Yahoo Tuning Groups Ultimate Backup tuning my lecture notes from 10/22

Here are the slides I used in a public lecture on Wednesday evening. It is an attempt to explain some of the most important tuning principles (and the operation of tonality, and diatonic scales) with as little math as possible, and without expecting the audience to be able to read music. An interesting challenge.

http://larips.50webs.com/

There is a long section in there about the reasons why circulating temps aren't very well understood.

Brad Lehman

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Certainly, and please do. The main site is here: http://www.larips.com

Brad Lehman

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>
> Can I post your email text (not address) and link to another forum for
> people who are getting curious about the world beyond 12-tet?
>
>
>
> On Fri, Oct 24, 2008 at 2:09 PM, Brad Lehman <bpl@...> wrote:
>
> > Here are the slides I used in a public lecture on Wednesday
evening. It
> > is an attempt to explain some of the most important tuning principles
> > (and the operation of tonality, and diatonic scales) with as
little math
> > as possible, and without expecting the audience to be able to read
> > music. An interesting challenge.
> >
> > http://larips.50webs.com/
> >
> > There is a long section in there about the reasons why circulating
temps
> > aren't very well understood.
> >
> > Brad Lehman
> >
> >
>

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>
>...people who are getting curious...
Hi Chris,
>
Attention:
Beware with cautious care the questionable claims there in:
> > http://larips.50webs.com/Tuning_lecture_Oct_2008_part1.pdf
on page 12:
"...the world's best early-keyboard experts never tune an
entire temperament by ear themselfs..."

Counter-examples against that untenable allegation are for instance,
my old friends and experts in that field:

http://en.wikipedia.org/wiki/Helmuth_Rilling

and especially

http://en.wikipedia.org/wiki/Ton_Koopman

Ton mostly insists to tune harpischords himself,
because he prefers to perform Bach
with the major-3rd C-E sounding beatingless pure
in matching the resonance to the 5th-partial,
without exceeding the range of "fusing" 5/4 : @ ~386+-~1 Cents.

Ton teached me so back in 2000 personally in Frankfurt
in an public discussion with the 'Bach-scholar'
http://en.wikipedia.org/wiki/Christoph_Wolff
at the occasion of presenting Wolff's Bach biography.

Meanwhile,
Ton convinced me to agree with his view,
that in modern so called neo-"Bach-tunings" for harpsichords
the 3rd C-E should sound acoustically just perfect
indistinguishable in resonance matching pure 5/4,

By now,
many colleagues widely accepted Ton's C-E = 5/4
in recent 21.th-century neo-"Bach-tunings".
as the actual state-of-the-art.

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

bye
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
>
> > > http://larips.50webs.com/Tuning_lecture_Oct_2008_part1.pdf
> on page 12:
> "...the world's best early-keyboard experts never tune an
> entire temperament by ear themselfs..."
>

Does Brad really say that? Googling for this phrase suggests not.

I wasn't planning on reading his latest core dump of (probably)
ahistorical self-verifying post-hoc argumentation (Principle: do
whatever I like and use any means necessary to convince people it was
'historical'). I'm not interested in what Brad personally likes, and
don't have the time and stamina to refute his argumentations, given
that (based on past experience) he will a) ignore any refutations and
b) come up with a completely different set of arguments in a few months.

But this quote suggests that its entertainment value may be more than
I expected.

I *would* be interested in seeing a short (few hundred word) summary
or precis of the lecture notes - assuming that isn't beyond the reach
of human intelligence.

I also wish Brad would spend some time going over his vast
(many-hundred-page?) previous documentation and selecting out the
parts (-if any-) that he still thinks are valid/meaningful, i.e. that
have not yet been contradicted or shown to be entirely circumstantial.
But I don't expect I will get my wish.

> Ton convinced me to agree with his view,
> that in modern so called neo-"Bach-tunings" for harpsichords
> the 3rd C-E should sound acoustically just perfect
> indistinguishable in resonance matching pure 5/4,

But what reasons could Koopman give...? I don't think you gain much
musically from having this, whereas you lose quite a lot in remote and
not-so-remote keys like A major and E flat major.

I think it quite likely that Bach could and did tune by controlling 3
major thirds C-E-G#-C or F-A-C#-F, now if C-E is 'acoustically pure'
(ie not audibly sharp) it is considerably harder to set G# so that
E-G#-C are good enough.
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
Hi Tom & all others,
> > > > http://larips.50webs.com/Tuning_lecture_Oct_2008_part1.pdf
> > on page 12:
in the *.PDF file accentuated in red letters

> > "Many of the world's best early-keyboard experts never tune an
> > entire temperament by ear themselfs..."

> Does Brad really say that? Googling for this phrase suggests not.
May be due to Google's new intelligent spam-filter?
>
> I wasn't planning on reading his latest core dump of (probably)
> ahistorical self-verifying post-hoc argumentation

http://en.wikipedia.org/wiki/Pseudoscience

>(Principle: do
> whatever I like and use any means necessary to convince people it
> was 'historical'). I'm not interested in what Brad personally likes,
> and
> don't have the time and stamina to refute his argumentations, given
> that (based on past experience) he will a) ignore any refutations and
> b) come up with a completely different set of arguments in a few months.
>
> But this quote suggests that its entertainment value may be more
> than I expected.

Fully agreed.

>
> I *would* be interested in seeing a short (few hundred word) summary
> or precis of the lecture notes - assuming that isn't beyond the
> reach
> of human intelligence.

Sorry:
Personally I also tryed to get an concise excerpt
of his views in vain.

>
> I also wish Brad would spend some time going over his vast
> (many-hundred-page?) previous documentation and selecting out the
> parts (-if any-) that he still thinks are valid/meaningful, i.e. >that
> have not yet been contradicted or shown to be entirely circumstantial.
> But I don't expect I will get my wish.
>
Never give up, the hope dies lastly.

>
> > Ton convinced me to agree with his view,
> > that in modern so called neo-"Bach-tunings" for harpsichords
> > the 3rd C-E should sound acoustically just perfect
> > indistinguishable in resonance matching pure 5/4,
>
> But what reasons could Koopman give...?

May be even more pronunced key-characteristics?
by yielding an fusing 5th partial at least for the 3rd C-E?

Sorry for my ignorance:
But Ton never told me why he did so.

> I don't think you gain much
> musically from having this, whereas you lose quite a lot in remote and
> not-so-remote keys like A major and E flat major.
>
> I think it quite likely that Bach could and did tune by controlling 3
> major thirds C-E-G#-C or F-A-C#-F, now if C-E is 'acoustically pure'
> (ie not audibly sharp) it is considerably harder to set G# so that
> E-G#-C are good enough.

That was already Schlick's problem:
The struggle with enharmonics G# = Ab
later still Paul Hindemith's.

bye
A.S.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> Does Brad really say that? Googling for this phrase suggests not.

Of course I didn't. Andreas misquoted it first before criticizing it;
and his comments were about only one (misquoted) part of one sentence
he didn't like, instead of the thrust of the whole argument (across
seven PDF files).

As I said the first time, that complete set of slides is here:
http://larips.50webs.com/
It was a PowerPoint presentation, and I saved it out to these seven
PDF files of less than 500K each.

Tom, it would probably take you less than the whole hour to read all
those (fewer than 60) slides in all the seven files. That would seem
a useful and responsible path for an expert scientist such as yourself
to take: read something directly, instead of posting pre-judgments
against it. Please do. My presentation explains my reasoning, very
clearly. I can see that you don't *understand* (or maybe just don't
like) my reasoning, in the direction of looking at Bach's compositions
that call for more than 12 notes.

Enjoy,
Brad Lehman

I wrote:
> Tom, it would probably take you less than the whole hour to read all
> those (fewer than 60) slides in all the seven files. That would
> seem a useful and responsible path for an expert scientist such as
> yourself
> to take: read something directly, instead of posting pre-judgments
> against it. Please do. My presentation explains my reasoning, very
> clearly. I can see that you don't *understand* (or maybe just don't
> like) my reasoning, in the direction of looking at Bach's
> compositions that call for more than 12 notes.

p.s. It would also help to have read Easley Blackwood's book more than
20 years ago, as I did, since it deeply informed the way I understand
the construction of diatonic scales: the generation of all the notes
by a series of (usually regular) 5ths. Harpsichord tuning by 5ths and
4ths is done not only because it's easy and it works, but more
basically because that's where we get a series of 7 and then 12
inter-related notes, and beyond. And, the notes of the C major scale
are central to that section of the spiral used most.

Brad Lehman

I have mentioned in some messages here very often terms "scale", "intonation", "temperament", "tuning" (somebody can add more?) are used chaotically, inconsistently and not in exact way. Maybe it would be good if some of our clever gurus here explains how to use these terms more scientifically and everybody should use it just that way. We should be careful enough even with using of such basic and simple terms. It would be good to unite opinions and use it properly. It's not totally interchangeable. I have some idea about it as well.

I'm sure it was discussed before, review or link as well as opinions are welcome.

Daniel Forro

Hi Daniel,

I try to use the terms thus:

scale - a list of pitches, finite under multiplications
by a *period* (such as the octave)

temperament - a homomorphism (mapping) from a finitely-
generated subgroup of the rational numbers (just intonation)
to an abstract free group of smaller rank

tuning - a monomorphism (1:1 mapping) from the temperament
to the positive reals (pitches)

These definitions are due to Gene Ward Smith. The idea is,
you can define temperaments abstractly. For instance,
meantone temperament is the thing in which a major third
is composed of four perfect fifths minus 2 octaves. This
+4 -2 mapping lets you reach any rational number that can
be composed of the primes 2, 3, and 5 by using an
arrangement of only two generators (the octave and fifth),
hence it has "smaller rank".

A tuning of meantone temperament is reached simply by
choosing sizes for the fifth and octave (e.g. 697 cents
and 1201 cents). Finally, one applies these "generators"
to get a scale of the desired number of tones/octave.

This setup has proven to be very fertile, in terms of
turning up dozens of temperaments like meantone yet...
different, each with their optimal tunings (much like
31-ET is about optimal for meantone) and characteristic
nested series of scales (e.g. 5-tone, 7-tone, 12-tone etc.).

I also think it works quite well as a generalization of
the common and historical use of these terms. However,
as you point out, the terms are not used consistently, so
in some cases it's hard to say.

-Carl

Far as I know...

Temperament is the ability to estimate a scale from slightly above or below a desired scale and still have it sound/feel relatively the same.
For example, 12 tone equal temperament is designed to estimate different transpositions/modulations of the 7-note Just Intonation Diatonic scale and each note is off by a few cents over or under the desired note (IE not off by much).

Far as tuning vs. scale...I am not sure, I have always thought of them as synonyms. I would be curious to learn the authoritative differences between them.

The term "Intonation" itself, to be honest, I have no clue about. All I know it just intonation locks notes in a scale to match possible harmonic overtones in a very precise fashion, resulting in something very "relaxed sounding" to most people.

--- On Wed, 11/5/08, Daniel Forro <dan.for@tiscali.cz> wrote:

From: Daniel Forro <dan.for@...>
Subject: [tuning] Re: scale vs. tuning etc
To: tuning@yahoogroups.com
Date: Wednesday, November 5, 2008, 9:08 PM

I have mentioned in some messages here very often terms "scale",
"intonation" , "temperament" , "tuning" (somebody can add more?) are
used chaotically, inconsistently and not in exact way. Maybe it would
be good if some of our clever gurus here explains how to use these
terms more scientifically and everybody should use it just that way.
We should be careful enough even with using of such basic and simple
terms. It would be good to unite opinions and use it properly. It's
not totally interchangeable. I have some idea about it as well.

I'm sure it was discussed before, review or link as well as opinions
are welcome.

