubart is one
of the major figures quoted in Rita Steblen's book. The key characters of
the time were in synch with the manner of well tempering on the keyboard, the
extreme keys being the most agreed upon.

>>I also know that Beethoven was one of the first to exploit the

capabilities of a new breed of piano that became available in his lifetime.

These newer pianos were the first to have cast-iron frames, making higher

string tension and greater dynamic range possible. It would be interesting

to research whether these newer pianos were primarily tuned ET or not.

Babcock was the first to successfully make an iron plate, this happened
around 1820, long after Beethoven's sense of tonality was in place. The
pianos of his formative years were of the older style. The iron plate pianos
began to be built after he had lost most of his hearing.

Paul writes:
>>Foote's CD uses some extreme well-temperaments whose pairings with the
pieces seem almost arbitrary, yet the music doesn't suffer at all -- it
merely gains a

little color.<<

Gee, I need to parse this out. First and last, is a point being made here
that "extreme" WT only produce a "little" color? The Kirnberger has a full
syntonic comma in the three highest keys,(Gb, Db, and Ab). This was near the
historically accepted limit if one was to escape the "wolf".
Now, as to my pairings (parings for pun), of temperament to pieces: The
Kirnberger is a near copy of the Neidhart/Prinz tunings published as far back
as 1732, and which seem to have been commonly used for much of the 18th
century. It's major characteristic is that the white keys are in a 1/4C
meantone arrangement, providing a Just C-E third. Beethoven's sense of
tonality could very plausibly have been formed under the influence of such a
tuning, as well as the assorted meantones still appearing through the late
1700's.
I chose this tuning so that there would be a landmark formed which
technicians could discuss,( the middle section of the Pathetique uses a
"curtain" of this dissonance behind the melody, it is tense, yes, but on
purpose), but what more believable temperament would do? Prior to selection,
we did listen to the pieces on a variety of tunings, rejecting the ones that
sounded "unmusical" on the Railsback-poisoned modern concert grand. It is
worth noting that this piano carries 45,000 lbs of string tension, so the
effects of tempering can be exaggerated.
The Young, published in 1799, was widely regarded as an ideal balance,
since its symmetry is perfect and encompasses a near pure third at the
historical "home" ( C-E at only 5 cents wide, which is beating near
heart-rate speed (1 bps) in the middle of the keyboard) and has only one key
with a full comma in its tonic third (F#-A#). The publication dates of the
Moonlight and Waldstein are within a few years of this temperament's formal
arrival. I don't think "arbitrary" is quite accurate! What other tuning
carries a better or more plausible pedigree for a Beethoven piece of 1804?
The Young also provides a good deal of contrast while avoiding any great
steps between adjacent keys, making the middle section of the Waldstein work
as it does.

Paul again:
>> Actually, retuning Beethoven is made more interesting by the fact that he

was deaf when he wrote most of his music. <<

Ah, we have a debate, here! This runs counter to everything I have read
about Beethoven's deafness. He became aware of the impending hearing loss
around 1801, but was capable of hearing at least until 1815, and some say
even later than that. Things didn't get profound until around 1820. His
"Hammerclavier" may have been written deaf, though.

I also wrote,

>From a tuning standpoint, the main feature of ET is a sameness to the keys.

To which Paul writes:
>>Agreed, but you have to modulate through all the keys before you can hear

that, which is why I said "in an immediately audible way" above.

There isn't any reason to modulate through all of them to hear the
sameness in ET and no reason to modulate through all of them to be affected
by the different harmonic textures in a WT.
When Beethoven modulates from the opening C tonality of the Waldstein to
the 2nd theme (in E) in measure 35, you can hear a distinctly different
harmonic texture offered by the key of E. This move to Emaj occurs
immediately after a series of descending arpeggios of a B major chord. The
tempering of this B triad, though masked by the notes not being struck
simultaneously, is greater than that of Emaj. (A similar approach is used
by Bach to mask the harshness of the C#-F in a Werckmiester while still
retaining the " active" feel of the tonality in the C#prelude in WTC 1)
By going so far around the circle of fifths, than dropping back a notch,
he creates a feeling of resolution for the 2nd theme, giving it a rather
complex context. This is a neat trick, to create a resolution to E following
32 measures of C! But there is more going on that that.
Not only is the 2nd theme in E whith its "brilliance" much greater than
C, but it is marked with a softer dynamic! Pianissimo is more sedative than
forte, yet the E triad, (in the Young or most any other temperament of this
period) possesses a tonic third that is 18 cents wide, which makes it more
stimulative than the C's tonic third, which has been drummed into the hearing
at the opening.
By combining these opposing emotional manipulations of loudness and
tempering, Beethoven creates a very complex sensation. This is the sort of
juxtapositon of effects that appear in well-tempered Beethoven, effects that
are totally lost in ET.
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

