The Keyboard Temperament of J. S. Bach
Charles
http://www.eunomios.org/contrib/francis1/francis1.html
Regards
Charles
Bradley Lehman
A review of Charles' findings is posted at
http://www-personal.umich.edu/~bpl/francis-paper.htm
Bradley Lehman
Max
Why is your review so strongly worded? Charles' brief report does not
pretend to be an exhaustive thesis, but you are applying standards
that would stifle most informal discussion on the web.
As far as his temperament being inadequate for certain keys - well, of
course you're right, but tuning schemes can be transposed as needed.
I would be more interested were you to transpose his temperament as
required by your test pieces, and then make your report.
Also, I did not follow your explanation of why it is easy to construct
a temperament that closely matches equal tuning. Can you elaborate?
regards,
Max
Charles
news:baa549eb.04070...@posting.google.com...
>
> As far as his temperament being inadequate for certain keys - well, of
> course you're right, but tuning schemes can be transposed as needed.
> I would be more interested were you to transpose his temperament as
> required by your test pieces, and then make your report.
For Bach's music, the temperament sounds just fine in all keys (to my ears
at least) without any transposition. Are you sure you're tuning it
correctly? I doubt Bradley is (given his damming review!), which is fully
understandable as it takes practice to master a new procedure.
Regards
Charles
Max
Do you really think so? Surely this temperament has key areas that
sound noticeably better than others. A facile tuner such as Bach
would have transposed his favorite temperament as needed. Perhaps,
you are searching for Bach's journeyman temperament so close to equal
that it may be fixed in place and still cover all the bases? (ie. the
tuning Bach ostensibly used when he performed his WTC straight
through).
Bradley, by the way, says that the C#-G# and Ab-Eb fifths are severely
impure. I don't have an instrument on hand, but this sort of thing
can be tested through math. Anyone care to check it out?
-Max
Bradley Lehman
The patronizing nonsense by Charles, above, "I doubt Bradley is (given
his damming review!), which is fully understandable as it takes
practice to master a new procedure," is just that: patronizing
nonsense. Charles' proposition in his paper is that the ten-year-old
Wilhelm Friedemann could follow these instructions. OK, fine. I've
been tuning harpsichords professionally for 22 years. I know that
I've tuned Charles' invented method correctly, following the
instructions in his paper. I have double- and triple-checked this, on
a real harpsichord. The temperament simply sounds musically silly:
very crude with the harsh fifths and the nearly-random (by 17th and
18th century standards) distribution of major third qualities. I have
detailed my objections at the page
http://www-personal.umich.edu/~bpl/francis-paper.htm
The intent here is not to start, or participate in, any flame war
about this. In my professional opinion as both a scholar and
performer, Charles' paper and his conclusions are absurd: for exactly
the reasons I pointed out in my review. If you (anyone) choose not to
believe my objections, fine: go have this same thing checked out by
others who really understand and do harpsichord tuning, and who play
Bach's repertoire. Science gives reproducible results. The
scientific point here is that Charles' "Temperament IV" is nonsense
both musically and historically, and this can be confirmed by
independent observers. Additional observers might even come up with
more reasons why it's nonsense, beyond the 20+ that I have already
pointed out.
Yes, a ten-year-old *could* (maybe) follow Charles' instructions
accurately enough; granted. The resulting temperament is still
absurd.
Bradley Lehman
Bradley Lehman
> > "Charles" <fra...@datacomm.ch> wrote in message news:<2k3mf9F...@uni-berlin.de>...
> > > For those interested in this topic, new findings are available at:
> > > http://www.eunomios.org/contrib/francis1/francis1.html
> > >
> > > Regards
> > > Charles
> >
> > A review of Charles' findings is posted at
> > http://www-personal.umich.edu/~bpl/francis-paper.htm
> >
> > Bradley Lehman
>
> Why is your review so strongly worded? Charles' brief report does not
> pretend to be an exhaustive thesis, but you are applying standards
> that would stifle most informal discussion on the web.