Daniel Forro

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
>...PowerPoint presentation, and I saved it out to these seven
> PDF files of less than 500K each.
...
>
> Tom, it would probably take you less than the whole hour to read all
> those (fewer than 60) slides in all the seven files.

Brevity is the soul of wit.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Brad Lehman" <bpl@> wrote:
> >
> >...PowerPoint presentation, and I saved it out to these seven
> > PDF files of less than 500K each.
> ...
> >
> > Tom, it would probably take you less than the whole hour to read all
> > those (fewer than 60) slides in all the seven files.
>
> Brevity is the soul of wit.
>

Thanks for the endorsement!

Brad Lehman

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:

> Thanks for the endorsement.
Sure!

One hour to read (that's on top of all the time I've already spent
with Brad's stuff), but - again based on previous experience - it
would probably lead to several days of ultimately pointless and
mutually half-comprehending debate producing nothing but exasperation
on my side. And there are an awful lot of things I should be spending
hours on.

All I want is *one* real new piece of information or
not-completely-subjective insight. The sort of thing you can type and
comprehend in two minutes flat.

Like "to play such-and-such music, flat keys should have better thirds
than sharp keys, but none should be quite as bad as Pythagorean."
(Just for example - though it's quite subjective!)

Or "Internal verbal evidence shows that Arnolt Schlick's early 16th
century organ tuning instruction survived into 18th century
Switzerland, though in a shortened and partially corrupted form
rendering it closer to plain meantone."
(An article I've been planning to write for some time.)

One or two sentences like this and I have a much higher probability to
be interested. OK, there are people in tuning who would just have to
say to me "Here's my new stuff, take a look!" - but they can be
counted on about one hand.

So Brad knows how to get my attention, if he wants to. (I'm not saying
my attention is necessarily *worth* getting ...)
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> All I want is *one* real new piece of information or
> not-completely-subjective insight. The sort of thing you can type
> and comprehend in two minutes flat.

http://larips.50webs.com/
The lecture showed the technical problem set up by Bach's music of
the WTC (book 1), within the context it arose from (older music that
*could have been* played in meantone schemes, being restricted to 12
or fewer notes in a piece). Only 6 of the 24 preludes and fugues
stick to as few as 12 notes...and it's a different 12 notes every
time. All the others go out to 13, 14, 15, 17, or 25 notes: forcing
musicians (players and tuners being the same people!) to deal with
enharmonic swaps. The diagram then shows how to do that: set up all
the notes of the C major scale first, and then fit the remaining
notes into their enharmonically proper places with these specific
adjustments, so the whole book of music can be played.

The lecture started from the basics of diatonic-scale construction,
showing why meantone is the way it is. (It is necessary to
understand what a problem is, before seeking solutions to it!) I
assumed that nobody in the audience had read the corresponding
section (pp 214-220) of my original paper, or understood why those
concepts of the enharmonic swaps are important in Bach's music. The
people who have argued most loudly against my hypothesis over the
past three years -- some in print, and some here in this and other
internet forums -- have all got stuck with their own negativity about
other sections. Nobody goes into this crucial area of the notes
actually called for by Bach's compositions! It's personally
frustrating that the nay-sayers have missed the point THAT BADLY.

So, in this lecture for JMU, I started fresh. I started with the
assumption that anybody showing up would be open-minded about music,
and open-minded about learning things they don't "know", and willing
to learn how the C major scale is put together, and how modulation
works. The lecture didn't require anybody to do any math, or to read
music scores. I showed why harpsichord tuning is done by 5ths/4ths.
I showed why meantone schemes typically give the notes they do, and
omit the notes they do. I showed how notes such as E-flat and D-
sharp are remarkably different from one another in actual pitch
(demonstrated live at the harpsichords), and showed how compromises
must be found between those spots. I showed the problem that Bach's
music *itself* sets up, and showed why I believe Bach's own solution
to his problem was such-and-such.

It's all very easy to "get" by people who come to it with ears and
minds willing to listen, not wrapped up in their own argumentation.
Look at it as shapes, the same way a one-year-old knows how to build
a successful tower of irregular blocks without having to measure the
angles or calculate a single thing. The audience was mostly
undergraduate music students, their professors, and a few guests. It
was probably "new" to most people there that F-sharp and G-flat are
not the same note, so I started from the basics.

Brad Lehman

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
Hi Tom, Brad and all others
that try to study Brad's reinterpretation attempts in vain,

>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> > All I want is *one* real new piece of information or
> > not-completely-subjective insight. The sort of thing you can type
> > and comprehend in two minutes flat.
Sorry Tom,
but as far as i have examined Brad's effusions of verbiage rant,
i'm not able to extract the slightest new information
from his verbose torrent of words.
Hence you may skip directly
to the final conclusion at the end of that meassage.
>

Hi Brad,
and all others, that are more patient with him than Tom:
let's have a closer look in order to
to understand Brad's 'esotheric' reinterpretation attempts....

> http://larips.50webs.com/
> The lecture showed

>(the)
Brad's blank-faced pretended

> technical problem

as he usually foists arbitrarily upon the

> set up by Bach's music of
> the WTC (book 1), within the context it arose from (older music that
> *could have been* played in meantone schemes, being restricted to 12
> or fewer notes in a piece).

In JSB's compsitions there exists no limit to only 12 classes of pitches.
The restriction to barely 12-classes arises only due to the limit of
keys in keyboards,
that became common usual since
the 1361 gothic Halberstadt organ
http://de.wikipedia.org/wiki/Orgel_des_Domes_zu_Halberstadt
with the approved keyboard-layout
http://upload.wikimedia.org/wikipedia/commons/c/cc/Syntagma14.png

without any further subsemitons.

> Only 6 of the 24 preludes and fugues
> stick to as few as 12 notes...and it's a different 12 notes every
> time. All the others go out to 13, 14, 15, 17, or 25 notes: forcing
> musicians (players and tuners being the same people!) to deal with
> enharmonic swaps.
Wrong,
because there is no need for
singers and fiddeling violinists
to enforce enharmonic swaps,
instead of performing fully aware
the corresponding comma-shifts in the correct manner,
as notated in the score by the composer's intensions.

Hence for that musicians the limitation to barely a dozen keys/octave
is irrelevant, except in combination with an keyboard instrument.

> The diagram then shows how to do that: set up all
> the notes of the C major scale first, and then fit the remaining
> notes into their enharmonically proper places with these specific
> adjustments, so the whole book of music can be played.

There's no obstacle to perform the JSB's 48 with more than
a dozen pitches per octave on none keyboard instruments.
>
> The lecture started from the basics of diatonic-scale construction,
> showing why meantone is the way it is.

That's again nonsene:
Starting from the base of an diatone-scale contructed scale,
doesn't leads necesariliy always to meantonics.

>(It is necessary to
> understand what a problem is, before seeking solutions to it!)
Agreed.
Good advice!
> I
> assumed that nobody in the audience had read the corresponding
> section (pp 214-220) of my original paper,

Remember:
http://muse.jhu.edu/journals/early_music/v033/33.2lehman.html
chapter "ENHARMONICS":
"
See table 1. The main things to notice here are the comma errors of
the less common accidentals, [End Page 214] i.e.the top row of
percentages in each. A positive percentage shows the amount by which
that note is too sharp, and a negative percentage shows flatness. Some
observations from the chart:

In regular ¹b6 comma, the 12 main notes from Eb- toGb/ are all exactly
in tune (0 per cent comma deviation) and the other 12 are 100 per cent
comma either too high or low. This confirms Tosi's pedagogical
analysis of the situation: for example, where the music says 'Db-', if
we took our pitch from the keyboard, we are singing it 100 per cent of
a comma too low, because the keyboard has it tuned primarily as a Cb/. ...

http://muse.jhu.edu/journals/early_music/v033/33.2lehman_tab01.html

> or understood why those
> concepts of the enharmonic swaps are important in Bach's music. The
> people who have argued most loudly against my hypothesis over the
> past three years -- some in print,
as Mark Lindley & Ibo Ortgies did so adaequate
for example in theirs critical review.

> and some here in this and other
> internet forums -- have all got stuck with their own negativity
> about
> other sections.

For those, that don't want to waste money for that empty passage,
here again Brads's pp. 214-220
"
Enharmonics

As Francesco Tosi pointed out in his 1723 manual of vocal instruction,
singers must be able to recognize and perform the enharmonic
difference of a comma in melodic contexts. A note such as Eb- is a
comma higher than its partner Db/, and if the wrong one is performed it
offends the ear. Furthermore, appoggiaturas and other passing notes
must always use the correct diatonic (not chromatic) notes of the
current harmony.37 Each time we pass through 12 consecutive 5ths, we
arrive a comma higher or lower than our previous position. That is,
the basic standard of intonation is a spiralling scale of regular ¹b6
comma 5ths, also known as the 55-division of the octave, where commas
are the individual tiny steps of this scale. The diatonic semitone and
chromatic semitone are in 5:4 ratio within a tone whose size is 9
commas. Therefore, of the 55 equal parts of the octave, the notes are
placed on the keyboard as follows: C=0, Cb/=4, D=9, Eb-=14, E=18, F=23,
Fb/=27, G=32, Gb/=36, A=41, Bb-=46, B=50, C=55.38 Other important notes
missing from a regular ¹b6 comma keyboard include Db-= 5,Db/=13, Eb/=22,
Gb-=28, Ab-=37, Ab/=45, Cb-=51, Bb/=54. Sauveur, Quantz, Telemann, Leopold
Mozart and other 18th-century musicians confirm this same standard in
both practice and pedagogy.39 A close reading of Quantz's chapter 'On
the Duties of Those Who Accompany a Concertante Part'40 suggests that
only the accidentals are exceptionally tempered on keyboards (i.e.
outside the equal comma points of the 55-division), while the naturals
are regular.41

What does this tell us? If possible, let us put ourselves for the
moment inside the heads of exceptionally good 18th-century performers,
such as Tartini or Tosi or Quantz, and bring our instruments and
voices to a harpsichord in some temperament. As we try to sing or play
with it, does it sound in tune or out of tune with our expectations
and our normal handling of commas? Does the harpsichord have any notes
that make a jarring effect by being a comma or more too high or low,
according to our standard of spiralling ¹b6 comma 5ths across the
entire 25-note range from Eb-b-Bb-;b-Fb-Cb-etc.
CGetc.Fb/Cb/etc.Bb/F×C×? Or are the compromises easy to find,
moderate, and comfortable for one's own performance (whether one tries
to match them exactly or not)?

Such a thing is easily measurable, and a useful way to analyse a
temperament's suitability for tonal music, but to my knowledge it has
not been published before. In the tuning literature, the measurements
we usually see are deviations in cents from equal temperament,42 which
is irrelevant by the 18th-century non-keyboard standard.

The notes on a standard 12-note keyboard must serve double duty, well
or badly as the case may be, in all the enharmonic contexts required
of them: this is a basic expectation of circulating temperament. Here
are comparative examples of various temperaments, next to Bach's. All
the notes are measured from their positions in the 55-division system,
i.e. a double cycle of regular ¹b6 PC (or ²b11 SC), with the common
note C always at 0 per cent.

See table 1. The main things to notice here are the comma errors of
the less common accidentals, [End Page 214] i.e.the top row of
percentages in each. A positive percentage shows the amount by which
that note is too sharp, and a negative percentage shows flatness. Some
observations from the chart:

In equal temperament, enharmonics are organized symmetrically in pairs
outward from C in [End Page 215]both directions. Because the
progression around the 5ths is smooth and steady, no single notes ever
stick out as 'wrong'. The sharps are increasingly bright (and
uncommonly high in general) while the flats are mellow (being only a
few positions around the spiral of 5ths from C). Db- and Ab- are quite
well in tune, while their counterparts Cb/ and Gb/ are much higher in
their own contexts; this creates an effect of brilliance in sharp-key
music.

