Yahoo Tuning Groups Ultimate Backup tuning Lehman's WTC tuning....

J.Smith wrote:
> I've just spent a frustrating 40 minutes or so trying to sort through
> Bradley Lehman's material at LaripS.com -- and I'd pull my hair out by
> the roots, if I had any left. Maybe I didn't follow the correct link (of
> which there are dozens) or whatever, but shouldn't there be a simple
> table that compares his proposed WTC tuning against 12-ET and other
> tunings, using cents? If anyone can provide me with this tuning in cents
> -- to save me from downloading a ton of PDF files and hours of reading
> -- please be kind to this non-technical student of historical tunings.
> I'd like to know what all the fuss is about....

It's actually not hard to calculate, given the size of an untempered fifth (701.955 cents) and the size of a comma (23.46 cents); 1/6 of a comma is 3.91 cents and 1/12 of a comma is 1.955 cents. So going around the circle of fifths:

C 0.000
G 698.045
D 196.090
A 894.135
E 392.180
B 1094.135
F# 596.090
C# 98.045
G#/Ab 798.045
Eb 298.045
Bb 998.045
F 501.955

So the fifths tempered narrow by 1/6 of a comma are 698.045 cents, and the fifths tempered narrow by 1/12 of a comma are 700.000 cents. The single fifth Bb-F is actually tempered wide by 1/12 of a comma, which works out to be 703.910 cents.

I think it's actually easier to compare tunings like this by comparing how the fifths are tempered in fractions of a comma; e.g. comparing Lehman's Bach tuning to Sorge's tuning from 1758:

C-G G-D D-A A-E E-B B-F# F#-C# C#-G# Ab-Eb Eb-Bb Bb-F F-C
Lehman -1/6 -1/6 -1/6 -1/6 0 0 0 -1/12 -1/12 -1/12 +1/12 -1/6
Sorge -1/6 -1/6 -1/6 -1/12 0 -1/12 -1/12 0 -1/12 -1/12 -1/12 0

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> J.Smith asked:
> > I'd like to know what all the fuss is about....??
The history behind is documented in:
http://en.wikipedia.org/wiki/Well-Tempered_Clavier
there under the topic: " What tuning did Bach intend?"
>
> the circle of fifths:
>
> C 0.000
> G 698.045
> D 196.090
> A 894.135
> E 392.180
> B 1094.135
> F# 596.090
> C# 98.045
> G#/Ab 798.045
> Eb 298.045
> Bb 998.045
> F 501.955
>
critial review in:
http://em.oxfordjournals.org/cgi/content/full/34/4/613?
maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=ortgies&searchid=1&
FIRSTINDEX=0&resourcetype=HWCIT

> So the fifths tempered narrow by 1/6 of a comma are 698.045 cents,
and
> the fifths tempered narrow by 1/12 of a comma are 700.000 cents.
The
> single fifth Bb-F is actually tempered wide by 1/12 of a comma,
which
> works out to be 703.910 cents.
most experts consider L's modern 1/12 PC step-wide as to coarse
especially for J.S. Bach, hence historically inacceptable.

>
it's barely an approximative reinterpretation of the
much finer desigend original discovery version of 1999:
http://www.strukturbildung.de/Andreas.Sparschuh/
Contains a copy of the genuine publication in german.

that
reads JSB's string of 11 loops: ?-111000222222-?
as an advise of an tuning-script

start-x1-x2-x3-y1-y2-y3-z1-z2-z3-z4-z5-end cycle of 5hts

beginning and terminating @:
A x1 E x2 B x3 F# y1 C# y2 G# y3 Eb z1 Bb z2 F z3 C z4 G z5 D _ A

Concrete tuned in absolute pitch frequencies on the corresponding
keys:

A 420 cps 210 105 start
x1 = 314/315
E (315>) 314 157
x2 = 470/471
B (471>) 470 235
x3 = 704/705
F# (705>) 704 352 176 88 44 22 11
y1 pure 5th
C# 33
y2 pure 5th
G# 99
y3 pure 5th
Eb 297 148.5 the 5 triple squiggles mean half intergal beatings
z1 = 890/891
Bb (445.5>) 445 222.5
z2 = 1334/1335
F (667.5>) 667 333.5
z3 = 2000/2001
C (1000.5>) 1000 500 250 125 62.5
z4 = 374/375
G (187.5>) 187 93.5
z5 = 560/561
D(280.5>) 280 140 70 35
conclude with an pure 5th back
A 105 returning to the initial start

yielding a subdivision of the
PC = x1*x2*x3*z1*z2*z3*z4*z5

that's in ascending order:

C4 250 cps middle-C frequency
C# 264 132 66 33
D4 280
Eb 297
E4 314
F4 333.5
F# 352 176 88 44 22 11
G4 374 187
G# 396 198 99
A4 420 coeval Leipzig Cammerthon pitch
Bb 445
B4 470
C5 500