>
His paper was posted in a public place, "published" as it were, at
Eunomios. Therefore it is subject to public scrutiny, including
expert scrutiny: the public includes people who really do have
experience and scientific background in the topic. Apart from
"informal discussion on the web", historiography and research are not
voted on as true/false/silly by their ability to convince people who
don't bring backgrounds of history or practice; things are determined
to be true according to the way they align with evidence (and,
especially, in the way they don't simply dismiss any evidence that is
either inconvenient to or unknown to the researcher).
> As far as his temperament being inadequate for certain keys - well, of
> course you're right, but tuning schemes can be transposed as needed.
> I would be more interested were you to transpose his temperament as
> required by your test pieces, and then make your report.
Of course tuning schemes can be transposed as needed; but, Charles
didn't make that point in his paper, or indeed explain at all why F
major (such a common key) should bear the brunt of poor harmony in its
fifth and third (by 17th/18th century standards and expectations).
>
> Also, I did not follow your explanation of why it is easy to construct
> a temperament that closely matches equal tuning. Can you elaborate?
>
> regards,
> Max
That's not what I said. Rather, I pointed out that it's easy to
construct temperaments that are so oddball, and then use them as a
standard against which historically valid temperaments are measured,
such that equal temperament comes out as the closest match. That's
done by simply changing and/or randomizing the musical goals, which
(in those centuries, at least) included the property of having the
most commonly-played keys be the best in tune as to their thirds and
fifths, while any less-pleasing intervals are put into the places that
are not used so often in music.
You want some other oddball temperaments, invented so that equal
temperament ends up with the smallest least-squares deviation compared
with other historical temps? Happy to oblige, as it's trivial.
Simply rotate some existing temperaments or turn them inside-out; or
shuffle their features around as Charles has done with rearranging
Werckmeister's fifths. Viz.:
1. F-C-G-D-A-E-B all pure fifths; B-F#-C#-G#-D#-A#-F all 1/6
Pythagorean comma narrow. Very smooth, no wolf anywhere, "all the
thirds are sharp" everywhere, and overall this temperament is
inoffensive...if one doesn't care that the triads F-A-C, C-E-G, and
G-B-D have the worst (sharpest) major thirds of any. [This is an
inside-out version of the "Vallotti" temperament.]
2. Bb-F-C-G-D-A-E pure fifths, E-B-F#-C# narrowed by 1/4 Pythagorean
comma, C#-G#-D# pure, Eb-Bb the remaining 1/4 comma narrow. [This one
is simply a rotation of Werckmeister's most famous scheme, transposing
it all up a major third.]
3. 1/5 Pythagorean comma fifths at E-B, Eb-Bb, F#-C#, Bb-F, and G#-D#;
all the others pure. To make this one (a freshly steaming one,
today!) I observed that Herbert Kellner's temperament (an invention of
the 1970s, as he described in his own papers) has five 1/5 comma
fifths and seven pure fifths in it. I took 12 cards from a deck of
playing cards, and assigned ace=Eb, 2=Bb, 3=F, 4=C, ..., J=C#, Q=G# as
the roots of the twelve available fifths; then I shuffled them all and
dealt five cards, and reported the results here. Sure enough, it
gives a temperament that has a smooth and pleasing series of keys, no
harsh fifths anywhere (because by definition we didn't use any!), and
it's really easy to tune: it turned out that F-C-G-D-A-E are all pure,
and the pattern of the tempered fifths is merely a rotation and
reflection of Kellner's own. Whoopee. Coincidences and truisms can
be forced to yield any alleged meaning, in the estimation of the
unwary; that's the point. It's the difference between pseudo-science
and real science.