🔗D.Stearns <STEARNS@CAPECOD.NET>

Ed Foote wrote,

<< By going so far around the circle of fifths, than dropping back a
notch, he creates a feeling of resolution for the 2nd theme, giving it
a rather complex context. This is a neat trick, to create a
resolution to E following 32 measures of C! But there is more going
on that that.

Not only is the 2nd theme in E whith its "brilliance" much greater
than C, but it is marked with a softer dynamic! Pianissimo is more
sedative than forte, yet the E triad, (in the Young or most any other
temperament of this period) possesses a tonic third that is 18 cents
wide, which makes it more stimulative than the C's tonic third, which
has been drummed into the hearing at the opening.

By combining these opposing emotional manipulations of loudness and
tempering, Beethoven creates a very complex sensation. This is the
sort of juxtapositon of effects that appear in well-tempered
Beethoven, effects that are totally lost in ET. >>

Yeah, really nice explanations Ed, thanks.

This very sort of thing in a nutshell is why I support a full pitch
continuum, all tunings, whatever you can organize for the better of
the music type of an approach. And this is why I clock in with my
protests of adaptive retuning as espoused by John deLaubenfels despite
the fact that I think it's a brilliant bit of problem solving given a
particular approach. But to my mind that approach is a tuning first,
music second one that immediately lops off a huge array of fascinating
and emotionally rich horizons by way of an overriding (tuning)
assumption; all thirds = 5/4 = good, for example...

I don't mean to single John -- out as his work in tuning is
exceptional -- but it is also a very good counterexample to a full
pitch continuum, whatever works on an example to example basis works,
type of an approach: you simply won't get "more stimulative" (or 'more
restive', etc., etc.) moments if they're thrown right out from the get
go!

Anyway, thanks again for the nice post.

--Dan Stearns

🔗John A. deLaubenfels <jdl@adaptune.com>

[Ed Foote wrote:]
>>By going so far around the circle of fifths, than dropping back a
>>notch, he creates a feeling of resolution for the 2nd theme, giving it
>>a rather complex context. This is a neat trick, to create a
>>resolution to E following 32 measures of C! But there is more going
>>on that that.

>>Not only is the 2nd theme in E whith its "brilliance" much greater
>>than C, but it is marked with a softer dynamic! Pianissimo is more
>>sedative than forte, yet the E triad, (in the Young or most any other
>>temperament of this period) possesses a tonic third that is 18 cents
>>wide, which makes it more stimulative than the C's tonic third, which
>>has been drummed into the hearing at the opening.

>>By combining these opposing emotional manipulations of loudness and
>>tempering, Beethoven creates a very complex sensation. This is the
>>sort of juxtapositon of effects that appear in well-tempered
>>Beethoven, effects that are totally lost in ET.

[Dan Stearns:]
>Yeah, really nice explanations Ed, thanks.

Agreed! Fascinating stuff!

[Dan:]
>This very sort of thing in a nutshell is why I support a full pitch
>continuum, all tunings, whatever you can organize for the better of
>the music type of an approach. And this is why I clock in with my
>protests of adaptive retuning as espoused by John deLaubenfels despite
>the fact that I think it's a brilliant bit of problem solving given a
>particular approach. But to my mind that approach is a tuning first,
>music second one that immediately lops off a huge array of fascinating
>and emotionally rich horizons by way of an overriding (tuning)
>assumption; all thirds = 5/4 = good, for example...

As I've said in past post(s), this is the one argument against my work
that makes real sense to me. I'm gonna send Ed a check for the CD he's
already got out, and eagerly await the one now pending.

