Bach's minor-key WTC preludes

Dear Claudio and list,

A student of mine, Steven Cannon, performed the very analysis you describe, on Bach's minor-key pieces, following Barnes's methodology. I'll see if Steven would like to follow up with you here, but his results were extremely interesting: the curve Barnes obtained for the major-key preludes was mirrored, in an almost perfect inversion, in the minor-key preludes. If we accept Barnes's premise that his curve shows which thirds were the best tuned in Bach's tuning, by virtue of their appearing more frequently or more prominently in the major-key works, then we see a completely opposite aesthetic approach in the minor-key pieces--as if Bach were deliberately *avoiding* the better major thirds in the context of minor-key works. Statistically the inverse correlation had a very high degree of significance.

Regards,

Jon Wild

> Posted by: "Claudio Di Veroli" dvc@... � diveroli
>
> Pity that for what you are trying to find out here, Carl, it would be VERY
> interesting to have Barnes's statistics for Minor Mode WTC pieces!
> [If Barnes ever did any statistics for minor-key pieces, he never wrote
> about it as far as I know.]
>
> Well, the WTC is always there, and Barnes's method has been fully
> scrutinised, shown to make sense and added some complements that make work
> both easier and more precise, whether for major thirds or any other
> consonant intervals, whether for Bach, WTC or else.
> (I had two writings published on the matter long ago, they are now included
> in my U.T. book, sections 9.6, 9.7, 21.2, 21.8 and 21.9.)

Very interesting indeed!
Barnes major-keycurve has many features that discard any possible chance:
- the differences between the use of "diatonic" vs "chromatic" major thirds
is huge
- if you calculate separate statistics for WTC I and WTC II, the two curves
look almost identical but for a small shift, thus it was deliberate, not
chance.
Certainly the only possible explanation to Seven Cannon's statistics is that
Bach avoided the good major thirds in minor pieces on purpose.
Avoiding consonance in minor keys makes perfect sense from Bach's
standpoint.
Problem is, I never heard of any ancient document ever describing such a
practice.

Kind regards

Claudio

PS:
Where did Steven get Barnes's criterion for the "weights" to the major
thirds as per prominence?
Steven could not have read my paper of 1985 in Spanish and surely did not
read my recent U.T. Book, where I explain in full detail something Barnes
describes in very ambiguous terms.
Guess Steven has developed his own rules for the weights: would like to read
them first of all, to see whether the two statistics can really be compared.

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Jon Wild
Sent: 01 April 2009 19:54
To: tuning@yahoogroups.com
Subject: [tuning] Bach's minor-key WTC preludes

Dear Claudio and list,

A student of mine, Steven Cannon, performed the very analysis you
describe, on Bach's minor-key pieces, following Barnes's methodology. I'll
see if Steven would like to follow up with you here, but his results were
extremely interesting: the curve Barnes obtained for the major-key
preludes was mirrored, in an almost perfect inversion, in the minor-key
preludes. If we accept Barnes's premise that his curve shows which thirds
were the best tuned in Bach's tuning, by virtue of their appearing more
frequently or more prominently in the major-key works, then we see a
completely opposite aesthetic approach in the minor-key pieces--as if Bach
were deliberately *avoiding* the better major thirds in the context of
minor-key works. Statistically the inverse correlation had a very high
degree of significance.

Regards,

Jon Wild

> Posted by: "Claudio Di Veroli" dvc@braybaroque.
<mailto:dvc%40braybaroque.ie> ie diveroli
>
> Pity that for what you are trying to find out here, Carl, it would be VERY
> interesting to have Barnes's statistics for Minor Mode WTC pieces!
> [If Barnes ever did any statistics for minor-key pieces, he never wrote
> about it as far as I know.]
>
> Well, the WTC is always there, and Barnes's method has been fully
> scrutinised, shown to make sense and added some complements that make work
> both easier and more precise, whether for major thirds or any other
> consonant intervals, whether for Bach, WTC or else.
> (I had two writings published on the matter long ago, they are now
included
> in my U.T. book, sections 9.6, 9.7, 21.2, 21.8 and 21.9.)

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:

> Certainly the only possible explanation to Seven Cannon's
> statistics is that Bach avoided the good major thirds in minor
> pieces on purpose.