Meanwhile there's also an improved version in todays 440Hz norm,
that i do prefer acoustically on my piano,
because i do consider barely half integral pitch-frequencies
in the middle-octave as to coarsely rough-textured alike
L's 1/12 PC reinterpretation, JSB's "squiggles" deserve i.m.o.
a even keener resolution more smooth in finesse of the resolution
for subtle ears, as Bach once had:
My proposal sounds:

a: 440 Hz
start = 1319/1320
e: (3*a = 1320>) 1319 659.5 339.75
x1 = 3569/3957
h: (3*e = 989.25>) 989 494.5 247.5
x2 = 2966/2967
f#=Gb (3*h = 741.75>) 741.5 370.75
x3 = 4448/4449
c#=Db (3*f# = 1112.25>) 1112 556 278 139
Ab = 3*Db = 417 ; triple pure 5ths
Eb = 3*Ab = 1251 625.5 312.75
Bb = 3*Eb = 938.25 469.125 (>469)
z1 = 3752/3753
F: 3*469 = 1407 703.5 351.75 175.875
z2 = 4220/4221
C: (3*F = 527.625>) 527.5 263.75 131.875
z3 = 3164/3165
G: (3*C = 395.675>) 395.5 197.75 98.875
z4 = 181.5/182.5
D: (3*G = 296.625>) 295 (>294 147)
z5 = 176/177
a: (441>) 440 Hz

That's chromatically in ascending order:

C4 263.75 middle-C
c# 278
D4 295
Eb 312.75
e4 339.75
F4 351.75
f# 370.75
G4 395.5
g# 417
a4 440 cps
Bb 469.125
h4 494.5
C5 527.5

or on a 4" organ stop in the discant as integral beating version:

a 440 cps
e (1320>)1319
h (3957>) 3956 1978 989
f# (2967>) 2968 1483
c# (4449>) 4448 2224 1112 556 278 139
g# 417
Eb 1251
Bb 3753 (>3752 1876 938 469)
F 1407
C (4221>) 4220 2110 1055
G (3165>) 3164 1582 791 (>790 395)
D (591>)590 295 (>294 147)
a (885>) 880 440 cps

!sparschuhJSBloops440Hz.scl
!
Sparschuh's 2007 interpretation of J.S. Bach's WTC loops @ 440 cps
!
12
!
! 1055 = (263.75 middle C) *4
!
1112/1055 ! c#
1180/1055 ! D
1251/1055 ! Eb
1319/1055 ! e
1407/1055 ! F
1483/1055 ! f#
1582/1055 ! G
1668/1055 ! g#
1760/1055 ! a with 1760 := 440 * 4
3753/2110 ! Bb
1978/1055 ! h
2/1
!
!

have a lot of fun in trying out that actual refined version

Any comments or suggestions on that recent relase?

A.S.

🔗Tom Dent <stringph@gmail.com>

🔗Brad Lehman <bpl@umich.edu>

"J.Smith" wrote:
> I've just spent a frustrating 40 minutes or so trying to sort through
> Bradley Lehman's material at LaripS.com -- and I'd pull my hair out by
> the roots, if I had any left. Maybe I didn't follow the correct link (of
> which there are dozens) or whatever, but shouldn't there be a simple
> table that compares his proposed WTC tuning against 12-ET and other
> tunings, using cents? If anyone can provide me with this tuning in cents
> -- to save me from downloading a ton of PDF files and hours of reading
> -- please be kind to this non-technical student of historical tunings.
> I'd like to know what all the fuss is about....

Hi JLS, those cent offsets from ET are *in* that "ton of PDF files", specifically the one downloadable from
http://www-personal.umich.edu/~bpl/larips/outline.html
"Appendix: Comparison of Bach's method with other temperaments. Two summary charts, explanation of the included temperaments, and 44 full-page analyses of these competing layouts."

They're also in the main table on this page:
http://www-personal.umich.edu/~bpl/larips/math.html

There is a possibly useful table at the bottom of this page:
http://www-personal.umich.edu/~bpl/larips/enharmonic.html
...comparing a couple dozen there, but I use percents of the comma instead of cents.

But, your suggestion is a good one: sometime I should prepare a simpler side-by-side table of some of the most prominent examples, in cents. Maybe these same ones. (I'm just not a big fan of using cents, personally, because I believe they don't give us particularly clear information when talking about 17th-18th century material! Comma splits are much clearer, at least to me. The 17th-18th century people did not use cents, as the unit hadn't been invented yet. Several *did* use the approximately 2-cent interval of a schisma, i.e. 1/12 Pythagorean comma or 1/11 syntonic comma, as their basic unit: Neidhardt and Sorge, principally, in their tables that present the sizes of all 12 major 3rds, and their tables that describe the tempering of 5ths. They use 0, 1, 2, or 3 of this schisma unit.)

To "learn what the fuss is about", isn't another good way by listening to the recorded samples? :)

Sorry about your hair!

If there were some simpler way of presenting the material, for people who don't fancy reading the expositions first, I'm open to suggestions. I've tried it at several different levels, including these:
http://www-personal.umich.edu/~bpl/larips/art.html
http://www-personal.umich.edu/~bpl/larips/informal.html
http://www-personal.umich.edu/~bpl/larips/outline.html

See also a good explanation in Ross Duffin's book, and his additional "web letter to readers":
http://www2.wwnorton.com/catalog/fall06/006227.htm
http://music.cwru.edu/duffin/Norton/Letter.html
His book has your requested cent tables on page 163.