4. Just as easily, I could have decided by definition (in exercise #3
here) that the five cards I pick are pure fifths and the other seven
intervals each take 1/7 of the comma. We get one that sounds really
good this way, and indeed going by results it's nothing more than what
Barnes did to Kellner's, or what Kellner before him did to
Werckmeister's. Make the comma split be (N+1) of the other guy's
split, and otherwise preserve the pattern of having all the tempered
fifths except one in sequence, then skip, then stick the final
tempered fifth into some place that will take some of the resulting
major thirds down a bit. Voila, a temperament that sounds smoother
(and closer to equal temperament) than its predecessor, simply through
the use of a clever strategy reusing somebody else's ideas. None of
this proves that Bach did it; indeed, I made this one up today
(literally a few minutes ago) simply by dealing cards as I said, and
then interpreting the outcome in the most advantageous way. Such a
1/7 comma temperament could be said to be "inspired by Werckmeister"
exactly as I've described here: a bunch of tempered fifths (all but
one) in sequence and then stick the leftover one somewhere else. So
what?
5. Going back to example #2 above, where we're spraying four 1/4 comma
fifths among eight pure ones, there are plenty of ways to do that with
nice musical results. For example, J P Bendeler published one in 1739
having the four tempered fifths be at C-G-D, E-B, and G#-Eb. He also
(as Charles did) came up with several that use only 1/3 comma division
(while all other fifths are pure): one of these has C-G-D and B-F#,
and another has C-G, D-A, and F#-C#. Again, so what? The fact that
these all sound pretty good and allow all keys to be used in music is
neither here nor there; there isn't proof that *Bach* used any of
these, any more than Charles has presented where he's taken mordents
and trills as if they mean anything more than their usual musical
meanings. (And, in the case of Charles' paper, he's switched tacitly
to a different comma but hasn't explained why, or even shown that he
understands his own switch!)
It's all just a forcing of coincidences, dressed up to look
meaningful, to impress any who don't know the historical record and
who don't notice when truisms are being pressed beyond their
significance. Smoke and mirrors! Scientific inquiry into music
history is a lot more substantial than Charles gives any credence (on
the evidence of his paper as "published"); and he's run right over all
that research by real experts by simply not using any of the standard
literature on this topic (especially, anything from the past 20
years). His paper celebrates the fact that he's managed to avoid
wolves by splitting up a comma and shuffling it around until he likes
his results. Whoopee; people have been doing that for centuries
already, and Charles has presented no believable proof that his
favored solution has anything to do with Bach...other than the
coincidences he's forced into it.
The fact that his solution is awful in F major is quite a strong
argument *against* it having anything to do with Bach, since Bach
wrote so much music in that common key. Why would Bach trouble to
retune to something else whenever he needed to play music in F, forced
to do so by having put something silly on to begin with? That's a
picture of a Bach who didn't understand music, or understand tuning,
being so much at the mercy of old debbil physics! (Gotta put some
tempered fifths *somewhere* to make it come out; what, we should just
spray them around randomly until everything is close enough to equal
temperament so it doesn't offend people whose ears aren't very
sensitive to pitch?!)
If Charles would have us believe that his solution is anything other
than pseudo-science (which is exactly what it is), then he's implying
with this paper that real scientific inquiry is worth nothing more
than his own dabblings are: the ability to sell coincidences and
truisms to the unwary. That brings us back to Max's question posed
above: my review is so strongly worded because Charles' paper itself
is such a mockery of the whole field!
=====
In a spot of good news: Dover Publications has in the first half of
2004 republished the classic study by J Murray Barbour: _Tuning and
Temperament: A Historical Survey_ (previously published in 1951 and
1972, and itself a revision of Barbour's earlier dissertation). In
addition to issuing the book at a ludicrously low price, in paperback,
Dover has repaginated it and therefore also fixed the errata of
page-numbering in the index--which had plagued both the two earlier
printings by other presses. Barbour's original text is still all
there, presenting hundreds of historical temperaments and attempting
to chart a meaningful path through them. This book is absolutely
essential reading for anyone who would learn the background behind
this stuff. There is still the problem of the way Barbour read
20th-century musical expectations and measurement systems into the way
he assigned value (and that problem is much too pervasive to go into
here); but the presentation of the temperaments themselves, as to
recipes and ratios and whatnot, lays these hundreds of solutions out
for direct comparison. Barbour could have gone a lot further with the
musical analysis, but that's what musical instruments and spreadsheets
are for: a lifetime of study and listening, and continuing to search
for other temperaments that he didn't address (such as the well-known
Vallotti, and the Kellner and Barnes methods invented in the 1970s,
and a 17th century temperament from Siracusa Cathedral, etc etc).
http://store.yahoo.com/doverpublications/0486434060.html
Bradley Lehman
Bradley Lehman
> J P Bendeler published one in 1739
> having the four tempered fifths be at C-G-D, E-B, and G#-Eb. He also
> (as Charles did) came up with several that use only 1/3 comma division
> (while all other fifths are pure): one of these has C-G-D and B-F#,
> and another has C-G, D-A, and F#-C#. Again, so what?