I'm not sure exactly what these statistics show (having never
seen even Barnes paper myself), but keep in mind that in a WT
the good minor thirds must be located in certain relationships
to the good major ones...

> Avoiding consonance in minor keys makes perfect sense from Bach's
> standpoint.

We also have to be careful using 6/5 as the ideal minor third.
5/4 has a very clear consonance maximum, but 6/5 does not.
There are a host of relatively small numbers in the vicinity
of a diatonic minor 3rd, and when combined with the 5th things
can get very complicated very quickly.

In light of the above two facts, I usually ignore minor thirds
entirely when designing WTs.

Incidentally, Barnes happens to be a very unique well temperament.
See:

http://library.wustl.edu/~manynote/unique.html

Mind you, I don't think this is a terribly *significant* result
in well temperaments, but it is an interesting bit of trivia.

-Carl

Incidentally, Barnes happens to be a very unique well temperament.
See:
http://library. <http://library.wustl.edu/~manynote/unique.html>
wustl.edu/~manynote/unique.html
Mind you, I don't think this is a terribly *significant* result
in well temperaments, but it is an interesting bit of trivia.
-Carl

You are absolutely right, it does not add a iota to the historical
likelihood of Barnes, but it is a very interesting property
(I acknowledge Hahn's finding in my p. 126).

Claudio

Claudio wrote:

> Where did Steven get Barnes's criterion for the "weights" to the major
> thirds as per prominence?
> Steven could not have read my paper of 1985 in Spanish and surely did not
> read my recent U.T. Book, where I explain in full detail something Barnes
> describes in very ambiguous terms.
> Guess Steven has developed his own rules for the weights: would like to read
> them first of all, to see whether the two statistics can really be compared.

You're correct, Steven had not read your papers (I wish I had known of them!) and he developed his own guidelines for the weights. In my opinion while this means his numbers can't be compared absolutely with Barnes's, the relative shapes of the key curves can certainly still be compared.

Carl wrote:

> I'm not sure exactly what these statistics show (having never
> seen even Barnes paper myself), but keep in mind that in a WT
> the good minor thirds must be located in certain relationships
> to the good major ones...
>
> We also have to be careful using 6/5 as the ideal minor third.
> 5/4 has a very clear consonance maximum, but 6/5 does not.
>
> In light of the above two facts, I usually ignore minor thirds
> entirely when designing WTs.

Carl, there were no minor thirds involved with any of the calculations. The inverse relationship Steven Cannon found was between major thirds (by the way voiced as thirds, never tenths) as they are distributed in the major-key preludes, versus major thirds as they are distributed in the minor-key preludes.

Cheers -- Jon

You're correct, Steven had not read your papers (I wish I had known of
them!) and he developed his own guidelines for the weights. In my opinion
while this means his numbers can't be compared absolutely with Barnes's,
the relative shapes of the key curves can certainly still be compared.

Yes I suppose so.

Expect further news about this most interesting development.

Yours,

Claudio

Jon wrote:

> Carl, there were no minor thirds involved with any of the
> calculations. The inverse relationship Steven Cannon found was
> between major thirds (by the way voiced as thirds, never tenths)
> as they are distributed in the major-key preludes, versus major
> thirds as they are distributed in the minor-key preludes.

Same difference. But best to give a citation so I can see
what you're talking about.

-Carl

Claudio wrote:

> Certainly the only possible explanation to Seven Cannon's statistics
> is that Bach avoided the good major thirds in minor pieces on purpose.
> Avoiding consonance in minor keys makes perfect sense from Bach's
> standpoint. Problem is, I never heard of any ancient document ever
> describing such a practice.

Sorry, I'm a couple of days behind in reading digests (and completely swamped with other responsibilities...). But: this assertion that "Bach avoided the good major thirds in minor pieces on purpose" is frankly absurd, when we look at the Bb minor prelude/fugue of WTC2. There are wide-open major 10ths and 17ths here that put Barnes's temperament and analysis into the ash can.

So do at least the B minor and the Eb/D# minor of book 1; the F minor of both books; the F# minor of book 2; the F *major* of book 2 (a key signature of only one flat!); B major and Ab major of both books....