Cheers,

Bradley Lehman
http://www.larips.com

CC: Duffin

🔗Brad Lehman <bpl@umich.edu>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

It bewilders me that Western academic circles specializing in music theory
are not that much different from their Turkish counterparts. These reprisals
remind me of the polemics between Tura and Zeren on the tuning of Turkish
Music.

Oz.

----- Original Message -----
From: "Brad Lehman" <bpl@umich.edu>
To: <tuning@yahoogroups.com>
Sent: 15 Haziran 2007 Cuma 19:03
Subject: [tuning] Origin of: Re: Lehman's WTC tuning....

> > > So the fifths tempered narrow by 1/6 of a comma are 698.045
> cents,
> > and
> > > the fifths tempered narrow by 1/12 of a comma are 700.000 cents.
> > The
> > > single fifth Bb-F is actually tempered wide by 1/12 of a comma,
> > which
> > > works out to be 703.910 cents.
> > most experts consider L's modern 1/12 PC step-wide as to coarse
> > especially for J.S. Bach, hence historically inacceptable.
>
>
> "Most experts?!" Nope, that's just YOU (Dr Sparschuh) saying over
> and over that you don't fancy it.
>
> Meanwhile, a 704-cent 5th sounds THE SAME in quality as a 700-cent
> 5th (e.g. from 12-equal); it's merely beating the same amount in the
> opposite direction. They're difficult to tell apart from one
> another, in practice on a harpsichord! If you're going to say nasty
> things about an interval you don't fancy, please at least take the
> time to understand what it sounds like first, and not just a bunch of
> numbers on a table.
>
> "Coarse" and "historically inacceptable" indeed? Some of Neidhardt's
> published temperaments from 1732 have one, two, or even THREE of
> those 5ths of that size, 1/12th comma wide.
> http://harpsichords.pbwiki.com/Tuning
> And some of the Werckmeister and Bendeler circulating temperaments of
> the 1690s have 5ths even wider than that. It wasn't verboten to
> them, so why is it verboten to you in these your allegations?
>
>
> Brad Lehman
>

🔗Gordon Rumson <rumsong@telus.net>

🔗Tom Dent <stringph@gmail.com>

Libel? That's a new one on me. Please specify where the supposed libel
occurs. (Libel means a personal remark which is both derogatory and
deliberately dishonest.)

Early Music, notoriously, asks for its authors to express their theses
or opinions strongly and unequivocally. That's what Brad did in his
articles, telling us how sure he was that Bach must have used this
particular tuning, and how we should all use it too all the time.

Was this a good or a bad thing? How would one know? I think it is a
bad thing if it is not definitely correct, but nevertheless causes
many people to believe that the question is settled, and to play Bach
henceforth in only this one tuning, to the exclusion of others, and
even of their own research and creativity. I think it also is a bad
thing if people follow a supposedly historical claim without knowing
how much uncertainty it carries. (Which also happened with previous
supposely historical 'Bach tunings'...) I also think it is a bad thing
for history and performance practice if methods of research are
adopted which depend to a great extent on the writer's personal tastes
or whims, and systematically confuse personal taste with historical
evidence.

Now we have Lindley and Ortgies telling us that Lehman's historical
methods are bad and are very unlikely to give any good idea of Bach's
tuning or tunings.

Is this a good or a bad thing? If they are correct, then it is a good
thing, whether they express themselves politely or rudely. If it
causes people to think carefully about accepting pre-mixed temperament
recipes, and to start using their ears carefully instead, it might
also be a good thing. It would only be a bad thing if their arguments
are definitely weaker than Brad's.

So what is the problem with well-qualified people expressing, in plain
language, negative opinions about other people's claims of historical
research, if they can put forward clearly comprehensible arguments why
it is bad?

How would one know whether or not Lindley and Ortgies give serious
examination to the question, without reading the article? An abstract
can only point roughly to the conclusions, without giving a full
account of the reasoning.

The situation is rather asymmetrical in that everything on Brad's
website (which is naturally enough arranged to let him have the last
word) can be publicly seen - whereas the Lindley article is only
available to subscribers of Early Music. One may try to peruse Brad's
comments on the Lindley article on his own webpage. But do you think
it is possible or likely that Brad will accurately and fairly
summarize the arguments of his own most powerful critics?

One should at least suspect whether *both* sides might not be engaged
in doing everything possible to prove the other guy wrong. And whether
clearly displayed opinions are better or worse than biases hidden
under a mound of formal analysis.

.....

Where is Bach in all this? If the result is that performers' options
in tuning their instruments ever more restricted (as Brad is, in fact,
arguing for), I would say Bach is the victim. Since I believe that
Bach can sound perfectly good in many dozens of different - but not
vastly different! - tunings, I think it would be a great shame if this
were reduced to just a single tuning realised more or less exactly.

Also, since choosing and realizing a good tuning is an important part
of being a good instrumentalist, I think it would be a great
inhibition of the creativity and mastery of keyboard players if they
all followed the same recipe.