Bach's temperament progresses outward from C, with the sharps rising
more quickly than the corresponding lowering of the flats. This is its
most unusual feature, and the reason why it works so uncommonly well
for tonal music. Its crossover point of 50 per cent is at Cb//Db-; i.e.
exactly half way, as major 3rds between A below and F above. Db-
therefore sounds suave (not quite wide enough from F to be harsh),
while Cb/ is exciting (very noticeably sharp, e.g. in D minor context).
This temperament favours Ab- ahead of Gb/; again emphasizing the
smoothness of the flat and the brilliant colour of thesharp. Six of
the seven naturals are exactly in tune, making it easy for our singer
or instrumentalist to find them; the only exceptional attention must
be paid to the treatment of accidentals, being some portion of a comma
too high or low, in a smoothly organized pattern outward.

'Vallotti' also has a smooth and symmetric progression in both
directions, and it obviously favours the quality of the 12 main notes
from Eb- to Gb/. Gb//Ab- is the crossover point of 50 per cent; Db- and Gb-
quickly become quite harsh in tonal contexts, as is familiar to
keyboardists who play in this temperament frequently. (Music in C
minor, F minor and Ab- major brings out some of the melodic flatness of
those notes.) All seven naturals are exactly in tune by the
55-division standard, and the accidentals rise or fall gradually.

Sorge 1758 has a pattern similar to Bach's, but starts the rise and
fall closer to C in each direction. Cb/ is slightly lower (more settled
as a major 3rd above A), at the expense of quality in the Db-. Again
compared with Bach's, this temperament has the trade-off of slightly
faster-beating major 3rds CE, FA and GB, for the benefit of more
harmonious EGb/, ACb/ and BDb/, while preserving the same overall
shape. In practice it sounds like the musical meeting of
unequal-temperament expert Bach with equal-temperament expert Sorge
(two consecutive members of the Mizler society in 1747), coming to the
complex problem of tonal music from opposite sides and striking a
brilliantly tuned compromise.

'Werckmeister III' and 'Kellner' share a serious problem in their
treatment of melody, vis-à-vis the 55-division. This phenomenon,
precisely, is the reason why these temperaments can seem so
arbitrarily and suddenly sour when normal tonal music is played in
them. Specifically, the notes Db-, Gb- and C♭ are placed much too low,
and Db/ and Ab/ too high. Harshness shows up in the Pythagorean major
3rds (actually the misspelled diminished 4ths) Cb/F, Fb/Bb-, BEb- and
Gb/C, the legacy of regular mean-tone layouts; but it also appears in
melodic contexts having nothing to do with major 3rds. Melodic leaps
up or down to A 837; and Db- can come across like singing with poor breath
support as the tuning of these notes is so unexpectedly low. But, so
is the note A in the simple melody FAC!43 The misspelled notes
simply stick out obtrusively, because their deviations from the
55-division skip across the set of notes rather than being
well-organized outward from C. In Werckmeister III, the C and Fb/(!)
are best in tune; then the G, E and B. Then, the F, D and Cb/; and so
forth, leaping in ways that are not intuitively obvious. How are our
singer and instrumentalist to find their pitches accurately, when the
deviation patterns on the keyboard are clustered around both C and Fb/?

These latter two temperaments have plenty of faithful and enthusiastic
fans, especially due to the way they sound reasonably good in earlier
music (based mostly on regular mean-tone layouts). But it cannot be
denied that their melodic bumpiness borders on the effect of
randomness, by the 18th-century standard itself. I suspect that
musical ears more readily tolerate notes that are slightly sharp than
notes that are noticeably flat within melodies.44 I cannot explain
that phenomenon adequately. I can, however, offer a suggestion as to
the technical cause of this problem in Werckmeister III.

In a well-known remark in his New Grove 'Well-tempered clavier'
article, Lindley has observed that Werckmeister III was probably
designed for theconversion of existing organs from regular [End Page
216] quarter-comma mean-tone. Some of the pipes of each octave can be
left at or near their original pitch, and the conversion will take
less work and expense. Direct examination of frequency charts, always
keeping C constant, shows that Werckmeister's scheme (by this
hypothesis) is even more clever than that; it allows conversion from
any of the regular ¹b4, ¹b5 and ¹b6 layouts by keeping C along with
three or four other notes. These notes need to be moved a smaller
distance than 2.5 cents (i.e. only an easy revoicing):
¹b6 syntonic: leave C, Cb/, Fb/, G, B
¹⁄6 Pythagorean: leave C, E, Fb/, G, B
¹b5 syntonic: leave C, E, Fb/, G
¹b5 Pythagorean: leave C, D, E, G
¹b4 syntonic: leave C, D, G, A

Viewed from this angle, the axis of CFb/ also makes additional sense.
Fb/ is left at or near its position from regular ¹b6 comma temperament,
namely the tritone 45b32 above C, one syntonic comma flat! The
temperament begins with CFBb-Eb-Ab-Db- Gb- pure 5ths, establishing
'F 839;' at one Pythagorean comma below C. Therefore the six remaining
5ths from C up to Fb/ must absorb 100 per cent of this comma amongst
themselves, since we have not done any tempering yet. The assignment
of quarter-PC tempering to CGDA and to BFb/ is simply the pattern
that allows the most purity to be preserved in C, G, D and F majors
without making the major third CE flatter than pure, and it is only
coincidental that this spacing is a quarter of a [Pythagorean] comma.
It is not really a quarter-comma temperament, in most of its organization.

It appears to me (revising Lindley's hypothesis) that the main purpose
of this temperament is to convert regular ¹b6 or ¹b5 comma organs, not
quarter-comma organs. Werckmeister himself had already remarked about
the circulating temperament shape we know as 'Vallotti' (¹b6 comma
tempered 5ths FCGDAEB), referring to it as an ordinary Venetian
temperament, in 1681: long before Vallotti, Tartini or Barca did.45
Furthermore, Werckmeister IV is even more obviously a conversion
temperament, squaring off regular ¹b6 Pythagorean comma and splitting
its wolf in two; and Werckmeister V isa conversion of regular ¹bo?=à
Pythagorean comma. Inthis perspective, I believe it is plausible that
the familiar Werckmeister III started from the premise that C and Fb/
should be left alone, and everything else arranged around them. The
resulting shape of it, as I have demonstrated here, suggests as much:
the Fb/ and its nearest neighbours are serious liabilities in music
that treats them enharmonically.

Kellner's temperament, in turn, was his attempt to take the model of
Werckmeister III to the next steps that seemed logical to him,
slightly moderating its intensity while keeping essentially the same
pattern.46 Devie, Rasch and Lindley have offered perceptive further
comments about Kellner's methods, which I need not repeat here.47 The
resulting temperament has some attractive symmetries and balances for
music that never strays far from the basic set of mean-tone notes, but
it does not handle enharmonic equivalences gracefully; and therefore
it sounds remarkably rough in Bach's music.

Buxtehude's extant organ music uses Gb/, Db/, Ab/, Eb/ and B♯ with
impunity, with occasional forays to F× and C×. On the flat side it
goes only as far as Ab- (which in context must be decent as a 5th
against Eb-) frequently, and there are only several pieces48 that use
Db-. That suggests to me that if Buxtehude's organ temperament(s) were
regular, only something as light as ¹b6 comma makes musical sense;49
and if irregular, having at least a compromised Gb//Ab- and perhaps also
a lowered Eb- and Bb-.50 Werckmeister III fits very well for music that
avoids the flats as thoroughly as Buxtehude's does. Saying the same
thing in another way: Buxtehude's æuvre (as corroboration) makes
Werckmeister III look like a practical method to convert regular ¹⁄6
comma 'mean-tone' to smoother chromaticism, but only around the sharp
side.

To summarize my remarks about enharmonics: any keyboard temperament as
a candidate to play Bach's music must be able to handle all 25 notes
from Eb-b- up to C×, gracefully and in a sequence that singers and
instrumentalists can find without undue trouble. The same feature (and
restriction) that makes a temperament good for accompaniment, namely
its conformance to the 55-division, also makes it good for solo
repertory, as the accidentals are constrained to be in moderate and
logical positions. [End Page 217]

This is a prerequisite to vocal-sounding melodic contours: never
having any individual notes that protrude too noticeably from their
melodic and harmonic contexts, in steps and leaps. If the notes within
scales are not absolutely regular, the irregularities must be
tastefully subtle lest they begin to sound like mere errors from
incompetence. This is a difficult balance to achieve. The 12 available
pitches must be viewed (heard) from all possible angles, anddeliver
something reasonable to every possible context.
Ex.1 Intervals in Bach's temperament, measured melodically in cents:
(a) tones; (b) semitones
Click for larger view Example 1
Intervals in Bach's temperament, measured melodically in cents: (a)
tones; (b) semitones
Recognizable scales through the distinct intonation of their steps

As Ledbetter's book reminds us repeatedly, every key has a distinctive
'grip' (Griff) in the player's hands. The player must learn to grasp
them all, and the WTC provides terrific examples. As Bach's
temperament makes clear, that distinctiveness in physical layout on
the keyboard also has a counterpart in distinctive intonation patterns
in every key.51 The contrasts, to the player, are not only
psychological (from the physical Griff) but also audible. To the close
listener (which is also a crucial component of playing), these
differences in tension further affect phrasing and timing: perception
of the motion in tonal music.

Why should it matter to have distinctive diatonic scales? The
perceptible dimensionality of the music is multiplied. The playing of
a keyboard fugue is the simultaneous control of three or four melodic
shapes, and 'counterpoint' and 'harmony' are the complex interactions
of those shapes. Modulation comes from the introduction of foreign
notes (irregularities) into a melody's prevailing scale: the
listener's mind notices the irritation and assigns the anomalous notes
to whatever competing scale best contains them. Is that not the way
basic human perception of language works: noticing irregularities in
the flow of sound, and parsing the stream of input into meaningful
packets by analogy with already known patterns?52

The mind is very good at dealing with unexpected and seemingly
irrelevant stimuli, such as the mention of strawberries. When all the
scales have distinctive aural signatures, as in Bach's temperament,
the listener's task of parsing the music is much easier (especially
when receiving several contrapuntal voices simultaneously).
Furthermore, the mind is continually challenged by the dynamics of all
this: attention is captured and maintained. Passive voice, active,
tart strawberry, fragments, unorthograffy Violation of Expectations,
just the right balance ofasymmetric contrasts and flow and purposeful
irritation. In summary: when heard in a carefully balanced unequal
temperament, the music is much more transparent, interesting, and
engaging, all the way through.

Ex.1 shows all tones ('whole steps') and semitones ('half steps') of
Bach's temperament, measured in cents.53 In my notation here, the
notes are to be played in succession either ascending or descending,
not crushed together simultaneously. The measurement here is of
melodic quality.

There are four different sizes of tones and eight different sizes of
semitones. That is: these linear intervals have a perceptibly
different sound from one another, providing expressive inflections
within melodies. At the same time, the differences are subtle enough
that they do not draw undue attention or ruin melodic smoothness:
listeners may choose to notice or ignore them as they wish.54 The
differences are most noticeable when listening very closely at a
harpsichord, in isolation, playing the notes slowly. [End Page 218]
Press one note, hold it long enough to establish it in the ear as home
base, then move to the neighbouring note.
Scale (tetrachord and hexachord) analysis of all available tones and
semitones in Bach's temperament,measured melodically in cents (a) ut
re mi (tertia major); major scale: utremifa, utremifa
Click for larger view Table 2
Scale (tetrachord and hexachord) analysis of all available tones and
semitones in Bach's temperament,measured melodically in cents (a) ut
re mi (tertia major); major scale: utremifa, utremifa

Tones of size 196 are characteristic of regular ¹b6 comma; of 204 from
Pythagorean intonation (generated by pure 5ths); and 200 from equal
temperament. The 200 of AB is a coincidence from the raising of B,
and the 202 of Fb/G 839; and Bb-C arise from the crossover points from one
type of 5th into another.