A huge problem with Barnes's analysis, in his article, is that he omits 10ths and 17ths from his data set. He also omits all the fugues! The only pieces that carry much weight in his experiment are the preludes that happen to have close/dense texture. Pieces like the Ab major of book 2 hardly get to come to the table, in this business of assessing major 3rds and any alleged "avoidance" of discord therein.

The way to test all this is to play the actual music on a medium-to-bright-toned harpsichord, not just to stare at scores and spreadsheets and articles.

Brad Lehman

Brado wrote:

> Claudio wrote:
>> Certainly the only possible explanation to Seven Cannon's statistics
> is that Bach avoided the good major thirds in minor pieces on purpose.
> Avoiding consonance in minor keys makes perfect sense from Bach's
> standpoint. Problem is, I never heard of any ancient document ever
> describing such a practice.

But: this assertion that "Bach avoided the good major thirds in minor pieces
on purpose" is frankly
absurd, when we look at the Bb minor prelude/fugue of WTC2.
(note that this assertion is by Jon Wild: I still have to examine the
statistics).

There are wide-open major 10ths and 17ths here that put Barnes's
temperament and analysis into the ash can.
... A huge problem with Barnes's analysis, in his article, is that he omits
10ths and 17ths from his data set.

Sorry to disagree with this Brad.
I have an example in my website showing how, in a modified meantone with
awful Ab-C as a major third, it sounds fine as a 10th.

So do at least the B minor and the Eb/D# minor of book 1; the F minor of
both books; the F# minor of book 2; the F *major* of book 2 (a key
signature of only one flat!); B major and Ab major of both books....

Remember that I am just commenting on a statistic made by somebody else,
which I haven't examined yet.
You are just mentioning a few preludes, I could also mention a few others in
the opposite way.
I would rather deduce the true trend once we can read the full statistics of
the 24 minor-key preludes, not just a few selected ones.

He also omits all the fugues!
Yes he did and he explained why: statistically the major thirds from the
Fugues would not add significant different curve.
I have followed John Barnes's activity and he was a very serious man, he
would not have said that if he had not found it true.
But of course, you have a point here: he may have been wrong.
I will read with interest a major-third statistics from the Fugues, and see
whether the amount of weighted major thirds is significant compared the
preludes.
If it does then it is to be seen whether the resulting curve differs
significantly from Barnes's original prominence curve.

The way to test all this is to play the actual music on a
medium-to-bright-toned harpsichord, not just to stare at scores and
spreadsheets and articles.

Let me see: you mean, instead of all that scientific methodology, let us
just tune and play.
Problem is, we are trying to find here a truth about the past.
There is no other method than scientific methods.
If we all do what you suggest, every harpsichordist will make his own
subjective deduction.
Because these are not clear-cut situations with separation of statistical
variables and design of experiments.
I find that the only way to proceed the way you suggest is to have several
identical harpsichords, carefully tuned to different temperaments, and spend
months doing comparisons.
And even that would not substitute for basic research on the musical scores
and the spreadsheets that allow us to gauge mistunings.
Barnes's found, in agreement with modern musicology, that that to scrutinise
scores and numbers is as important and actually comes first.
He thus achieved results much more economically and scientifically.

You are also suggesting that Barnes (and those who have studied his methods
and results) have NOT tested the results in harpsichords.
Let me remind you that Barnes, who was in charge of tuning the Russell
Collection in Edinburgh, DID NOT just stare at scores and numbers, he
carried out extensive experimentations with instruments tuned and played.
Actually, he had with the WHOLE WTC PLAYED IN PUBLIC with his temperament,
TWO YEARS before his paper appeared in Early Music!
So you cannot accuse Barnes of "just staring" and not playing.
Many musicians have used Barnes since, myself included, and are VERY happy
with it.
Besides, as I have shown in my recent work, regardless of the WTC and
Barnes's statistics, his temperament is a plain average circular one, so it
is not surprising that it fits very well the typical late Baroque fare with
more frequent use of tonalities with few accidentals.

Kind regards,

Claudio

Just joined the group, at Jon's recommendation.

Since Barnes's description of his criteria for assigning "weights" was rather vague, I developed my own method, as Jon has already mentioned.