Since Lehman (like several before him) appears on the side of a
one-size-fits-all magic bullet approach to 'Bach tuning', wheres
Lindley and Ortgies appear on the side of debunking the magic bullet
and thereby reinstating a degree of individual artistic freedom and
responsibility, my conclusion is obvious. "There are nine and sixty
ways of constructing tribal lays, And every single one of them is right!"

~~~T~~~

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> The abstract by Lindley and Ortgies is riddled with bias and libel. The
> language itself is needlessly abusive. Why show such blatant lack of
> appreciation facing the original, albeit unorthodox, approach by Bradley
> which requires serious examination bereft of insults and taunts?
>
> Oz.
>
> ----- Original Message -----
> From: "Brad Lehman" <bpl@...>
> To: <tuning@yahoogroups.com>
> Sent: 15 Haziran 2007 Cuma 18:51
> Subject: [tuning] Origin of: Re: Lehman's WTC tuning....
>
>
> > > critial review in:
> > > http://em.oxfordjournals.org/cgi/content/full/34/4/613?
> > maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=ortgies&searchid=1&
> > FIRSTINDEX=0&resourcetype=HWCIT
> >
> >
> > And a critical review of those reviewers' arguments, at:
> > http://www-personal.umich.edu/~bpl/larips/lindleyortgies.html
> > http://www-personal.umich.edu/~bpl/larips/odonnell.html
> >
> >
> > Brad Lehman
> >
> >
>

🔗Aaron K. Johnson <aaron@akjmusic.com>

Yikes...the Brad Lehman thing keeps rearing it's ugly head around here. I wonder if we get bored, and someone just mentions it to start a hot topic again. It's like mentioning abortion or gay marriage at a Baptist family reunion.

Anyway, good thoughts, Tom. I would add that I think Brad seems like a good guy, smart, interesting, etc. And an able musician. I disagree with his conclusion strongly, however, like you do, that Bach should only work in his tuning, and that somehow we weren't 'getting' Bach before he let us see the colors.

In this and other discussions, I would refer you to the blind audio tests I did a while back using a Bach piece. I think I proved that these differences between various WTs are tiny enough to fool people into thinking the audibly best one is the one they hate the most _on paper_. I will stand by the results of these tests again and again. Johnny Reinhard didn't think WerckIII was the best, and I think Brad didn't recognize his own tuning, and preferred another. Granted, it *was* an electronic sample rendition, but it was good enough, I think, in spite of the inevitable caveats that followed.

I was also a victim--WerckIII sounded decent enough to me, although not my favorite by far, even though I fought against it on paper.......perhaps this whole business of caring all that much is a bit silly!? Anyway, that's what I brought away from my tests....Bach sounded anywhere from fascinatingly and grotesquely 'off' (interesting for it's own sake, I think) to passable to very fine in a variety of tunings, and it seems that at least some of this might be accountable to individual taste, which is to me how it should be. Most agreed that whatever the truth of Brad's assertions, his tuning suits Bach well. Ditto, for me, Francis's tunings, which Brad despises. Anyway---I'm not much into finding 'the one true tuning' to invest my entire being into...I don't get that point of view, but I want to be careful not to dismiss it either--to each his own, as they say.

Yes, 19/15 is a good ratio, I've made a couple of temperaments using it. I'm fond of one that uses 5/4,24/19, and 19/15. Check the Scala archives for this and others. I don't under what conditions I'd ever be able to do 19/15 by ear; I'm doubtful, but I also haven't tried very hard.

Speaking of 19/15 vs. 81/64---have you ever done my listening test about trying to distinguish between them? I was amazed that a couple of folks around here could...however, it really wasn't designed to be a large enough random sample---I think the results would be stronger and more convincing if I did it for many more trials.

-A.

Tom Dent wrote:
> Libel? That's a new one on me. Please specify where the supposed libel
> occurs. (Libel means a personal remark which is both derogatory and
> deliberately dishonest.)
>
> Early Music, notoriously, asks for its authors to express their theses
> or opinions strongly and unequivocally. That's what Brad did in his
> articles, telling us how sure he was that Bach must have used this
> particular tuning, and how we should all use it too all the time. >
> Was this a good or a bad thing? How would one know? I think it is a
> bad thing if it is not definitely correct, but nevertheless causes
> many people to believe that the question is settled, and to play Bach
> henceforth in only this one tuning, to the exclusion of others, and
> even of their own research and creativity. I think it also is a bad
> thing if people follow a supposedly historical claim without knowing
> how much uncertainty it carries. (Which also happened with previous
> supposely historical 'Bach tunings'...) I also think it is a bad thing
> for history and performance practice if methods of research are
> adopted which depend to a great extent on the writer's personal tastes
> or whims, and systematically confuse personal taste with historical
> evidence.
>
> Now we have Lindley and Ortgies telling us that Lehman's historical
> methods are bad and are very unlikely to give any good idea of Bach's
> tuning or tunings. >
> Is this a good or a bad thing? If they are correct, then it is a good
> thing, whether they express themselves politely or rudely. If it