[Dan:]
>I don't mean to single John -- out as his work in tuning is
>exceptional -- but it is also a very good counterexample to a full
>pitch continuum, whatever works on an example to example basis works,
>type of an approach: you simply won't get "more stimulative" (or 'more
>restive', etc., etc.) moments if they're thrown right out from the get
>go!

No offense taken! Efforts like Ed's, to sleuth out and bring to life
historical tunings should definitely be applauded. It's possible I'll
decide I like that treatment better than my own. But even if I don't,
some others no doubt will. In any case, the musical world is enriched
by a multiplicity of choices.

JdL

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, a440a@a... wrote:

http://www.egroups.com/message/tuning/17447

> Ah, we have a debate, here! This runs counter to
> everything I have read about Beethoven's deafness. He
> became aware of the impending hearing loss around 1801,
> but was capable of hearing at least until 1815, and some say
> even later than that. Things didn't get profound until
> around 1820. His "Hammerclavier" may have been written deaf,
> though.

Thanks much for this, Ed. It corrects an error which I just
posted a few minutes ago ("Beethoven went totally deaf in his
30s").

> When Beethoven modulates from the opening C tonality of
> the Waldstein to the 2nd theme (in E) in measure 35, you can
> hear a distinctly different harmonic texture offered by the
> key of E. This move to Emaj occurs immediately after a series
> of descending arpeggios of a B major chord. The tempering of
> this B triad, though masked by the notes not being struck
> simultaneously, is greater than that of Emaj. ...<snip>...
> By going so far around the circle of fifths, than dropping
> back a notch, he creates a feeling of resolution for the 2nd
> theme, giving it a rather complex context. This is a neat
> trick, to create a resolution to E following 32 measures of C!
> But there is more going on that that.
> Not only is the 2nd theme in E whith its "brilliance"
> much greater than C, but it is marked with a softer dynamic!
> Pianissimo is more sedative than forte, yet the E triad, (in
> the Young or most any other temperament of this period)
> possesses a tonic third that is 18 cents wide, which makes
> it more stimulative than the C's tonic third, which has been
> drummed into the hearing at the opening.
> By combining these opposing emotional manipulations of
> loudness and tempering, Beethoven creates a very complex
> sensation. This is the sort of juxtapositon of effects
> that appear in well-tempered Beethoven, effects that are
> totally lost in ET.

And thanks *very* much for this!! I agree completely with
the comments made by Dan Stearns on this:

http://www.egroups.com/message/tuning/17454

My question: why in the world did you not include detailed
technical commentary like this in the booklet accompanying
the CD? I, for one, would really love to read lots more of
this kind of thing. *Please* be copious with comments on
your subsequent releases!!!

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗Monz <MONZ@JUNO.COM>

🔗John A. deLaubenfels <jdl@adaptune.com>

I've sent Ed Foote a check for his Well Tempered Beethoven CD, including
the Waldstein Sonata discussed recently on this list. I'm sure the
sound and performance from a grand piano will be much more exciting than
any realization of a MIDI file. However... I also found a pretty decent
MIDI sequence of the Waldstein on prs.net, which I have, as is my habit,
subjected to several tunings options. Some interesting things popped
out!

For the set of intervals present in the piece, my program calculates
5-limit vertical pain (== pain of mistuned intervals) as follows:

Fixed tunings:

12-tET Total spring pain: 1902472.969
Werckmeister III spring pain: 1755256.711 (92% of 12-tET)
Kirnberger III Total spring pain: 1572885.583 (83% of 12-tET)
Thomas Young Total spring pain: 1542156.918 (81% of 12-tET)
COFT Total spring pain: 1362917.444 (72% of 12-tET)

Adaptive (5-limit) tuning (showing also horizontal and grounding pain),
using fairly soft vertical springs gives:

After relaxing, Total spring pain: 578536.049 (30% of 12-tET)
Final vertical spring pain: 297621.677
Final horizontal spring pain: 27006.588
Final grounding spring pain: 253907.784

Here's what I find very interesting: the Calculated Optimized Fixed
Tuning gives a slightly MORE extreme contrast between the keys of C
major and E major (discussed by Ed Foote in his posts) than Young does.