Because these criteria might be different, we can't really compare my analysis to Barnes's--apples and oranges. Eventually of course, I plan to re-do Barnes's analysis, using my own criteria; this way the analyses of the major and minor preludes will be compatible. However, counting up the intervals by hand is tedious work, and I plan to use the Humdrum toolkit to do future work. Hopefully using the computer will speed things up enough that we can examine other consonant intervals (minor 3rds, perfect 4ths and 5ths, minor and major sixths, tenths, etc.).

But this temperament work is not related to my dissertation topic. Besides, I haven't had the time yet to teach myself how to use the software. Perhaps after I finish my comprehensive exams...

If any of you haven't yet read the Barnes article, It's Early Music 7/2 (1979), p. 236-249. You can only access it online if you (or your institution) have a subscription to it with Oxford Journals. Just in case you do, here is the link: http://em.oxfordjournals.org/cgi/reprint/7/2/236 .

Glad to hear that others are interested in this aspect of WTC.

-Steven

--- In tuning@yahoogroups.com, Jon Wild <wild@...> wrote:
>
>
> Dear Claudio and list,
>
> A student of mine, Steven Cannon, performed the very analysis you
> describe, on Bach's minor-key pieces, following Barnes's methodology. I'll
> see if Steven would like to follow up with you here, but his results were
> extremely interesting: the curve Barnes obtained for the major-key
> preludes was mirrored, in an almost perfect inversion, in the minor-key
> preludes. If we accept Barnes's premise that his curve shows which thirds
> were the best tuned in Bach's tuning, by virtue of their appearing more
> frequently or more prominently in the major-key works, then we see a
> completely opposite aesthetic approach in the minor-key pieces--as if Bach
> were deliberately *avoiding* the better major thirds in the context of
> minor-key works. Statistically the inverse correlation had a very high
> degree of significance.
>
> Regards,
>
> Jon Wild
>
> > Posted by: "Claudio Di Veroli" dvc@...   diveroli
> >
> > Pity that for what you are trying to find out here, Carl, it would be VERY
> > interesting to have Barnes's statistics for Minor Mode WTC pieces!
> > [If Barnes ever did any statistics for minor-key pieces, he never wrote
> > about it as far as I know.]
> >
> > Well, the WTC is always there, and Barnes's method has been fully
> > scrutinised, shown to make sense and added some complements that make work
> > both easier and more precise, whether for major thirds or any other
> > consonant intervals, whether for Bach, WTC or else.
> > (I had two writings published on the matter long ago, they are now included
> > in my U.T. book, sections 9.6, 9.7, 21.2, 21.8 and 21.9.)
>

--- In tuning@yahoogroups.com, "sccnnn" <sccnnn@...> wrote:
>
> Just joined the group, at Jon's recommendation.
>
> Since Barnes's description of his criteria for assigning "weights"
> was rather vague, I developed my own method, as Jon has already
> mentioned.
>
//
> If any of you haven't yet read the Barnes article, It's Early Music
> 7/2 (1979), p. 236-249. You can only access it online if you (or
> your institution) have a subscription to it with Oxford Journals.
> Just in case you do, here is the link:
> http://em.oxfordjournals.org/cgi/reprint/7/2/236 .
>
> Glad to hear that others are interested in this aspect of WTC.
>
> -Steven

Thanks Steven! I'll get the Barnes article. I can't believe
you did the stats by hand! I was just going to ask what toolkit
was used. I'll try to look at this over the weekend.

-Carl

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

>
> But: this assertion that "Bach
> avoided the good major thirds in minor pieces on purpose" is frankly
> absurd, when we look at the Bb minor prelude/fugue of WTC2. There are
> wide-open major 10ths and 17ths here that put Barnes's temperament and
> analysis into the ash can.
>
> So do at least the B minor and the Eb/D# minor of book 1; the F minor of
> both books; the F# minor of book 2; the F *major* of book 2 (a key
> signature of only one flat!); B major and Ab major of both books....
>

Certainly, there are many prominent 'good' major thirds in the minor-key preludes, such as in the B-minor set from Book 1, the F-minor from both books, and even the B-flat-minor set from Book 2. On average across the entire two collections, however, Bach does seem to emphasize the 'bad' major thirds in the minor-key preludes even more than the 'good' ones. Some of Brad Lehman's examples actually support this claim. The B-flat-minor prelude from Book 2 also contains many prominent 'poorly tuned' thirds, as does the F-sharp-minor from Book 2. The E-flat-minor prelude from Book I uses even more! As for examples where Bach avoids the 'good' major thirds in minor-key preludes, refer to the A- and E-minor in Book 2, and the D- and B-minor in Book 1.