In table 2 these steps are arranged into the four- and six-note
subsets of the major and minor scales. The chart therefore describes
all 'ut re mi' and 're mi fa' combinations in Bach's temperament. In
addition to being higher or lower in pitch, every scale sounds
absolutely distinct from every other scale, dueto the different sizes
and relationships of their intervals. Theeffect, or one might even say
'personality', of every musical key becomes recognizable. Compositions
inherit this character from the home key (tonality) and any other
major or minor keys the composer visits as the music moves along from
section to section.

A tetrachord is a set of four rising notes in a major scale: ut, re,
mi, fa. One can divide the complete scale [End Page 219] of eight
notes into two halves: 'lower' and 'upper' tetrachords of four notes
each:55 utremifa; utremifa (e.g. CDEF; GABC). The upper
tetrachord GABC then begins the next scale, continuing DEFb/G.
The Fb/ is the new note, and it gets a new (raised) key lever on the
keyboard as wealready have an F. The new note each time is the mi of
the upper tetrachord, tuned (as some size of fifth) from the already
available mi of the lower tetrachord.56

The older system of hexachords uses the set of six rising notes: ut,
re, mi, fa, sol, la.57 Like a complete major scale, a major hexachord
(natural hexachord, hexachordum naturale) can also be broken down into
halves: as 'ut re mi' twice in succession. Similarly, aminor hexachord
(soft hexachord, hexachordum molle) has 're mi fa' twice in
succession. These two groups of three notes are mentioned in Bach's
introduction to WTC: 'The Well-Tempered Clavier, or, preludes and
fugues through all the tones and semitones, both as regards the tertia
majoror ut re mi and as concerns the tertia minor or re mi fa.'

The only symmetric major hexachord in Bach's temperament is
CDEFGA. Its symmetry comes from the regular naturals: the home
key of C major, 'ut re mi'. The most nearly symmetric minor hexachords
are similarly in the simplest 're mi fa' minor keys: DEFGABb- and
ABCDEF.58 That is: the keys with fewest accidentals are
melodically the smoothest, having tones of equal size.

The most remarkable features in table 2 are the columns 'remi' and
'mifa' shared by the major and minor tetrachords. The lower and upper
tetrachords to assemble each scale are distinct, in the paired
qualities of those two melodic intervals 'remi' followed by 'mifa'.
Listeners can therefore recognize any tonality immediately by its
subtle 'remifa' inflections, and hear an objective difference
whenever the music modulates.59

Taking a step out to the big picture, to show the importance of this
observation: all the scales are equally usable in musical quality, yet
distinct. Transposition of any theme, any section, any entire piece
causes a profound change in the relationships of all the intervals; an
audible change of character in the music. There are exponentially
increased musical resources available, compared with the assumption of
equal temperament upon which so much of modern music theory is based.
Change the melodic sizes of steps and leaps from a constant to a
subtly variable parameter, and everything becomes fluid: more
challenging to control analytically, but also more exciting. It is a
world of sound-relationships, each with particular and recognizable
identity. Pieces of tonal music ebb and flow organically, through
their modulations of character.

Tonal theory will have to catch up with this, supplementing
approximately 250 years of simplification. The choice of temperament
(and this is true of all 12-note unequal temperaments, not only
Bach's) is not independent of the content of a piece of music, at
least where keyboards are concerned. The field of music theory has
typically kept intervallic analysis and tuning details apart for
convenience; all three-note and four-note chords with a particular
pattern of tones and semitones are treated as basically equivalent,
regardless of key centre. The little-examined assumption behind this
is the consistency of equal temperament (and behind that, the broader
collection of regular 'mean-tone' layouts with their easily
predictable equivalences and transposition patterns).

As Bach's temperament (along with some others) makes clear, melodic
motion from Cb/ to D is not equivalent to motion from D to Eb-, even
though in both cases we are dealing with correctly spelled diatonic
semitones, and even if we shifted the frequencies of everything so the
starting pitches were identical. Those semitones are perceptibly
different sizes, and that fact is a musically expressive resource. For
example, transpose the Sarabandes of the suites BWV823 and 819 to
various different keys; the music loses much of its poignancy and in
compensation it gains other characters altogether, depending on what
key is chosen.

Such things can also be heard directly, with a chord in isolation as a
representative exercise. CD FB and Eb-FAb-D do not sound at all
alike in Bach's temperament; the former is gentle and the latter is
piquant. EFb/ADb/ is brisk and crisp, while Fb/Gb/BEb/ seems both
delicate and clean. Other listeners will come up with different words
here, akin to the descriptions of competing wines, but thepoint is
that all these equivalently spaced chordssound radically different
from one another. [End Page 220] Absolute placement within the complex
set of 12 notes matters, absolutely! Even more complex chords than
that, generated by linear passing motion or ornamentation, are
delightfully rich for study: a good place to start is the modally
ambiguous material in Clavierübung III, tuned correctly.
Ex.2 Qualities of the major 3rds in Bach's temperament. The number
with each interval indicates the sharpness (being wide of a pure 5/4
ratio), as percentage of the SC.
Click for larger view Example 2
Qualities of the major 3rds in Bach's temperament. The number with
each interval indicates the sharpness (being wide of a pure 5/4
ratio), as percentage of the SC.
Fig.1 Graph of the major 3rd qualities, Bach's temperament.
Click for larger view Figure 1
Graph of the major 3rd qualities, Bach's temperament.
"

Sorry for lacking graphics inbetween the tattle.

> Nobody goes into this crucial area of the notes
> actually called for by Bach's compositions!

Poor Bach, nobody understood the deeper sense of
his compositions until Brad came.

http://www.emu.edu/bach/2008/artists/brad-lehman
"As a musicologist, Dr. Lehman's major achievement has been the
discovery of a keyboard temperament believed to have been Johann
Sebastian Bach's own preference for the Well-Tempered Clavier. "

the most famous alumnus of
http://en.wikipedia.org/wiki/Goshen_College
"....a 1600-pipe tracker pipe organ, the first in the world with
tempering based on alumnus Bradley Lehman's research of Johann
Sebastian Bach's notation."

http://www.goshen.edu/news/pressarchive/04-20-05-bach-temper.html
claims rant:
"Then in March 2004, Lehman received an e-mail message from British
harpsichord and clavichord enthusiast David Hitchin who reported that
two German researchers suggested that the drawing might be a clue to a
temperament. But Lehman felt the temperament that the Germans were
proposing didn't make sense; some of its premises were clearly incorrect.

"Then it hit me: Bach's diagram does describe his temperament and
merely needed to be interpreted correctly," Lehman said. "Bach wrote
down the math of his tuning method here in a simple way, not by a
chart of numbers, but by drawing a picture of it. This picture tells
us exactly how the tuning should be set up, unequally, so the music in
that book and his other books sounds best."
....
Bach turned his book upside-down to draw the diagram so that when
viewed right side up, it appeared in reverse. "The different types of
shapes in Bach's drawing tell the tuner how to make the specific notes
almost in tune together, but slightly out of tune by a little amount,
on purpose. This drawing is Bach's recipe to set up all 12 of the
notes exactly right. I believe that he was hiding a family secret, by
writing it upside down and making it appear unimportant," Lehman said.

As soon as Lehman translated Bach's 1722 drawing and tuned his own
harpsichord according to Bach's lesson on paper, "the way it sounded,
so beautiful and unexpected, made me cry. I knew I was on to something
big."
....
""I feel as if I have had the best single music lesson of my entire
life, and that it's happened at Bach's house."

http://www.english.bachhaus.de/
http://de.wikipedia.org/wiki/Bachhaus_Eisenach
http://de.wikipedia.org/w/index.php?title=Bild:Gedenktafel_Bachhaus-2.jpg&filetimestamp=20070724155210
"Relikt eines historischen Irrtums:
Gedenktafel am Bachhaus in Eisenach"
re:
'Relict of a historically error:
Memorial tablet on the (so called) Bach-house in Eisenach's city.'

> It's personally
> frustrating that the nay-sayers have missed the point THAT BADLY.

Byond the wrong 19.th-century allegations about JSB's original
birth-place, now in the 21.th-- we have to suffer
even worser claims about his 'original' tuning?

>
> So, in this lecture for JMU, I started fresh.
http://www.jmu.edu/
https://caal.jmu.edu/VisitingScholarsF08.html
"
Bach's Tuning Diagram for the Well Tempered Clavier
Bradley Lehman
Musician
Wed., October 22
Anthony-Seeger Auditorium
7:30p.m.
"

> I started with the
> assumption that anybody showing up would be open-minded about music,
> and open-minded about learning things they don't "know", and willing
> to learn how the C major scale is put together, and how modulation
> works.

Rameau invented the modern term of
http://en.wikipedia.org/wiki/Modulation_(music)
but C.P.E. confirms again and again his fathers and his own

/tuning/topicId_77237.html#77245
C.P.E. in different translations:

"That my basic principles and those of my late father are
anti- Rameau you may loudly proclaim."

"... that my fundamental principles and those of my late father are
anti- Rameau. ..."

> The lecture didn't require anybody to do any math, or to read
> music scores.

> I showed why harpsichord tuning is done by 5ths/4ths.

Without demonstrating JSB's demand: "...all 3rds sharp..."?

> I showed why meantone schemes typically give the notes they do, and
> omit the notes they do. I showed how notes such as E-flat and D-
> sharp are remarkably different from one another in actual pitch
> (demonstrated live at the harpsichords), and showed how compromises
> must be found between those spots.
Fine.

> I showed the problem that Bach's
> music *itself* sets up,
> and showed why I believe Bach's own solution
> to his problem was such-and-such.

Probably without mentioning yours prominent criticians.
>
> It's all very easy to "get" by people who come to it with ears and
> minds willing to listen, not wrapped up in their own argumentation.

When hearing yours personal private wide 5th of ~704Cents
ther's more resistance in my ears than against a ~700Cents narrowed one.

> Look at it as shapes, the same way a one-year-old knows how to build
> a successful tower of irregular blocks without having to measure the
> angles or calculate a single thing.

Would you trust an air-plane pilot, that claims such an nonsense
about aerial navigation?

> The audience was mostly
> undergraduate music students, their professors, and a few guests.

Presumably they were deep impressed?

> It
> was probably "new" to most people there that F-sharp and G-flat are
> not the same note, so I started from the basics.

No wonder, that you gained there acceptance, when telling yours story
to such an untaught audience.

"Among the blind the one-eyed is king."
http://www.stat.washington.edu/peter/Srebotnjak.htm
http://www.answers.com/topic/in-the-country-of-the-blind-the-one-eyed-man-is-king

Conclusion,
sorry Brad:
The more i had occupied myself with such cant,
the more i have to agree with Tom's negatory review.

bye
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote: [A LOT]
/tuning/topicId_78801.html#79150

I liked your "brevity is the soul of wit" comment better.

Brad Lehman

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@>
> wrote: [A LOT]
> /tuning/topicId_78801.html#79150
>
> I liked your "brevity is the soul of wit" comment better.
>
> Brad Lehman
>

Me too, infinitely so.

Methinks Shakespeare might have said "full of sound and fury
(especially the latter) and signifying nothing." My goodness what a
rant! Or "methinks he doth protest too much!"

I ran out of steam somewhere about the second paragraph I'm afraid Mr
Sparschuh. My apologies. Perhaps Bach-like I am not a fan of this dry
mathematics that tells me nothing about how it sounds nor how to tune
an instrument. Now a couple of nudges clockwise or counter makes
perfect sense to me, upside down Snörkel or not!

I did manage to read the whole of the set of pdfs in just one sitting,
thank you Brad, and found it to be a good way of describing, to non
tuning oriented people, why one does what one does in tuning a
harpsichord to one temperament or another. (Hope I got that right?) In
fact just as you described. To misquote a much overused British TV
advert. "It did what it said on the tin."