I got the numbers on Thomas Young's Well Temperament of 1799 from Kyle
Gann's excellent web page on historical tunings:
http://home.earthlink.net/~kgann/histune.html

C 0.0 0.0
C# 93.9 -6.1
D 195.8 -4.2
Eb 297.8 -2.2
E 391.7 -8.3
F 499.9 -0.1
F# 591.9 -8.1
G 697.9 -2.1
G# 795.8 -4.2
A 893.8 -6.2
A# 999.8 -0.2
B 1091.8 -8.2

Looking at the intervals of this piece, my program finds 5-limit COFT to
be:

C 2.84 +2.84
C# 99.34 -0.66
D 203.80 +3.80
Eb 301.72 +1.72
E 394.44 -5.56
F 501.79 +1.79
F# 599.92 -0.08
G 704.71 +4.71
G# 800.46 +0.46
A 895.64 -4.36
A# 1000.92 +0.92
B 1094.41 -5.59

C-E in Young is 391.7 cents; in COFT, it's 391.6, almost identical!
E-G# in Young is 404.1 cents; in COFT, it's 406.0. Almost Pythagorean.

Certainly these numbers provide reinforcement (if any were needed) to
Ed's claim that Young works well as a fixed tuning for the piece.

[Dan Stearns:]
>This very sort of thing in a nutshell is why I support a full pitch
>continuum, all tunings, whatever you can organize for the better of
>the music type of an approach. And this is why I clock in with my
>protests of adaptive retuning as espoused by John deLaubenfels despite
>the fact that I think it's a brilliant bit of problem solving given a
>particular approach. But to my mind that approach is a tuning first,
>music second one that immediately lops off a huge array of fascinating
>and emotionally rich horizons by way of an overriding (tuning)
>assumption; all thirds = 5/4 = good, for example...

>I don't mean to single John -- out as his work in tuning is
>exceptional -- but it is also a very good counterexample to a full
>pitch continuum, whatever works on an example to example basis works,
>type of an approach: you simply won't get "more stimulative" (or 'more
>restive', etc., etc.) moments if they're thrown right out from the get
>go!

Well, though my adaptive tunings DO soften the characteristics of
individual keys within a piece, they don't completely obliterate the
character of different keys, because all notes are grounded to
quasi-COFT values. So, in the adaptive treatment of the Waldstein
Sonata, C-E will still be closer to 5:4 than E-G# will be. The
grounding springs can be stiffened to force the final tuning to approach
COFT values with little to no adaptive movement, if it is desired to
accentuate key color differences more.

JdL

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/17485

> Joseph Pehrson wrote,
>
> << I can't see what Ed Foote's work has to do with John's work at
all.
> >>
>
> I think you might've missed my point here. I was using Ed's
Beethoven
> example (as it was particularly sharp) to set up some much general
> questions about tuning, aesthetics and music. John's work just
> happened to be a very strong opposite type of an example, and a good
> way to help frame some of these questions I think.
>
> --Dan Stearns

Hi Dan...

I don't believe I missed the point at all. John and Ed both set out
to do completely different work. As you said, John's work puts
tuning BEFORE the music, in a theoretical sense, and Ed Foote is
going for a kind of historical veracity...

However, in John's work, we get to partake in interesting tuning
experiments while listening to fine music at the same time...

I don't believe John ever claimed that his versions were historically
accurate. We have called them "distortions," but they are very
interesting and show how the different n-limit tonalities affect the
listener...

They both have totally different objectives, and are achieving
totally different results. The two approaches have nothing to do
with one another...

_________ ____ ___ _
Joseph Pehrson

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗John A. deLaubenfels <jdl@adaptune.com>

[Joseph Pehrson:
>>>The two things, to my mind, have absolutely nothing to do with
>>>one another...

[Monz:]
>>I'm not so sure about this. Ed is trying to present Beethoven's
>>music the way it would have been *heard* on a piano during
>>Beethoven's lifetime. John is trying to present it the way
>>it might have been *imagined* in Beethoven's mind. I'd say
>>that there's a subtle intimate link there.