> causes people to think carefully about accepting pre-mixed temperament
> recipes, and to start using their ears carefully instead, it might
> also be a good thing. It would only be a bad thing if their arguments
> are definitely weaker than Brad's.
>
> So what is the problem with well-qualified people expressing, in plain
> language, negative opinions about other people's claims of historical
> research, if they can put forward clearly comprehensible arguments why
> it is bad? >
> How would one know whether or not Lindley and Ortgies give serious
> examination to the question, without reading the article? An abstract
> can only point roughly to the conclusions, without giving a full
> account of the reasoning.
>
> The situation is rather asymmetrical in that everything on Brad's
> website (which is naturally enough arranged to let him have the last
> word) can be publicly seen - whereas the Lindley article is only
> available to subscribers of Early Music. One may try to peruse Brad's
> comments on the Lindley article on his own webpage. But do you think
> it is possible or likely that Brad will accurately and fairly
> summarize the arguments of his own most powerful critics? >
> One should at least suspect whether *both* sides might not be engaged
> in doing everything possible to prove the other guy wrong. And whether
> clearly displayed opinions are better or worse than biases hidden
> under a mound of formal analysis.
>
> .....
>
> Where is Bach in all this? If the result is that performers' options
> in tuning their instruments ever more restricted (as Brad is, in fact,
> arguing for), I would say Bach is the victim. Since I believe that
> Bach can sound perfectly good in many dozens of different - but not
> vastly different! - tunings, I think it would be a great shame if this
> were reduced to just a single tuning realised more or less exactly. >
> Also, since choosing and realizing a good tuning is an important part
> of being a good instrumentalist, I think it would be a great
> inhibition of the creativity and mastery of keyboard players if they
> all followed the same recipe. >
> Since Lehman (like several before him) appears on the side of a
> one-size-fits-all magic bullet approach to 'Bach tuning', wheres
> Lindley and Ortgies appear on the side of debunking the magic bullet
> and thereby reinstating a degree of individual artistic freedom and
> responsibility, my conclusion is obvious. "There are nine and sixty
> ways of constructing tribal lays, And every single one of them is right!"
>
> ~~~T~~~
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >> The abstract by Lindley and Ortgies is riddled with bias and libel. The
>> language itself is needlessly abusive. Why show such blatant lack of
>> appreciation facing the original, albeit unorthodox, approach by Bradley
>> which requires serious examination bereft of insults and taunts?
>>
>> Oz.
>>
>> ----- Original Message -----
>> From: "Brad Lehman" <bpl@...>
>> To: <tuning@yahoogroups.com>
>> Sent: 15 Haziran 2007 Cuma 18:51
>> Subject: [tuning] Origin of: Re: Lehman's WTC tuning....
>>
>>
>> >>>> critial review in:
>>>> http://em.oxfordjournals.org/cgi/content/full/34/4/613?
>>>> >>> maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=ortgies&searchid=1&
>>> FIRSTINDEX=0&resourcetype=HWCIT
>>>
>>>
>>> And a critical review of those reviewers' arguments, at:
>>> http://www-personal.umich.edu/~bpl/larips/lindleyortgies.html
>>> http://www-personal.umich.edu/~bpl/larips/odonnell.html
>>>
>>>
>>> Brad Lehman
>>>
>>>
>>> >
>
>
>
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🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Tom Dent" <stringph@gmail.com>
To: <tuning@yahoogroups.com>
Sent: 15 Haziran 2007 Cuma 22:14
Subject: [tuning] Origin of: Re: Lehman's WTC tuning....

>
> Libel? That's a new one on me. Please specify where the supposed libel
> occurs. (Libel means a personal remark which is both derogatory and
> deliberately dishonest.)
>

Among several definitions for "libel" in my MS Bookshelf British Reference
Collection, I choose "any malicious defamatory publication or statement".

The abstract in question, one can clearly discern the ill-will of the
authors in such remarks as:

"The premise that a mathematically rigid tuning-scheme is hidden cryptically
in a decorative scroll on the title-page of WTC I is daft..."

"Lehman's idea that Bach's secret tuning is uniquely beautiful for music by
Frescobaldi et al. is outlandish."

(Brad refutes ever having stated as such)

> Early Music, notoriously, asks for its authors to express their theses
> or opinions strongly and unequivocally. That's what Brad did in his
> articles, telling us how sure he was that Bach must have used this
> particular tuning, and how we should all use it too all the time.
>

He has demonstrated with skill that his conclusions may have a bearing, and
may not be summarily dismissed. I support his convictions based on pure
scholarly pursuit (to the detriment of the orthodoxy), even if I don't share
his passions.

> Was this a good or a bad thing? How would one know? I think it is a
> bad thing if it is not definitely correct, but nevertheless causes
> many people to believe that the question is settled, and to play Bach
> henceforth in only this one tuning, to the exclusion of others, and
> even of their own research and creativity.

It is his conviction that Bach has intended for this tuning, and historical
performance would then necessitate such a tuning per se. There is nothing
wrong with holding such a position if one can produce convincing
demonstrations and proof, which Brad has done I believe.