If I may, I should like to use the material with MIDI, almost
correctly tuned, examples (I don't happen to have a couple of Cembalo
hanging around) to illustrate modern interpretations of Baroque and
other tunings to the non-cognoscenti?

P.S. I like to think that Bach, when he had to describe to others in
Leipzig, how he had tuned his Cembalo, looking around for a piece of
paper to draw a diagram, and finding none (paper was a relatively
scarce commodity in his day, I believe) pulled over his document with
WTCI flipped it around and drew his series of squiggles to illustrate
just what he had performed in his typical 15 minutes.

Of course there is not a shred of evidence to support my hypothesis
but it creates a nice image in my mind. Just as on my recent visit to
Ohrdruf I imagined a lost lonely little orphan, where the church and
the organ builder offered his only refuge from a hard new world. He
lost himself in music. To our great joy.

John Garside.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> Or "Internal verbal evidence shows that Arnolt Schlick's early 16th
> century organ tuning instruction survived into 18th century
> Switzerland, though in a shortened and partially corrupted form
> rendering it closer to plain meantone."
> (An article I've been planning to write for some time.)

Dear Tom,
an similar idea can already be mentioned by:
http://de.wikipedia.org/wiki/Robert_Eitner
in
http://de.wikisource.org/wiki/ADB:Schlick,_Arnolt

"....die Stimmung der Orgel,
wobei er merkwürdiger Weise die erst 200 Jahre später angewendete
Methode, die Quinten schwebend (temperirt) zu stimmen vorschlägt
und weitläufig auseinandersetzt."

'...tuning of the organ,
in that (Chapter 8) Schlick strangely proposes primary 200 years
later used method, to temper down 5ths by counting beats,
in ample terms.'

bye
A.S.

--- In tuning@yahoogroups.com, "John Garside" <garsidejl@...> wrote:

Hi John,

> Now a couple of nudges clockwise or counter makes
> perfect sense to me, upside down Snörkel or not!

An expert:
http://www.bavington.nildram.co.uk/peter.htm
remarked in:
http://www.bavington.nildram.co.uk/temperament.htm
on that:
"Before I leave Ross Duffin's book, I must express my disappointment
that he has perpetuated the idea that Bradley Lehman has `discovered'
J. S. Bach's keyboard tuning, encoded in the decorative device on the
title page of the 1722 autograph manuscript of the first book of the
Well-Tempered Clavier.[3] All that Lehman, and his predecessor Andreas
Sparschuh, have shown is that it is possible to interpret the
`squiggles' as a key to a practical keyboard temperament: there is no
evidence to suggest that this was really Bach's intention. Readers
will be left with the impression that the question of Bach's keyboard
tuning has been settled without doubt, which is very far from being
the case."

or also:

http://ibo.ortgies.googlepages.com/errataandcorrigendatolindleyortgies:%22bac
"In it we discuss some of the historically wild and methodologically
wrong speculations published last year (2005) by Bradley Lehman in his
article in Early Music (Note 1), where he claimed to have discovered
"Bach's temperament."
The Lehman temperament is of modern design. It is, like the one
designed by the late Herbert Anton Kellner on July 7th, 1977 (i.e.
7/7/77 so Kellner said), based on an imaginative interpretation of a
small image from the year 1722: for Kellner, Bach's seal; for Lehman,
the ornamental scroll at the top of the title-page of Part 1 of Das
Wohltemperirte Clavier ("The Well-tempered Clavier").
Lehman is following previous musings, especially by Andreas Sparschuh,
who published the ornamental-scroll idea on September 9th, 1999
(9/9/99) as a kind of practical joke to make fun of Kellner.
"
.....in order.....

> .....to illustrate modern interpretations of Baroque and
> other tunings to the non-cognoscenti?
>
> P.S. I like to think that Bach, when he had to describe to others in
> Leipzig,

But JSB composed his
http://en.wikipedia.org/wiki/Well-Tempered_Clavier
"The first book was compiled during Bach's appointment in Köthen;"
in 1722 before he moved later to Leipzig in 1723.

Tom's conclusion:
"Despite this recent research however, many musicologists say it is
insufficiently proven that Bach's looped drawing signifies anything
reliable about a tuning method. Bach may have tuned differently per
occasion, or per composition, throughout his career."

> how he had tuned his Cembalo, looking around for a piece of
> paper to draw a diagram, and finding none (paper was a relatively
> scarce commodity in his day, I believe) pulled over his document
> with
> WTCI flipped it around and drew his series of squiggles to
> illustrate

That's barely modern wishfull thinking alike Brad's reinterpretion.

> just what he had performed in his typical 15 minutes.
>
> Of course there is not a shred of evidence to support my hypothesis
> but it creates a nice image in my mind.
Agreed.

bye
A.S.

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> > That would
> > seem a useful and responsible path for an expert scientist such as
> > yourself
> > to take: read something directly, instead of posting pre-judgments
> > against it. Please do. My presentation explains my reasoning, very
> > clearly. I can see that you don't *understand* (or maybe just don't
> > like) my reasoning, in the direction of looking at Bach's
> > compositions that call for more than 12 notes.

Well I understand rather well what enharmonic equivalence is, but I
don't understand what can be so unexpected or wonderful about it that
makes it so necessary to follow Brad's taste or lead in tuning, or
even to attribute something resembling this to Bach. To be
'historical' for a moment I think Werckmeister and Neidhardt
understood enharmonic equivalence just about as well.

Pre-judgment as to what to read is - unfortunately - an absolute
necessity in science. You know there are literally dozens of new
papers every day. It is usually based on experienced post-judgment of
what I read from the same author(s) previously, plus a brief glance at
the abstract. If what an author presented before amounted, or so I
thought, to a load of technical mush and wishful thinking...

But let's not pretend anything we can do with historical tunings comes
anywhere close to 'science', or even 'logic' or 'reasoning'. It seems
to me almost exclusively entertainment (and mostly self-entertainment
at that). To do 'reasoning' you need a basis of objective
propositions, whereas the whole point of tiny adjustments of musical
tuning is aesthetic and depends almost totally on one's individual
listening and playing experiences.

> p.s. It would also help to have read Easley Blackwood's book more than
> 20 years ago, as I did, since it deeply informed the way I understand
> the construction of diatonic scales: the generation of all the notes
> by a series of (usually regular) 5ths.

It would help to have read also Printz, Werckmeister, Schlick,
Sauveur, Rameau, CPE Bach, and a small truckload of other people in
the original, as I have (Lindley much more so), if one is ever serious
about getting the history. Most of them seemed to understand OK, with
or without Blackwood's help. Anyway a few months on this list were
enough for me to more than get the hang of the idea of constructing a
scale from combining two or more distinct intervals.

> Harpsichord tuning by 5ths and
> 4ths is done not only because it's easy and it works, but more
> basically because that's where we get a series of 7 and then 12
> inter-related notes, and beyond.

If you tune by successive minor thirds you can also get a series of
19, by major thirds a series of 31, it all depends how picky you are
about 'going beyond'... but this row-of-fifths is kindergarten stuff,
or beginners level in history of European music, a medieval proceeding
that doesn't lead to any one specific tuning and certainly not to
anything clearly connected with one Bach, except for - Bach using a
cycle of fifths! That's one clear, though not terribly helpful, fact.
I am also open to the possibility that harpsichords should be tuned
initially by thirds anyway (a la Sorge/Norwegian Parrot)...

> And, the notes of the C major scale
> are central to that section of the spiral used most.

What is 'used most' by who and when is a very slippery concept. It
might lead one to think that different periods or styles require
different tunings!

Don't worry, I probably will get round to dealing with more recent
messages ... ain't seen nothin' yet, as someone once said.
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> Pre-judgment as to what to read is - unfortunately - an absolute
> necessity in science. You know there are literally dozens of new
> papers every day.

While you're making excuses for not reading the piece, meanwhile, here
is Egarr's concert of the complete WTC 1 in Baltimore tomorrow (using
this). I hear from the harpsichord builder that it's already been
sold out for a while.

http://www.artbma.org/calendar/films.html
http://www.baltimoreathome.com/detail.aspx?dct=8&mid=933&eid=14660

Enjoy,

Brad Lehman

Thought this would help readers get the sense of the book I've written:
BACH & TUNING Synopsis by Johnny Reinhard
Chapter 1 Johann Gottfried Walther

Walther was like a brother to J.S. Bach throughout his lifetime, and an
eyewitness to his cousin’s musical world. Not inconsequently, Walther was also
author of the first lexicon of the German Baroque.
Chapter 2 Dieterich Buxtehude
Buxtehude was renowned for his organ improvisations, and a profound influence
on J.S. Bach. This chapter examines the primacy of virtuosic improvisation
in necessitating a circle of keys.
Chapter 3 Andreas Werckmeister
Werckmeister was responsible for a revolution in tuning through his invented
temperaments as alternatives to the limitations of meantone, and in spite of
the obviousness of equal temperament.
Chapter 4 Tuning
The twelve major and minor keys are examined, key by key, in cents (1200
cents to the octave). Comparisons are made between quarter and sixth comma
meantone, Werckmeister III, IV, V & VI tunings, Kirnberger I & II, Trost, and
Neidhardt I, II & III tunings.
Chapter 5 Bach Cities
Bach worked prominently in Leipzig, Arnstadt, Mühlhausen, and Anhalt-Kothen.
The organs in these cities were tuned prior to Bach’s employment and retained
their tuning.
Chapter 6 Thuringian Aesthetic
The Bach family belonged to the Thuringian tribe in central Germany.
Thuringians were notably fascinated with tuning keyboards that praised the
irregularity -- or unequalness -- of the scale.
Chapter 7 Notation

Notation gives valuable clues for identifying a tuning system, while the
compositional usage of the notes is indicative of an aesthetic. Works examined
include The Passion According to St. Luke, 6 Brandenburg Concertos, A Musical
Offering, and The Well-tempered Clavier.
Chapter 8 Johann Philipp Kirnberger

Kirnberger, a former private student of Bach’s in Leipzig, was a tuning
pedagogue famed for the promotion of the Bach legacy. Kirnberger introduced his
own innovations in tuning for the Classical era.
Chapter 9 Refreshed Perspectives

After arranging the prevailing possibilities for Bach’s tuning categorically,
a multiple choice question is constructed that leaves only one answer, the
direct result of eliminating all other possibilities.
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Sounds interesting! Where is the book available? I'd like one.

In chapter 9, did you allow for the possibility that Bach (as an
expert musician) chose to tune in a way that nobody else around him
had PUBLISHED? If not, why not?

Or was Bach constrained to use only ideas that were in print? If so, why?