Brad Lehman's references to major-key examples also seem to support (at least in part) Barnes's claim that Bach emphasizes the 'good' major thirds in these keys: the F-major of Book 2 contains many prominent 'good' major thirds. And while the B-major and A-flat major might contain more 'bad' major thirds than some of the other preludes in similar keys, they certainly do not emphasize these thirds as strongly as other preludes do the 'good' major thirds.

The problem with cherry-picking examples like this is that we can use them to support any claim about the collection. A broad, statistical study, such as Barnes's, attempts to balance out the effects of individual preludes, hopefully revealing any underlying trends.

> A huge problem with Barnes's analysis, in his article, is that he omits
> 10ths and 17ths from his data set. He also omits all the fugues! The
> only pieces that carry much weight in his experiment are the preludes
> that happen to have close/dense texture.

I fully agree. At best, Barnes's analysis is incomplete. At worst, it could be totally irrelevant. But I won't be convinced that it deserves the "ash can" until we make a valid comparison of the major to minor keys, incorporate the fugues, and take intervals other than major thirds into account.

> Pieces like the Ab major of
> book 2 hardly get to come to the table, in this business of assessing
> major 3rds and any alleged "avoidance" of discord therein.
>

Yes, Barnes's analysis of this particular prelude is questionable. I hear the 'poor' thirds as being very prominent, but Barnes chose to give them very little weight. This is one of the reasons why I intend to redo an analysis of the major-key works, using my own criteria for assigning prominence.

> The way to test all this is to play the actual music on a
> medium-to-bright-toned harpsichord, not just to stare at scores and
> spreadsheets and articles.
>

Again, I couldn't agree more. But unfortunately some of us don't have the time (or the facility at the keyboard) to play the entire set of 48, retune, play again to compare, then repeat the entire process for each temperament we wish to evaluate against the WTC. Analysis along the lines of Barnes's allows a broad and inclusive--and at the same time very fast and easy--evaluation of a temperament against the 48. Such an evaluation remains, however, woefully superficial.

I am much more interested by Bach's apparent emphasis of pure versus impure intervals in major versus minor keys than I am in using the analysis as a tool to evaluate temperaments. If Bach really does prefer purer major thirds in major keys, and less pure major thirds in minor keys, the analysis could give us a glimpse of how he conceived the sonic worlds of major and minor. A concordant major versus a discordant minor is compelling, given the affects we generally assign to these modalities.

-Steven Cannon

Another important piece for tuning problems, but overlooked by Barnes's analysis (because of its two-voice texture, more than an octave apart: i.e. scarcely any major 3rds), is the F# major prelude of book 1.

Brad Lehman

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
> Another important piece for tuning problems, but overlooked by
> Barnes's analysis (because of its two-voice texture, more than an
> octave apart: i.e. scarcely any major 3rds), is the F# major prelude > of book 1.

My longer remarks about that, from January:
http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0901&L=HPSCHD-L&P=R7900&D=1&H=0&I=-3&O=D&T=0

Brad Lehman

Brad wrote:
Barnes's analysis ... My longer remarks about that, from January:

<http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0901&L=HPSCHD-L&P=R7900&D=
1&H=0&I=-3&O=D&T=0>
http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0901&L=HPSCHD-L&P=R7900&D=1
&H=0&I=-3&O=D&T=0

Thanks for mentioning my book in the January post, Brad, even if not
precisely to agree with it!
At this stage both of us have written quite a few pages on the pros and cons
of Barnes's work.
Let's interested members read my book and your interesting comments and form
their own opinion.

Kind regards,

Claudio
http://harps.braybaroque.ie

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Brad Lehman
Sent: 05 April 2009 12:18
To: tuning@yahoogroups.com
Subject: [tuning] Re: Bach's minor-key WTC preludes

--- In tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com, "Brad
Lehman" <bpl@...> wrote:
>
> Another important piece for tuning problems, but overlooked by
> Barnes's analysis (because of its two-voice texture, more than an
> octave apart: i.e. scarcely any major 3rds), is the F# major prelude > of
book 1.