I think it also is a bad
> thing if people follow a supposedly historical claim without knowing
> how much uncertainty it carries. (Which also happened with previous
> supposely historical 'Bach tunings'...) I also think it is a bad thing
> for history and performance practice if methods of research are
> adopted which depend to a great extent on the writer's personal tastes
> or whims, and systematically confuse personal taste with historical
> evidence.

But music is the goal here, not a simple side-effect of theory. Brad is
convinced that Bach would demand the best temperament for his music, and
goes on to show that the composer has taken the trouble to scribble it down
in the one place where hardly anybody bothered to look. It is fascinating
enough that a crude squiggle could yield such a beautifully resonating
temperament in the first place.

>
> Now we have Lindley and Ortgies telling us that Lehman's historical
> methods are bad and are very unlikely to give any good idea of Bach's
> tuning or tunings.
>

Which Brad refutes in his lengthy reprisals.

> Is this a good or a bad thing? If they are correct, then it is a good
> thing, whether they express themselves politely or rudely. If it
> causes people to think carefully about accepting pre-mixed temperament
> recipes, and to start using their ears carefully instead, it might
> also be a good thing. It would only be a bad thing if their arguments
> are definitely weaker than Brad's.
>

How established is this Bach-scholarship on tuning anyway? Brad questions
the orthodoxy, and points out several crucial points to his favour as far as
I can read. It is a bad show if, instead of sound criticism, we are
countenanced by such defamations as "daft" and "outlandish" based on Allah
knows what.

> So what is the problem with well-qualified people expressing, in plain
> language, negative opinions about other people's claims of historical
> research, if they can put forward clearly comprehensible arguments why
> it is bad?
>

It is bad if they do not suggest anything more convincing, or if their whole
pursuit is to kindle senseless bigotry.

> How would one know whether or not Lindley and Ortgies give serious
> examination to the question, without reading the article? An abstract
> can only point roughly to the conclusions, without giving a full
> account of the reasoning.
>

An abstract gives away the intent of the authors. Brad seems to be justified
in his retort. Though somewhat unacademic in language, I personally found it
quite amusing and to the point.

> The situation is rather asymmetrical in that everything on Brad's
> website (which is naturally enough arranged to let him have the last
> word) can be publicly seen - whereas the Lindley article is only
> available to subscribers of Early Music. One may try to peruse Brad's
> comments on the Lindley article on his own webpage. But do you think
> it is possible or likely that Brad will accurately and fairly
> summarize the arguments of his own most powerful critics?
>

It is indeed asymmetrical if some people tend to exploit such reputed
journals as Early Music to scratch "unorthodox newbies" through adversely
influencing hundreds of venerable readers who do not use the internet. Early
Music must now make room for Brad to express himself if it hopes to be
impartial.

> One should at least suspect whether *both* sides might not be engaged
> in doing everything possible to prove the other guy wrong. And whether
> clearly displayed opinions are better or worse than biases hidden
> under a mound of formal analysis.
>

I enjoy such expositions to my own amusement. On the whole, I would prefer
unbiased academical study and criticism. One should never revert to hurtful
language there of course.

> .....
>
> Where is Bach in all this? If the result is that performers' options
> in tuning their instruments ever more restricted (as Brad is, in fact,
> arguing for), I would say Bach is the victim. Since I believe that
> Bach can sound perfectly good in many dozens of different - but not
> vastly different! - tunings, I think it would be a great shame if this
> were reduced to just a single tuning realised more or less exactly.
>

That is a difference of taste, and has nothing whatsoever regarding Brad's
conviction that Bach has intended and specified a single well-temperament
for at least a repertory of his music.

I agree that Bach sounds exotic in many other tunings. There are possibly an
infinite number of temperaments in which Bach would sound "acceptable", but
it is quite a moot argument. While Brad may be looking for the "best" and
"true", I am searching for the "historically plausible". Lehman's
temperament seems to be "historically plausible" and earns merit.

> Also, since choosing and realizing a good tuning is an important part
> of being a good instrumentalist, I think it would be a great
> inhibition of the creativity and mastery of keyboard players if they
> all followed the same recipe.
>

Agreed. But still, it is a matter of taste and preference.

> Since Lehman (like several before him) appears on the side of a
> one-size-fits-all magic bullet approach to 'Bach tuning', wheres
> Lindley and Ortgies appear on the side of debunking the magic bullet
> and thereby reinstating a degree of individual artistic freedom and
> responsibility, my conclusion is obvious. "There are nine and sixty
> ways of constructing tribal lays, And every single one of them is right!"
>

So is Lehman's then. So why this attack by Lindley and Ortgies?

> ~~~T~~~
>

Oz.

🔗Brad Lehman <bpl@umich.edu>