Brad Lehman

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Thought this would help readers get the sense of the book I've written:
> BACH & TUNING Synopsis by Johnny Reinhard
> Chapter 1 Johann Gottfried Walther

>
> Walther was like a brother to J.S. Bach throughout his lifetime, and an
> eyewitness to his cousinâs musical world. Not inconsequently,
Walther was also
> author of the first lexicon of the German Baroque.
> Chapter 2 Dieterich Buxtehude
> Buxtehude was renowned for his organ improvisations, and a profound
influence
> on J.S. Bach. This chapter examines the primacy of virtuosic
improvisation
> in necessitating a circle of keys.
> Chapter 3 Andreas Werckmeister
> Werckmeister was responsible for a revolution in tuning through his
invented
> temperaments as alternatives to the limitations of meantone, and in
spite of
> the obviousness of equal temperament.
> Chapter 4 Tuning
> The twelve major and minor keys are examined, key by key, in cents
(1200
> cents to the octave). Comparisons are made between quarter and
sixth comma
> meantone, Werckmeister III, IV, V & VI tunings, Kirnberger I & II,
Trost, and
> Neidhardt I, II & III tunings.
> Chapter 5 Bach Cities
> Bach worked prominently in Leipzig, Arnstadt, MÃ¼hlhausen, and
Anhalt-Kothen.
> The organs in these cities were tuned prior to Bachâs employment
and retained
> their tuning.
> Chapter 6 Thuringian Aesthetic
> The Bach family belonged to the Thuringian tribe in central Germany.
> Thuringians were notably fascinated with tuning keyboards that
praised the
> irregularity -- or unequalness -- of the scale.
> Chapter 7 Notation

>
> Notation gives valuable clues for identifying a tuning system, while
the
> compositional usage of the notes is indicative of an aesthetic.
Works examined
> include The Passion According to St. Luke, 6 Brandenburg Concertos,
A Musical
> Offering, and The Well-tempered Clavier.
> Chapter 8 Johann Philipp Kirnberger

>
> Kirnberger, a former private student of Bachâs in Leipzig, was a
tuning
> pedagogue famed for the promotion of the Bach legacy. Kirnberger
introduced his
> own innovations in tuning for the Classical era.
> Chapter 9 Refreshed Perspectives

>
> After arranging the prevailing possibilities for Bachâs tuning
categorically,
> a multiple choice question is constructed that leaves only one
answer, the
> direct result of eliminating all other possibilities.
> **************Get the Moviefone Toolbar. Showtimes, theaters, movie
news &
>
more!(http://pr.atwola.com/promoclk/100000075x1212774565x1200812037/aol?redir=htt
> p://toolbar.aol.com/moviefone/download.html?ncid=emlcntusdown00000001)
>

Yes, an original tuning is one of the considerations. Chapter 9 will make
the most sense following the reding of the other 8. Still making final edits to
the last 3 chapters.

For all interested, check out my Microtonal Bach radio program on Christmas
Day (Dec. 25, 10 AM to 2 PM) on WKCR Radio (89.9 FM), simulcast on the
Internet.

best, Johnny Reinhard

_____________________
Brad: Sounds interesting! Where is the book available? I'd like one.

In chapter 9, did you allow for the possibility that Bach (as an
expert musician) chose to tune in a way that nobody else around him
had PUBLISHED? If not, why not?

Or was Bach constrained to use only ideas that were in print? If so, why?
Brad Lehman

**************Get the Moviefone Toolbar. Showtimes, theaters, movie news &
more!(http://pr.atwola.com/promoclk/100000075x1212774565x1200812037/aol?redir=htt
p://toolbar.aol.com/moviefone/download.html?ncid=emlcntusdown00000001)

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Yes, an original tuning is one of the considerations....

https://lists.wu-wien.ac.at/pipermail/earlym-l/2005-March/001075.html
"....questions about a temperament is a creative strategy for
exploration which I wouldn't take in any way to imply that the
original temperament is "wrong," only that one might also do things a
bit differently."

Nevertheless some
modern commercial tunings alike 'Kellner' or 'Lehman'
still persist in wrongly labeled the as "original"
in order to mislead astray the deceived customers by fraud.

For example:
http://www.virtuallybaroque.com/inco241.htm
"Temperament: Bach-Kellner (original)"
whatever "original" here may mean?

such underhand double-dealing of questionable records
continues without attending

C.P.E.'s remark in his fathers
necrology mentioned in a letter to Forkel,
[1774] The new Bach Reader, #394 :
"The exact tuning of his instruments as well as of the whole orchestra
had his greatest attention. No one could tune and quill his
instruments to please him. He did everything himself."

hence due to C.P.E.'s ignorance, his own practice of tuning
must be different than his father hidden secrets in that art.

Kristian Wegscheider's dares an satirical view about Kellner's 'Bach':
http://www.wegscheider-orgel.de/html/artikel.php?filename=artikel.php&tabname=Artikel&sz=22&Unterpunkt=H.C.%A0Snerha%A0und%A0die%A0Bachstimmung
"Seit Jahren stimme ich mein Cembalo nach der originalen Bach-Stimmung..."
'Since (many) years i tune my harpsichord in the original Bach-tuning...'
in the specification:
http://www.wegscheider-orgel.de/html/artikel.php?filename=artikel.php&tabname=Artikel&sz=22&Unterpunkt=H.C.%A0Snerha%A0und%A0die%A0Bachstimmung

fully aware of
http://grenfellmusic.net:8184/chpt__11.htm
"There is no method to identify what tuning methods were prevalent for
any given time or place. Debate is still ongoing concerning which
scale Bach's Well Tempered Clavier was designed for. If records are
insufficient for a piece whose title alludes to a family of tuning
systems, one can imagine the difficulty in accurately pinpointing the
original temperament for other pieces. "

Hence attend:
Beware of Greeks bearing "original-Bach-tunings" as gifts to their
naive listeners, in order advertise records
under the deceit label of JSB's squiggles.

http://www.uk-piano.org/edfoote/well_tempered_piano.html
" Research by Jorgensen and others strongly indicates that from 1700
to 1900, the age of Bach, Mozart, Haydn, Beethoven, Chopin, Brahms, et
al, a style of tuning was in use that was more complex than those
which came before or after. The Well Temperaments of this period
differ profoundly from Meantone or Equal. Not only do they allow full
modulation, they create a predictable variety of consonance and
dissonance, providing an acoustical palette of tonal "colors" for the
composer's use.

Keyboard compositions written during this period appear to make use of
harmonic values which do not exist in the other temperaments. The
evolving art of modulation, the development of sonata form with its
harmonic rules, and the known emotional-affective nature of tempering
variety, all indicate the use of a commonly accepted form of well
tempered keyboards.

Not only do the Well Temperaments provide tonal contrast, they also
offer a higher degree of consonance than is available in Equal
Temperament. They can, when called upon, be far more "in tune" than
today's norm. (By the same technique, if the composer desires, they
can produce sounds as dreary and tense as a funeral dirge, it all
depends on the choice of key).

Temperament thus forms the keyboard's intonation, and that it has
changed so profoundly has strong implications for musicians and
audiences who seek the fullest expression of a composer's work.
Substitution of a different intonation will necessarily change any
composer's harmonic organization, and it is reasonable to expect music
performed in non-original temperament to lose something of the
composers intention."

Despite to modern broade laymanish claims,
there's no historical evidence that JSB ever considered
the 5th Bb-F as an alleged "dimished-6th" of ~704 Cents.
That bias in the reverse direction
results in an additional artificial resistance
against modulations over that ~2Cents to much wide wrong 5th.

A. Sorge
http://jan.ucc.nau.edu/~tas3/sorge.html
considered such faulty cancerous-grown-strumatic over-wide 5ths
as "wholly unnecesarry" goiter.

If JSB would had used such an inept imputation
then
http://de.wikipedia.org/wiki/Johann_Adolf_Scheibe
probably would had critzised that 'dim-6th' botch
in 1737 as
"...sei unnatürlich, gekünstelt und sein Stil verwirrend."
'...beeing unnatural, artificial and confusing in style."
http://www.muzykologia.uj.edu.pl/conference/PDF/72Lutterman.pdf

http://www.albany.edu/piporg-l/FS/sr.html
"The tuning of the organ was in a then modern "well temperament", not
the quarter comma meantone prevalent in older organs of the time. The
tuning allowed the use of a wider range of keys than would have been
available in meantone temperament. This fact may have encouraged the
young Bach to experiment with bold modulations and excursions into
keys that would have seemed quite shocking to the conservative
parishioners. These experiments may well have led to the criticism of
Bach that was mentioned above. "
...
"The original pitch of the organ was restored and set at 465 Hz at 18
degrees Celsius. The original temperament and pitch was determined
from the pipes of the Gemshorn 8' on the Oberwerk."
....
"The numbers in parentheses indicate the number of original Wender
pipes that remained in each stop. 25.6% of the pipework is original.
The temperament is well tempered, based on temperaments used by Wender
around 1700. The pitch is 465 Hz at 18 degrees Celsius."
....
"The well temperament of the organ has some significant implications,
I think. I have already mentioned the fact that the temperament
allowed Bach to play in keys with more sharps and flats. C.P.E. Bach
writes that because his father "lived at a time when a gradual but
striking change in musical taste was taking place,...."
....
" Since the young Arnstadt Bach was free to use more remote keys on
the Wender organ, it seems likely that he already was making more
extensive use of the thumb at this early period than was previously
thought The fully chromatic bass octaves in both the manual and the
pedal of the Wender organ also freed Bach to use a wider variety of
keys as well."

Quest:
Does anybody here in that group know the exact specification
of the concrete pitches found in the Arnstadt "Wender"-organ?

bye
A.S.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Chapter 9 Refreshed Perspectives

>
> After arranging the prevailing possibilities for
> Bachâs tuning >categorically,
> a multiple choice question is constructed that leaves only one
> answer, the direct result of eliminating all other possibilities.

Hi Johnny & all others,

Recnetly David Backus wrote in

http://www.gdo.de/veroeffentlichungen/ars_organi/

"Backus, David:
Wie sollte man Bachs Orgelwerke aufführen und wie mag Bach selbst
gespielt haben? Ars Organi 56, 2008, 161-164."

How should we perform Bach's organ works,
and how might Bach played himself?

on p.161:

"Wir wissen nicht und wir werden nie wissen,
wie JSB selbst Orgel gespielt hat.
Wir können aus Notenmaterial, aus Berichten und
Dokumenten nur Rückschlüsse ziehen;
es muß aber jedem klar sein, daß man auf diesem Gebiet
mit 100%iger Sicherheit nichts behaupten kann.
Friedrich Konrad Griepenkerl bemerkte schon 1844, daß nach fast 95
Jahren eine ganze Denk- und Empfindungswelt endgültig und für immer
untergegangen sei, menschliche Kontinuitäten und Erinnerungen waren
allgemein, aber besonders im Falle JSBs, unterbrochen"

tr:

'We don't and will never know any more,
how JSB himself played (tuned) the organ.
We can barely draw back conclusions from scores, reports and documents;
but it must be evident for us all,
that nothing can be claimed in that topic 100% certain.

Already in 1844 Friedrich Konrad Griepenkerl...
http://de.wikipedia.org/wiki/Friedrich_Konrad_Griepenkerl
http://upload.wikimedia.org/wikipedia/de/5/5c/Friedrich_Konrad_Griepenkerl_%281782-1849%29.JPG
(responsible for: Edition-Peters of JSB's works)
Download for instance:
http://imslp.org/wiki/Image:PMLP03267-Bach_-_Two_Part_Inventions_-_Peters_Griepenkerl.pdf
http://imslp.org/wiki/Image:PMLP03268-Bach_-_Three_Part_Inventions_-_Peters_Griepenkerl.pdf
history 1801-1805
http://www.olms.de/pcgi/a.cgi?ausgabe=index&T=1227039483357{haupt_olms=http://www.olms.de/pcgi/a.cgi?T=1227039483357&alayout=428&ausgabe=detail&aref=8894}

...FKG remarked, that after nearly 95 years,
there had vanished for ever a wholly (different) world of
thinking and sensations, due to generally broken continuieties,
even more (drastic) in the special case of JSB.'

The whole article appears i.m.h.o. worth to be translated completely.

Conclusion:
Hence i do cast into doubt any reduction to one singular
so called "JSB" tuning, however stringent chosen was
the elimination process among ours today restricted possibilities.

Sorry for my caginess in accepting yours hypothesis due to experience.

bye
A.S.

Conclusion:
Hence i do cast into doubt any reduction to one singular
so called "JSB" tuning, however stringent chosen was
the elimination process among ours today restricted possibilities.

Sorry for my caginess in accepting yours hypothesis due to experience.

bye
A.S.