My longer remarks about that, from January:
http://listserv.
<http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0901&L=HPSCHD-L&P=R7900&D=
1&H=0&I=-3&O=D&T=0>
albany.edu:8080/cgi-bin/wa?A2=ind0901&L=HPSCHD-L&P=R7900&D=1&H=0&I=-3&O=D&T=
0

Brad Lehman

Claudio wrote, quoting Brad:

>> But: this assertion that "Bach avoided the good major thirds in minor pieces >> on purpose" is frankly absurd, when we look at the Bb minor prelude/fugue of >> WTC2.

> (note that this assertion is by Jon Wild: I still have to examine the > statistics).

Note that I actually wrote something much more guarded, namely "If we accept Barnes's premise [...][it is] as if Bach were deliberately *avoiding* the better major thirds in the context of minor-key works"

And in response to Brad:

Brad, I admire your practical approach and I enjoy the way you write introspectively about your process of listening to and evaluating temperaments. But your counter-evidence here is anecdotal--almost like the global-warming denier who says the climate can't be getting warmer, since they just had a snowstorm in May. Sorry for that insulting comparison--but until you count up the major thirds across all works in a systematic way (I know, this doesn't feel very musicianly), it's difficult to say.

Before seeing Barnes's (and Cannon's) results, I would never have believed that the distribution of a particular interval in the WTC would exhibit any meaningful pattern. But it's a fact that major thirds enjoy a distribution in the major-key preludes that correlates very well with their expected closeness to just, in several plausible well-temperaments. I don't think you can reliably deduce a particular temperament from it; the data is not fine-grained enough. But you can't *dismiss* the data just because it was obtained via spreadsheet instead of via musical experience. The fact the statistics are similar in WTC I and WTC II, and the close fit of the inverse curve when the minor-key pieces are considered, means there is some effect here that is worth an attempt at explanation.

I always thought that Barnes left out the fugues because the contrapuntal requirements there will lead to certain forced compositional choices, which could conceivably override the acoustic factors in some contexts. In the Preludes Bach is freer, and so the deviations from flat distribution are more meaningful. (I can't remember if this is what Barnes himself said, or if this is my own gloss.)

I also find plausible the notion that the perception of purity/impurity in M 3rds is different from that of 10ths. And anyway, the fact that there actually *is* a pattern in the distribution of 3rds--which is highly unlikely if attributed to random deviations--still deserves explanation, even if you'd prefer to see the data with tenths included.

There is another criticism, to the effect that a few pieces were first composed in other keys and transposed to new keys to fill gaps in the WTC. To this I'd say that Bach had a choice about which keys he transposed those previously-composed works into--and presumably he chose keys that worked well to his ear.

To the criticism that Barnes disregarded the minor-key music: Steven's study suggests it is sensible to separate out the minor-key works because they operate on different aesthetic principles.

I agree with you that it would seem the pieces with thick texture will overwhelm the experiment--that they have more M3rds just because they have more close spacings. But still, Bach had a choice about which keys to compose thick preludes in! Presumably they sounded better to him in the keys he wrote them in, than in other keys. Again, I wouldn't feel comfortable actually deducing a temperament from all of that--but *something* persists from all this data, and that something is not as meaningless as you believe it is.

Respectfully,

Jon Wild

With concerts up on the radar, it has not been possible to do much with the
List. However, I hope some of you catch some of the video posted by Mike
Shaffer on the AFMMM website (_www.afmm.org_ (http://www.afmm.org) ) shot during
last Christmas' Microtonal Bach broadcast on WKCR-FM in NYC.

And the book - Bach and Tuning - is done, and available as a file on a CD. I
retain the right to make pretty through the summer. In that vein, please, if
anyone is interested but cannot afford the requested recompense, please write
me privately.

I realize that there may be lots of different views expressed, hopefully in
the most positive of alternatives. :)

Hope you like the narrative. Johnny Reinhard
**************Worried about job security? Check out the 5 safest jobs in a
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