> > Where is Bach in all this? If the result is that performers'
options
> > in tuning their instruments ever more restricted (as Brad is, in
fact,
> > arguing for), I would say Bach is the victim. Since I believe that
> > Bach can sound perfectly good in many dozens of different - but
not
> > vastly different! - tunings, I think it would be a great shame if
this
> > were reduced to just a single tuning realised more or less
exactly.

I think this point has been pressed far overboard, turning Bach into
a
victim! Come on. Musicians can choose to use, or not to use, my
ideas as they see fit; they make choices for THEIR OWN musicianship
and their own musical goals for performance.

I'm not restricting or reducing anything. My intent is simply to
present a possible dimension in Bach's work (and in Bach's brilliance
as composer) that hasn't been explored before. And I encourage a
direct grappling with the material: not only studying the written
sources, but trying out the music hands-on with appropriate
instruments. Set it up and give it a play; that's part of the
research.

Rather than limiting anything, it frees up another OPTION that wasn't
given much focus before: playing with the various 18th century
temperaments that DON'T fit the usual Lindley hypothesis (in New
Grove and in other places) where Db major has to have the widest
major 3rd.

And Bach is some "victim" in this, where his music turns out to sound
(arguably) better this way? Where people are actually playing his
music to test this...the music is getting played and listened to.
Where's the victimization in that?

Brad IS NOT, "in fact", arguing for restrictions! Maybe some of
Brad's opponents are.

The newest one is an album I haven't heard yet, released just this
week: Paul Simmonds playing an hour of Wilhelm Friedemann Bach on
clavichord. He tells me he used my system, basically, but has
developed his own tweak of it over the past couple years where he
softens the E major triad a slight bit. That's all well and good, as
he's an excellent musician and can make his own choices as to what
sounds good on his own instruments. His disc:
http://www.london-independent.co.uk/home.htm

Another recent one was a young man from Budapest (Zsolt Kaltenecker)
improvising an album of jazz on his synthesizer, using my system.
Some quite attractive sounds, in my opinion:
http://www.kalteneckerzsolt.com/records
http://www.myspace.com/zsoltkaltenecker

Brad Lehman
http://www.larips.com

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Brad Lehman" <bpl@> wrote:
>
> > Meanwhile, a 704-cent 5th sounds THE SAME in quality as a 700-cent
> > 5th (e.g. from 12-equal); it's merely beating the same amount in the
> > opposite direction.
>
> I don't think sharp fifths sound the same as flat fifths; there's quite
> a notable difference between the 19-et fifth and the 22-et fifth, I
> think.
>
fully agreed Gene,
ih deed, they are percieved different:
That effect is well known and confirmed in history of acoustics
since about ~2.5 millenia:
Here some sources for example:

#1.
Johann Mattheson refers to that obvervation of
Aristoxenes in his: GroÃe Gernal-BaÃ-Schule, Hamburg 1732, facs.
reprint Hildesheim 1968 p.147, Chap. CXXXVII,
zur Organisten-Probe, addendum organist-examination:

Quotation in french (original in ancient greek):
"La Quinte trop forte, & la Quarte trop foible n'accomodant point
l'orielle, il faloit diminuer un peu la premiere, pour donner un peu
plus d' e'tendue a' l'autre." cit: BONTEMPI, dell'Istoria Musica, p.93
& ex illo Brossard p.172

Mattheson's german version:
"Da die gar zu starcke Quint / und gar zu schwache Quart / dem GehÃ¶r
nicht gelegen wÃ¤ren / mÃ¼Ãte man die erste ein wenig kleiner machen /
und der anderen etwas zugeben."

Engl.translation:
"The ear doesn't like the overwide 5th nor the weakend flat 4th,
therefore the first(the 5th) has to be diminshed and the other
(the 4th) extended" conversely.

Means that they agree in disliking broade wrong 5ths,
which are percieved by the human ear as more inept
than the common usual flattend 5hts,
when detuned by the same amount in seize in the
opposite direction.
Even Dr. L. recognizes ~704Cents as "diminished 6th",
but never refers to the 12-EDO 5th of 700Cents
as "augmented 4th". At least in his terminology he
expresses clearly that difference in his own perception.

#2.
The swiss organ-builder Victor Ferdinand Brossard
~1740 in his tuning instruction of an ancient out-dated instrument:
"Anderes stimmwerckh" Reprint: Ars Organi 45 Jhg. Heft 3 September
1993 p.174 Ed. B. Billeter "...ein quint dan diser wolf ein getheilt
wird und dergleichen, der Dackhel man's nennet under keine CONCORDANTZ
mag werden..."

Translation: "other organ...
resulting in an (tiny) wide wolf 5th, also called 'Dackel'-dog, that
doesn't want to become none CONCORDANCE..."

That 'Dackel'(sousage-dog) 5th disturbes free modulation over that
broade 5th already even if barely 1/12 PC exaggerated.

#3.
Georg Andreas Sorge's
"tuning-instructions" Hamburg 1744 p.22
SchÃ¼ler Frage:
"Kann man nicht auch einige Quinten Ã¼ber sich schweben lassen?"
Lehrer Antwort:
"Ja, aber es ist ganz unnÃ¶tig..."

Tr:
Pupil's question:
'Can one also let some 5ths beat larger than pure?'
Teacher's reply:
'Yes, but it's wholly unnecesarry...'

Sorge agrees here in with his teacher...

#4.
... C.P.E. Bach,
that wrote barely about only "pure or flattended 5ths"
but never mentioned broade ones in none of his instructions:
http://www-personal.umich.edu/~bpl/larips/cpeb.html
"Â§. 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...."

#5.
G. Armellino, Kunst des Klavierstimmens