Andreas, you quote ancient people who have doubts. Thank heavens it is still
possible to be original. Perhaps you shouldn't judge a book by its cover (or
chapter headings). ;)

all in good time, Johnny
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--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
> Nevertheless some
> modern commercial tunings alike 'Kellner' or 'Lehman'
> still persist in wrongly labeled the as "original"
> in order to mislead astray the deceived customers by fraud.

Andreas, my work is not "fraud", or any attempt to deceive or mislead
anyone. I am honest and sincere. I have presented my research and my
reasoning, clearly.

You obviously disagree with it (or at least, you disagree with YOUR
OWN MISUNDERSTANDING OF it!), but that does not make my work into
"fraud".

Here are Richard Egarr's program notes from last night's performance
of WTC book 1 in Carnegie Hall:
http://www.carnegiehall.org/textSite/box_office/events/evt_11373.html

Brad Lehman

'Excuses'? That is, really, absolute and unbelievable arrogance. Why
do I owe you a a single minute of my attention or effort? Why should I
have to offer any 'excuse' for temporarily (or indeed permanently)
ignoring you? What makes you think you deserve a hearing by so many
people so fast for all that you want to say?

Knowing what I know, I'd actually be perfectly, wonderfully, happy not
hearing a single word or note more from Brad my entire life. Why
should I give a single hour more of my life to his incurable need for
attention?

And what does Richard Egarr playing something in an auditorium in
Baltimore (whether empty or full) have to do with JS Bach's actual
tuning practice? Perhaps if you pack the audience members closely
enough together they will collapse gravitationally and create a
wormhole which will allow us to travel back to 1722 and actually find
some reliable or credible information? Sounds crazy? But it makes at
least as much sense as Brad's capitalistic boasting. Bruce Springsteen
would also sell out in Baltimore, but not for any historical reason
concerning his guitar tuning.

I see no evidence that Brad is or ever has been serious about
historical tuning, rather than treating it as a game to win academic
points, recognition and fame. History not as a thing in itself, but as
a means to an end. If you know what answer you want to get before you
start 'researching', the whole thing is just meaningless, but that's
how it seems to work, you know which tuning (or harpsichord or tempo
or rhythm) you want to sell, you just have to find the right
'musicology' to mix in in order to sell it to the people who matter.
May the best salesman win, history be damned!

That's what has made me unhappy, to read a whole lot of stuff and
realize that it's not intended to *educate* the reader in music or
tuning, it's just an extended commercial for the same product, because
all the 'facts' are (unlike in real life) lined up neatly in one
direction. Educate, meaning enable people to make their own judgments,
enable them to realize *their* musical abilities and tastes, not try
and lead them down a path to exactly the same opinion as me.

Brad is behaving as an Expert, as someone who has the right to tell
other people what to do, but there were no such Experts in historical
harpsichord tuning - players decided for themselves, learning from
their masters but having the absolute privilege and pleasure of doing
something different when they reached their own mastery. That is what
mastery means, being good enough to do things just a bit differently
from anyone else. Now if Brad succeeds, every Bach-tuning will be a
clone of the next...
~~~T~~~

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> > Pre-judgment as to what to read is - unfortunately - an absolute
> > necessity in science. You know there are literally dozens of new
> > papers every day.
>
> While you're making excuses for not reading the piece, meanwhile, here
> is Egarr's concert of the complete WTC 1 in Baltimore tomorrow (using
> this). I hear from the harpsichord builder that it's already been
> sold out for a while.
>
> http://www.artbma.org/calendar/films.html
> http://www.baltimoreathome.com/detail.aspx?dct=8&mid=933&eid=14660
>
> Enjoy,
>
> Brad Lehman
>

Tom, I used to admire you for your objectivity...and that's why I
asked your opinions, too. As I have seen across the past four or five
years, you are often inspiringly good with your careful and thoughtful
treatment of sources. But now, if you're just going to dismiss things
IN PUBLIC, and on your pre-judgments INSTEAD OF reading them, that's
not objectivity.

Can we have the "good scientist Tom" back, please? The admirable one
who gives fair assessments of things that he actually takes time to
look at (and try hands-on at a harpsichord), and who says NOTHING
about things he doesn't look at (or try hands-on at a harpsichord)?

Brad Lehman

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> 'Excuses'? That is, really, absolute and unbelievable arrogance. Why
> do I owe you a a single minute of my attention or effort? Why should I
> have to offer any 'excuse' for temporarily (or indeed permanently)
> ignoring you? What makes you think you deserve a hearing by so many
> people so fast for all that you want to say?
>
> Knowing what I know, I'd actually be perfectly, wonderfully, happy not
> hearing a single word or note more from Brad my entire life. Why
> should I give a single hour more of my life to his incurable need for
> attention?
>
> And what does Richard Egarr playing something in an auditorium in
> Baltimore (whether empty or full) have to do with JS Bach's actual
> tuning practice? Perhaps if you pack the audience members closely
> enough together they will collapse gravitationally and create a
> wormhole which will allow us to travel back to 1722 and actually find
> some reliable or credible information? Sounds crazy? But it makes at
> least as much sense as Brad's capitalistic boasting. Bruce Springsteen
> would also sell out in Baltimore, but not for any historical reason
> concerning his guitar tuning.
>
> I see no evidence that Brad is or ever has been serious about
> historical tuning, rather than treating it as a game to win academic
> points, recognition and fame. History not as a thing in itself, but as
> a means to an end. If you know what answer you want to get before you
> start 'researching', the whole thing is just meaningless, but that's
> how it seems to work, you know which tuning (or harpsichord or tempo
> or rhythm) you want to sell, you just have to find the right
> 'musicology' to mix in in order to sell it to the people who matter.
> May the best salesman win, history be damned!
>
> That's what has made me unhappy, to read a whole lot of stuff and
> realize that it's not intended to *educate* the reader in music or
> tuning, it's just an extended commercial for the same product, because
> all the 'facts' are (unlike in real life) lined up neatly in one
> direction. Educate, meaning enable people to make their own judgments,
> enable them to realize *their* musical abilities and tastes, not try
> and lead them down a path to exactly the same opinion as me.
>
> Brad is behaving as an Expert, as someone who has the right to tell
> other people what to do, but there were no such Experts in historical
> harpsichord tuning - players decided for themselves, learning from
> their masters but having the absolute privilege and pleasure of doing
> something different when they reached their own mastery. That is what
> mastery means, being good enough to do things just a bit differently
> from anyone else. Now if Brad succeeds, every Bach-tuning will be a
> clone of the next...
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, "Brad Lehman" <bpl@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> > > Pre-judgment as to what to read is - unfortunately - an absolute
> > > necessity in science. You know there are literally dozens of new
> > > papers every day.
> >
> > While you're making excuses for not reading the piece, meanwhile, here
> > is Egarr's concert of the complete WTC 1 in Baltimore tomorrow (using
> > this). I hear from the harpsichord builder that it's already been
> > sold out for a while.
> >
> > http://www.artbma.org/calendar/films.html
> > http://www.baltimoreathome.com/detail.aspx?dct=8&mid=933&eid=14660
> >
> > Enjoy,
> >
> > Brad Lehman
> >
>

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
>
> Here are Richard Egarr's program notes from last night's performance
> of WTC book 1 in Carnegie Hall:
> http://www.carnegiehall.org/textSite/box_office/events/evt_11373.html
>
> Brad Lehman

This paragraph (below) from these notes seems to me a perfect example
of the self-serving, self-deceiving, unthinking, anti-historical
'musicology' that leads listeners and readers to an even worse state
of information than those 'informing' them.

"The concept and tuning of an âequalâ tempered system were fully
understood and known well before Bachâs time. Bach clearly called his
book well-tempered, not equal-tempered. The search as to which
âunequalâ system Bach had in mind was something of a holy grail (...)"

First, this hides an unspoken assumption that Bach would care whether
any keyboard tuning was actually equal-tempered with any precision
(which is a theoretical and mathematical question) - or just
*sufficiently* equal. That Bach really cared at all about keeping the
theorists happy. Perhaps he didn't give a damn about the theoretical
status of a tuning in divisions of the comma, or about precisely which
key sounded slightly better or worse than another, as long as they all
sounded good enough.
To such a practical musician, the question 'But do you mean exactly
equal-tempered or not' is absolutely meaningless. Near-equal tunings
would be just as much 'well-tempered' as equal temperament itself.

Or if you want to argue with even more historical backing, the phrase
'well-tempered' is almost a straight quotation from Werckmeister, -
who certainly said that ET was a good tuning for the purpose of
playing in all keys.
So, from the only writer(s) before Bach's era who gave a meaningful
definition of a 'good temperament', equal temperament WAS one.

Historically, the great difference was not between equal and
nearly-equal, it was the much greater one between nearly-equal and
meantone. But Egarr ignores this and would like to have us believe
that Bach necessarily cared to differentiate between ET and all other
'good temperaments'. Assumes that Bach must have shared a 20th-century
(and probably Egarr's own) neurotic and pedantic obsession over tiny
differences in tuning between equal and not-quite-equal.

Second, the unspoken assumption that Bach had exactly _one_ 'unequal
system' in mind - which then necessarily assumes the status of a 'holy
grail'.
There is no evidence or reason at all for this assumption (which one
might call a late 20th century obsession), and plenty against it, such
as that Bach had dozens of pupils, but not one of them said anything
about a specific 'unequal system', let alone tried to describe it. We
have 'take away a small amount of the absolute purity from most of the
fifths and check all the chords' and 'all the thirds sharp' - and
that's all folks!

Carried along with this is the assumption that anyone in the Bach
household would bother or need to record any aspect of tuning with
enough exactness to reproduce it from one day to the next. To make it
a 'system'. It's the Holy Grail again, assuming there is a single
formula to be preserved forever for the enlightenment of the heathen,
rather than a general skill in listening which allows you or anyone
else to make a freshly 'good tuning' every day. If you don't need to
record your tuning from yesterday or last year, if you are happy to
let it be yesterday's, there is no point in writing down even a single
figure or symbol.

So the ideas that Bach 1) would necessarily care whether a keyboard
was equally tempered or not, and 2) needed a particular mathematical
or mechanical recipe aka 'system' to make a 'good tuning', and 3)
necessarily considered exactly one non-equal tuning as 'good' or
'well' tempered - are all absolutely groundless from a historical
perspective. And if they arise as unspoken assumptions in a line of
argument, absolutely misleading.

Is it intentionally misleading? One would hope not. Is it written with
an intent to persuade above all else, and a clear unwillingness to
think historically, to examine a wide range of evidence and to analyze
and question his own assumptions? Yes. It is salesmanship, it has
nothing at all to do with history, because Egarr uses legalistic
verbal tricks and leading phraseology. He doesn't think like an early
18th-century Capellmeister and harpsichordist (question: how does this
chord sound and how should I adjust the notes around it) but rather a
20th-century academic Early Music Expert (question: which one
mathematical division of the comma a.k.a. 'system' is most Authentic
for Bach).

I have no idea how much Egarr actually knows about history. But how
misleading is it for Brad to knowingly endorse the anti-historical
argument 'Bach said well-tempered so he can't possibly have meant
equal-tempered'?

How misleading is it to knowingly spread the idea 'Bach had just one
unequal "good temperament", which could be mathematically formulated'
as an unspoken assumption?

~~~T~~~

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@>
> wrote:
> > Nevertheless some
> > modern commercial tunings alike 'Kellner' or 'Lehman'
> > still persist in wrongly labeled the as "original"
> > in order to mislead astray the deceived customers by fraud.
>
B.L. replied:
> Andreas, my work is not "fraud",
> or any attempt to deceive or mislead
> anyone.