To clarify that "1739" date a bit: that's the second edition, 30 years
after Bendeler's death. His work was published for the first time in
c1690, i.e. the same time as Werckmeister's stuff. Indeed, the two
were colleagues at Quedlinburg: Bendeler was a teacher and the cantor,
while Werckmeister was the organist. Bendeler also wrote two books
about mathematics.
In any case, the important point here is: all three of these Bendeler
temperaments fit Bach's music more closely than Francis' "Temperament
IV" does...as to putting the most consonant major thirds where they
are used frequently in the music, and letting the less-good ones be in
places that musicians don't care so much about, as to harmony and the
behavior of melody.
For Mr Francis to make even half of a convincing case for his own
invention, he'd have to demonstrate at least two crucial things: (1)
that Bach clearly used the same Werckmeister/Bendeler offshoot that
Francis himself has come up with (having shuffled his tempered fifths
somewhat differently), and (2) that it sounds better in the music than
the several Werckmeister and Bendeler solutions do, beyond Francis'
rough improvement to the isolated A-flat major triad at the expense of
so much else.
Bradley Lehman
Alain Naigeon
ee0d6edc.04070...@posting.google.com...
Hi Bradley,
About Bradley's book on temperament, I had in mind to buy it
after your description (BTW, it costs 11.16 at amazon!), but I'm
now hesitating after having read the following customer's comment:
This book is a standard source on scales and temeraments, and their history.
It compares and contrasts Pythagorean tuning, just intonation, meantone,
irregular temperaments, and finally equal temperament. Barbour displays a
strong predisposition towards twelve tone equal temperament in this work,
and interprets the history of scales and temperaments as an inexorable march
towards equal temperament.
Would you mind to comment... this comment? ;-)
(I personnally hate this kind of "inexorable march" stuff - did the ancients
act by thinking about what we were supposed to think and do today?)
--
Français *==> "Musique renaissance" <==* English
midi - facsimiles - ligatures - mensuration
Bradley Lehman
Yes, that is a fair assessment of the problem with this otherwise
outstanding book (Murray Barbour's _Tuning and Temperament_). It's
still essential reading anyway because of the huge amount of
information he presents; even though the way he organized it (forcing
his own equal-temperament preferences onto the material) puts an odd
skew to the relative importance of some pieces of the research.
A few weeks ago I remarked about it _en passant_ as part of another
review, of Isacoff's book _Temperament_:
http://www.amazon.com/exec/obidos/tg/detail/-/0375703306
Barbour's biases were forgiveable, as they accurately reflect the
state of research (and musical attitudes) at the time of writing, in
the late 1940s. Isacoff's biases (basically the same ones, but
dressed up with tabloid journalism) are not; his book being a huge
step backward and against the field of serious work. There's so much
else available that Isacoff should have used and understood
additionally, instead of relying so heavily on merely recycling the
50-year-old work of Barbour...Isacoff's book gives the word
"dilettante" new lustre.
Bradley Lehman
chris
Some years ago, after listening to a CD recording done by Elaine
Thornburgh, on a splendid 1690 Grimaldi graf-replica harpsichord( which was
built in 1982 by John Phillips) I noted his tunings for these recordings
were listed as "quartercomma meantone" ( still don't know what that
is...lol)
In a effort to learn what this was or meant, at the time, I wrote to
performer/lecturer Igor Kipnis to see perhaps if he could shed some light on
this. Mainly I had hoped to learn something more about the matter of baroque
temperments and why they seemed so diverse.