[Joe:]
>Well, if that, indeed, is John's intention, then it is a more serious
>offense. John, you go to jail. I was under the assumption that John
>just wanted to hear these things as "interesting distortions" or ways
>of listening to n-limit tonalities as an exercise. I never believed
>John thought that Beethoven was imagining things like this...

>Perhaps John can clarify with reference to Ed Foote's historical
>investigations....

What could be more clear than that my work is completely disconnected
from historical accuracy and "authenticity"? Yes, there were theorists,
Vicentino and others, who advocated methods to achieve adaptive tunings
that would maximize JI, and IF they had had the tools I have available
to me, it's POSSIBLE they, and/or others, would have used methods
similar to the ones I'm using. My methods aren't obscure; they seem to
me to be a natural way to deal with the conflicts that exist in tuning
any complex work, given my own strong penchant for JI.

I would not presume to divine what Beethoven or anyone else imagined as
they composed. It would be wonderful if it were possible to go back in
time and introduce the tools we have today to past composers. Truly,
I have no idea what they would say! But, as I have stated before, it
seems to me to be a waste of time to debate such things that can never
be resolved.

There are many on this list who take a great deal of trouble to attempt
to figure out what tunings WERE made use of by given composers. This
is a worthy task, and certainly brings past music to life in a way that
12-tET cannot (for those many composers in the not too distant past who
didn't use 12-tET). That makes the effort doubly worthy.

By contrast, I can only make a single small claim: that, to my ear, the
tunings I present sound nice. That's enough for me. I do believe
strongly that music as a whole is the better for new interpretations
in general, and that the sanctification and rigidification of music is
also the death of music. I think it entirely possible that my work will
be washed away by history, left in the dustbin of misguided attempts to
breathe fresh life into old works. But, if I fail, others will succeed,
and will, I hope, live in mutual respect with those whose focus is an
attempt to unearth the way music was originally presented.

JdL

🔗Joseph Pehrson <joseph@composersconcordance.org>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Ed Foote wrote,

>Gee, I need to parse this out. First and last, is a point being made here

>that "extreme" WT only produce a "little" color? The Kirnberger has a full

>syntonic comma in the three highest keys,(Gb, Db, and Ab). This was near
the
>historically accepted limit if one was to escape the "wolf".

The reason I said a "little" color is that much of the music is in keys that
sound almost identical to equal temperament.

>I don't think "arbitrary" is quite accurate!

Well, I apologize for that, but in listening to the CD I did not get the
feeling that the tuning was particularly bringing out characteristics of the
music, the way unequally-tuned renditions of Bach's WTC, for example, do.
Just my initial impression (what _DID_ I do with that CD???)

>What other tuning
>carries a better or more plausible pedigree for a Beethoven piece of 1804?

Did Beethoven he tune his own pianos? Do we really feel _that_ confident in
the completeness of the documentation of tuning practices of the time, let
alone Beethoven's? And the clinical precision of these tunings -- any human
tuner in those days would have inevitably made rather large errors with
respect to the theoretical tuning, and would have had ways -- perhaps
taught, perhaps figured out through experience -- of "tweaking" after the
first pass so as to end up with an acceptable well-temperament that played
well in all keys -- which I think would usually tend to mean "tweaking" in
the direction of equal temperament.

>Ah, we have a debate, here! This runs counter to everything I have read
>about Beethoven's deafness. He became aware of the impending hearing loss
>around 1801, but was capable of hearing at least until 1815, and some say
>even later than that. Things didn't get profound until around 1820. His
>"Hammerclavier" may have been written deaf, though.

I thought I read that he was essentially deaf, having cut off the legs of
his pianos so that he could feel their vibrations, before most of his
symphonies were written.

Anyhow, I respect your views and the artistry to which they have led, just
trying to maintain a healthy skepticism . . . at least we can agree that a
_closed_ system of 12 pitches is clearly what Beethoven had in mind . . .

Well tempered Beethoven,(was enharmonic)

🔗a440a@aol.com

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Monz <MONZ@JUNO.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗Monz <MONZ@JUNO.COM>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Joseph Pehrson <joseph@composersconcordance.org>

🔗Joseph Pehrson <joseph@composersconcordance.org>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>