(Art of piano tuning in reference to J.S. Bach) Weimar 1881,p.36
"Der minder GeÃ¼bte pflegt die Schwebung meistens zu Ã¼bertreiben, um
sie deutlich zu erkennen, und bringt durch allzubedeutende SchwÃ¤chung
der Quniten das entgegengesetzte MiÃverhÃ¤ltniss von dem hervor, was er
ausgleichen soll."

Tr: 'The art of piano-tuning' p.36
"The less trained layman overpronounces usually the beating (of the
5ths) in order to detect and identify them (more) clearly,
but yields by that overdoing an to much weakening inbetween
the initial 5ths, resulting in an opposite mismatch
of what he should adjust/counterbalance/compensate"

That accumulated defect arises in L's case from 13/12 PC
overtempering in the first 11 5ths
hence results finally in an broadly 5th of ~704 Cents in the
last concluding one, the 1/12 PC "dackel-dog" 5th,
not to be confused with:
http://www-personal.umich.edu/~bpl/zade.html#fianna
that has to undergo in suffering Brad's
questionable dackel-dog 5th-tempering.
Who protects that poor animal acoustically?

But joke aside:

Even all my former tuner-colleagues from
http://www.euro-piano.org/html/index.php
refuse to tune the "Dackel"
considering that cumbersomely error as handicrafts-man's: "botch",
due to the 'use- and needless' additional beatings
arising from the wide 5ths,
inherently wrong in Lehman's private modern 21th century
doggy-style tuning.

It doesn't satisfy even the condition of:
/tuning/topicId_66654.html#66659
"an authentic well-temperament,
with no fifth wider than 3/2. "

http://bachtuning.jencka.com/essay.htm
fixed that appearent bug in L's reinterpretation,
in getting rid of the bricolage,
in missing the target without changing the direction
of underbeating in all tempered 5ths.

There's no accounting for taste
particulary if misleaded astray.

What are wide 5ths for?
Why looping circutious away round
for making a detour in the wrong direction,
by duffing the last 5th of the dozen in the cirlce?

No thanks,
but I do prefer the direct way without over-broade 5ths,
direct into the goal, when sub-dividing the PC,
avoiding "cobblestone" tuning, due to by-pass redirection.

I.m.h.o:
Alleged "wide-french" 5ths in a modern tuning,
remind me of my involuntary extra-orbiting
as naive tourist when i had been in the mercy of a taxi-driver
spinning around the
http://en.wikipedia.org/wiki/Arc_de_Triomphe
sitting caught in the trap, back of an Parisian taxi,
due to lack of next victim-passengers asking for a cab,
appearently in order to play for time
for accumulating charge on the running counter.

That was an silly expensive game,
reminding me again, when hearing
indirections in tempering of the PC.

Sorry, but no thanks!

A.S.

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@>
> wrote:
>
> > Even Dr. L. recognizes ~704Cents as "diminished 6th",
> > but never refers to the 12-EDO 5th of 700Cents
> > as "augmented 4th". At least in his terminology he
> > expresses clearly that difference in his own perception.
>
> I don't think you can conclude from that he thinks it sounds awful,
Far from it!
Quite the contrary seems to be true:
appearently he loves that questionable taste,
especially in his own preferred modern neo-Baroque tuning.
De gustibus non est disputandum.
http://www.jstor.org/view/00028282/di950131/95p0253l/0

> which is rather an extreme position.
in deed,
Brad knew exactly about C.P.E. Bach's statement on his father JSB:
"Nobody was able to tune his Clavier to his satisfaction"
It is 'outlandish' to assume that J.S. Bach was so inable in tuning,
as Dr. Lehman assumes and does prefer privately.
He simpy fails to close the circle of a dozen 5ths properly,
and dares to presume his own incompetence to the old JSB.
We have to agree with T. Dent:
JSB is the victim.

Unfortunately
JSB isn't any more able to defend his good reputatation
in tuning against Brad's imputed claims and unsustainbale allegations.

> I think 46-et does fine in the
> fifth department,
again agreed:

2^(27/46) = ~1.50207466...
or
1200 C * 27/46 = ~704.347826...Cents

http://en.wikipedia.org/wiki/Stretched_tuning
sounds well in modern pianos with extra thick strings due to:
http://en.wikipedia.org/wiki/Piano_acoustics
but miserable in coeval instruments of J.S. Bach's time
with almost vanishing inharmonicity from thinn strings.

>and sharper fifths than that have a lot of fans--look
> at all the hullabaloo about the 17-34-68 complex.

2^(10 / 17) = ~1.50340665...
or
12 000 C / 17 = ~705.882353... Cents

Do you mean by that?...:
http://en.wikipedia.org/wiki/Georg_Hajdu
" Heptadecatonic Drops for MIDI instruments and computer in 17-tone
equal temperament (1989/90)"
# 17 Tones. Proceedings of the International Computer Music
Conference, 1992, 449-450.
# 17 Töne. A collection of compositions in 17-tone equal temperament
by C. Barlow, C.Bauckholt, G. Hajdu, C.J. Walter, and C. Wilkens.
Georg Hajdu (editor).

that guys?

simply hear and study that 17-EDO "compositions"
for better understanding the meaning of
Brad's all to much over-broade 5ths, adaequate to:
http://home.ntelos.net/~bpl/afton/lullaby.JPG

A.S.

Lehman's WTC tuning....

🔗J.Smith <jsmith9624@sbcglobal.net>

🔗Herman Miller <hmiller@IO.COM>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗Tom Dent <stringph@gmail.com>

🔗Brad Lehman <bpl@umich.edu>

🔗Brad Lehman <bpl@umich.edu>

🔗Brad Lehman <bpl@umich.edu>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Gordon Rumson <rumsong@telus.net>

🔗Tom Dent <stringph@gmail.com>

🔗Aaron K. Johnson <aaron@akjmusic.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Brad Lehman <bpl@umich.edu>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>