Mr. Kipnis replied within a couple of days. And his email stated "there is
just too much information on this question, for a single email to provide
you with"
I wish I could find that letter now, as I'd of reproduced it for this
newsgroup. Much of what he pointed out to me in mere words occurred to me
the other night while reading both Charles' and Mr Lehman's pages.
It would seem to me that in JS Bach's time "clavier temperment" was more or
less a regional (Italian, Flemish, German) consideration. Certainly, no two
harpsichord builders used the same tuning / temperment schemes, so
performers probably were left to tweak and tune an instrument to their own
taste. Am I making a good or bad assumption here?
"Bradley Lehman" <b...@umich.edu> wrote in message
news:ee0d6edc.04070...@posting.google.com...
Alain Naigeon
ee0d6edc.04070...@posting.google.com...
[...]
> Barbour's biases were forgiveable, as they accurately reflect the
> state of research (and musical attitudes) at the time of writing, in
> the late 1940s.
[...]
Thank you very much Bradley, I think I'll get this book!
--
Français *==> "Musique renaissance" <==* English
midi - facsimiles - ligatures - mensuration
http://anaigeon.free.fr | http://www.medieval.org/emfaq/anaigeon/
Alain Naigeon - anai...@free.fr - Strasbourg, France
Alain Naigeon
VbrHc.89236$Nz5....@newssvr29.news.prodigy.com...
> Hi all...
>
> Some years ago, after listening to a CD recording done by Elaine
> Thornburgh, on a splendid 1690 Grimaldi graf-replica harpsichord( which
was
> built in 1982 by John Phillips) I noted his tunings for these recordings
> were listed as "quartercomma meantone" ( still don't know what that
> is...lol)
Hi!
I'll avoid too many calculations, but the principle of this family of
meantone temperaments is very simple :
A just third is the 5th harmonic (vibrating strings), shifted back down to
the
starting octave, that is, a frequency ratio equal to 5/4
Now, we'd like that the 4th fifth would lead to the same note, since, for
instance : C-G-D-A-E -> this E should be the same as the one which is
5/4 higher than the C.
Unfortunately, taking the 3/2 ratio of the fifth to the fourth power, and
then shifting down to the starting octave, we find 81/64, slightly different
from 5/4 : (81/64) / (5/4) = 81/80 This "difference" (more exactly,
this ratio
different from 1) is known as the "syntonic comma".
The idea of 1/4 comma meantone is to cheat slightly on the fifths, that is
to lower them by 1/4 of this comma, so that, after 4 fifths, you get the
just third (with the cost of slightly narrow fifths).
It's that simple, though there would be other things to be said (for example
why it is called *mean*tone).
Bradley Lehman
> Hi all...
>
> Some years ago, after listening to a CD recording done by Elaine
> Thornburgh, on a splendid 1690 Grimaldi graf-replica harpsichord( which was
> built in 1982 by John Phillips) I noted his tunings for these recordings
> were listed as "quartercomma meantone" ( still don't know what that
> is...lol)
See below....
"His" tunings? Phillips' and/or Grimaldi's? Once a keyboard
instrument is out of the workshop and in the hands of a player, the
tuning of it has nothing to do with the builder's preferences or
design, unless it's an instrument that has more than 12 keys in an
octave.
>
> In a effort to learn what this was or meant, at the time, I wrote to
> performer/lecturer Igor Kipnis to see perhaps if he could shed some light on
> this. Mainly I had hoped to learn something more about the matter of baroque
> temperments and why they seemed so diverse.
>
> Mr. Kipnis replied within a couple of days. And his email stated "there is
> just too much information on this question, for a single email to provide
> you with"
Indeed there is. In quarter-comma meantone, all the correctly-spelled
major thirds (i.e. those that aren't written as diminished fourths)
are tuned as pure 5/4 ratios; and there's a lot more to it than that,
additionally. The necessary mathematical background to this is
explained very well in Easley Blackwood's book _The Structure of
Recognizable Diatonic Tunings_; and a well-written but necessarily
brief history of temperaments is the "Temperaments" article by Mark
Lindley, in _New Grove_.
Bradley Lehman