What about with the kidded editor of Early-Music,
that you made belive in yours alleged "discovery" claims?

http://em.oxfordjournals.org/cgi/reprint/33/1/1.pdf
http://muse.jhu.edu/journals/early_music/v033/33.1knighton.html
"
Editorial:
4, November 2004

Over the last 30 years a number of exciting discoveries have appeared
in the pages of Early music: many of these have helped to shape
thinking on questions of performance practice, and have thus been
influential on the way we perform and hear early music today. So I am
very happy to present a further discovery, made last year by
harpsichordist and scholar Bradley Lehman, whose fascinating article
clearly establishes the temperament Bach had in mind when he composed
Das wohltemperirte Clavier, and, very probably, much of the rest of
his uvre.
Lehman has risen to the challenge offered by Malcolm Boyd in his
discussion of performance practice in Bach's music. 'The quest', wrote
Boyd in his biography of Bach, 'continues, not for the complete
"authenticity" in performance which is unattainable and probably
undesirable, but to establish what conditions are indispensable for
any performance that hopes to capture the true essence of Bach's art.
Possibly the most revealing discoveries still to be made await a more
thorough application than has so far been attempted of the
temperaments (tunings) in use during Bach's time.' I will leave Lehman
to describe and substantiate the evidence for the temperament he has
discoveredor more accurately, perhaps, uncovered, for the story
begins with a brilliant piece of detective work or, again more
accurately, decodingin this and the next issue. Based on a unique
blend of three different 'equal' scales, the temperament works equally
well in any key, or genre. This discovery should indeed afford further
insight into the 'true essence' of Bach's art. "

> I am honest and sincere.
Agreed.

> I have presented my research...
...without proper reference to earlier work on the squiggles,
when claiming it as yours own alleged "discovery",
except a cryptic hidden remark in "supplementary" file:
http://em.oxfordjournals.org/cgi/data/33/1/3/DC1/2
there on p.45 out of 46pages,
appears an distorted reference to:
http://keithbriggs.info/bach-wtc.html
of May 31, 2003

> and my
> reasoning, clearly.
by
http://www.larips.com/
"In a favorite term from my wife's field, this caused a "cognitive
dissonance" in my mind as I studied Bach's drawing. No one, to my
knowledge, has ever tuned in such a manner with a constant arithmetic
beat rate (as opposed to a constant geometric size) across a number of
fifths ; and surely Bach did not,... "

Who did entiteled to selfproclaim that in his name?

When did JSB himself told you that he didn't tuned just in
just that Schlick's/Werckmeister's manner of counting beats?

instead of reinterpreting the 1722/1723 WTC squiggles:

-2-2-2-1-1-1-3-3-3-3-3-

'upside-down- as yours personal "esotheric":

F"C"G"D"A"E B F# C#'G#'D#'A# ~704Cents~ F

'upside-down' in PC^(1/12) units?
>
> You obviously disagree with it
Yep, of course,
because i do agree with C.P.E.
that his father's tuning was lost for ever
with his passing away togehter .

> (or at least, you disagree with YOUR
> OWN MISUNDERSTANDING OF it!),
Well, i do even disagree with yours wife opinion:
http://www-personal.umich.edu/~bpl/larips/lindleyortgies.html
"That his wife agrees with him is not substantial evidence as to 17th-
or 18th-century taste. "
http://www.larips.com/
"Musical colleagues would have to adjust every one of their pitches
from regular positions, ad hoc, to perform accurately with a keyboard
so tempered. Hence the "cognitive dissonance" in my mind."

Sorry, but not in mines.

> but that does not make my work into
> "fraud".
What about that obvious swindle?:
http://www-personal.umich.edu/~bpl/larips/1003cover.jpg
wrongly labeled as:
"JSB & Wilhelm Friedemann Bach in the family's tuning"
offered on yours own page:
http://www-personal.umich.edu/~bpl/larips/cd1003.html

bye
A.S.

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> Andreas, you quote ancient people who have doubts.
Just in order to learn from that old masters.

> Thank heavens it
> is still
> possible to be original.
Because i do commit myself to theirs views as far as i can.

> Perhaps you shouldn't judge a book by its cover (or
> chapter headings). ;)
Fully agreed,
because i do trust secure in yours fair-minded truthfullness,
of treating all the known historialy sources properly correct.

with the best wishes for yours intended publication &
in looking forward for studying yours book in preparation

A.S.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> I have no idea how much Egarr actually knows about history.

hi Tom,
here an sample of that questionable layman-musicologist:

http://www.goldstar.com/events/los-angeles-ca/harpsichordist-richard-egarr-at-doheny-mansion.html?expired=true
http://www.houstonearlymusic.org/archives/334
http://www2.carnegiehall.org/textSite/box_office/events/evt_11373.html
http://www.carnegiehall.org/article/box_office/events/evt_11373_pn.html?selecteddate=11182008

"Although not directly dedicated to Wilhelm Friedmann, the first
volume of Das Wohltemperirte Clavier would be the natural follow-up
volume for his now prodigiously gifted 12 year-old. The title of this
work alone continues to raise discussion and sets temperatures at a
high level in musicological circles, as it throws up two very specific
questions: what is the meaning of `Wohltemperirte' and which `Clavier'
should we use for this music. Quite honestly I see little problem
myself. The concept and tuning of an `equal' tempered system were
fully understood and known well before Bach's time. Bach clearly
called his book `well'-tempered, not `equal'-tempered. It is amazing
to me that hugely respected musical reference publications can in 2007
still describe this collection in the following way: "Presumably Bach
brought [the Preludes and Fugues] together for convenience, partly to
serve as the last step in his keyboard course, partly to exhibit the
advantages of equal temperament." The search as to which `unequal'
system Bach had in mind was something of a `holy grail' until Bradley
Lehman `decoded' the `decoration' that adorns the title page. His
conclusions have now been thrown around the Internet and hugely
debated, resulting in the seemingly inevitable opposing camps of
believers and non-believers. I am a believer. The tuning system's
simplicity and brilliance lends an amazing yet perfectly balanced set
of colours to each of the keys within the cycle the world's first
musical cycle to climb steadily through all the keys, major and minor.
...
"
so far about R.Egarr's statements as selfproclaimed musicologist.

Don Satz critizies Egarr's performance on the harpsichord:

http://www.classical.net/music/recs/reviews/h/hmu07425a.php
http://www.musicweb-international.com/classrev/2006/Jun06/Bach_Goldberg_HMU90742526.htm

"In Egarr's quest to find cantabile heaven, he uses two unique
features. First, he employs a tuning system that has recently been
advanced as the one Bach may have used for his own keyboard works.
This system was researched and developed by the musicologist and early
keyboard artist Bradley Lehman. Without going into the details of the
research, Lehman has taken a 17th century sixth comma meantone tuning
and adjusted it to accommodate the most remote key areas. In doing so,
Lehman is confident that he has developed a tuning regimen that
highlights the musicality and attractiveness of the harpsichord. Egarr
is of like mind, and uses Lehman's tuning system to assist in reaching
cantabile heaven.....
.....His articulation is generally on the weak side, and it has been
quite a few years since I've heard a version of the Goldberg
Variations with so little determination; pointed phrasing simply gets
little attention from Egarr, and the quills do not help the matter.
Perhaps most important, Egarr conveys little of the excitement, drive,
and momentum of the faster variations that comes from the best
harpsichord versions including those of Kenneth Gilbert on Harmonia
Mundi, Gustav Leonhardt on Teldec, and Pierre Hantai on Mirare. Egarr
takes the fast variations at a pace much slower than the norm, robbing
them of their inherent exuberance and propulsive elements and
substituting an unappealing restraint and sluggishness. Another
problematic aspect is that Egarr is not interested in representing the
underbelly of the human condition as Variations 9, 13, 15, and 25 (The
Black Pearl) are not sufficiently characterized.

Disappointment also comes to center stage with Egarr's performance of
Variation 30. In this variation, a singing tone is an absolute
necessity; yet, Egarr abandons his own stated cantabile goals and
offers us quite a choppy presentation. "

Finally Don Satz concludes:
"
....But those looking for a broader set of qualities might be
disappointed. Personally, I find the interpretations rather
soft-grained with a very low excitement/drive quotient.....
....If it seems that I have been straddling the fence a little, allow
me to correct the situation by stating clearly that Egarr's Goldberg
Variations is not one of the great recorded performances of the work."

Or less "straddling" reviewed by
Lyne Heffly in:
http://articles.latimes.com/2006/mar/06/entertainment/et-weekarts6
" Egarr, an internationally known keyboard virtuoso and conductor and
the director of Amsterdam's Academy of the Begijnhof, plays the
"Goldberg Variations" using a tuning only recently published by
harpsichord scholar Bradley Lehman.

Lehman decoded a "squiggle" on the title page of Bach's "The
Well-Tempered Clavier" that he believes described the composer's
tuning system, Egarr explained in a phone interview.

"Other people have been trying to find Bach's tuning," Egarr says.
"It's a bit of a Holy Grail in a way." Although not universally
accepted, Lehman's discovery is "quite a convincing and most brilliant
piece of detective work. It really sounds fantastic in Bach's keyboard
music and that seems to me proof, if anything. It really does work
with the music.""

Tom asked:
> But how
> misleading is it for Brad to knowingly endorse the anti-historical
> argument 'Bach said well-tempered so he can't possibly have meant
> equal-tempered'?

here an example of such an misleaden view:
http://www.guyguitars.com/eng/handbook/Tuning/temperament.html
"Unfortunately neither Bach nor his sons ever saw fit to write down
explicit instructions on how to tune this temperament, and it has thus
sadly been lost to us for almost 250 years. However, according to Dr.
Bradley Lehman, A.Mus.D. (harpsichord), of Goshen College, Indiana,
the key to the mystery has been hidden in plain sight since 1722 - in
Bach's own hand, on the title page of the original manuscript of "Das
Wohltemperirte Clavier". Dr. Lehman's intimate knowledge of Bach's
music, and extensive hands-on experience of harpsichord tuning,
enabled him to crack the code at last.

His breakthrough came in April 2004 and is making huge waves
internationally in the world of the harpsichord and the pipe organ....
"

Quest: (how to convince Brad? about his):
http://en.wikipedia.org/wiki/Much_Ado_About_Nothing
else than an perhaps merely decorative ornament?
>
> How misleading is it to knowingly spread the idea
>'Bach had just one
> unequal "good temperament", which could be mathematically
> formulated'
> as an unspoken assumption?

I.m.h.o:
http://dict.leo.org/forum/viewWrongentry.php?idThread=45577&idForum=3&lp=ende&lang=de
"Don't believe the guff in those tabloids."

bye
A.S.

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

> Now if Brad succeeds, every Bach-tuning will be a
> clone of the next...

Already Roland Hutchinson feared that evil prognosis in:
https://lists.wu-wien.ac.at/pipermail/earlym-l/2005-February/000887.html

"4. This is not the first time that Early Music
has published a claimed Bach Tuning" discovery.
It probably won't be the last.
It's definitely an area beset
(as Sybrand Bakker pointed out upthread) with
"Hineininterpretatationsprobleme"
that will keep speculation going for a
long as Bach's music continues to played."

sorry Tom, i must regret:
But as long as EM accepts again and again
papers about JSB's alleged tuning
of such selfproclaimed know-it-all authors:

There is no cure for that.

Sadly!

bye
A.S.

my lecture notes from 10/22

🔗Brad Lehman <bpl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Brad Lehman <bpl@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Tom Dent <stringph@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Brad Lehman <bpl@...>

🔗Brad Lehman <bpl@...>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Brad Lehman <bpl@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Tom Dent <stringph@...>

🔗Brad Lehman <bpl@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Brad Lehman <bpl@...>

🔗John Garside <garsidejl@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Tom Dent <stringph@...>

🔗Brad Lehman <bpl@...>

🔗Afmmjr@...

🔗Brad Lehman <bpl@...>

🔗Afmmjr@...

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Afmmjr@...

🔗Brad Lehman <bpl@...>

🔗Tom Dent <stringph@...>

🔗Brad Lehman <bpl@...>

🔗Tom Dent <stringph@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>