Werckmeister (1698)

Hi Tunas! Following up on Paul Poletti's discussions of what we could even
call Werckmeister VII tuning (unless I missed one along the way). I have
deduced its identity using a translation by Ellen J. Archambault from her PhD
dissertation at Florida State University's School of Music in 1999. Let me
hear your thoughts. Johnny
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Another Werckmeister publication that contained important tuning information
came in the form of a 1698 essay entitled “Short Lesson and Addition, how
one can tune and temper well a clavier.” It was added to “Essential
Annotations and Rules Concerning the Proper Realization of the Basso Continuo or
Thorough-Bass” (Die nothwendigsten Ammerckungen und Regeln, wie der Bassus
continuus oder General-Bass wohl könne tractiret warden). Werckmeister directed this
amendment towards beginners in tacet recognition that organs will always
need to be tuned by trained professionals. Werckmeister once again attempted to
aid the more naïve readers in the actual tuning of a harpsichord.
We might consider calling this newly introduced tuning Werckmeister (1698),
especially if we consider calling Werckmeister III tuning, “Werckmeister
(1681)” as it was the first well temperament introduced by the author, the other
being an older, Trost family tuning. This new 1698 tuning was not included
on the published copper-plate monochord, and it was distinguished from its
predecessors for being easier to tune, and without having to split commas.
Essentially, it is simpler language for getting started.
In following the Werckmeister’s directions, it is possible to make some
basic assumptions as to what constitutes Werckmeister 1698. Since Werckmeister
rails against the “horrible” 696 cent fifth of quarter comma meantone as “
lame,” and admittedly, four keys in Werckmeister III tuning have the same
lameness, the direction given this time is to detune a pure fifth “a little bit
lower,” I will take to mean a 698 cent fifth. This is the same fifth as in
sixth sixth comma meantone. It is likely a nod by Werckmeister to the realities
on the ground. It provides a reasonable alternative to the straight
meantone. The audience for this new tuning is would not be expected to understand
the intricacies to tune any other way. Besides, they would need the odder
intervals for improvisation that Buxtehude, Werckmeister, and Bach needed. They
might not rally around depicting gloomy sentiments.
Werckmeister’s instruction for the fifth on the note B-natural to be “low
very subtly” is taken by me as a 700 cent fifth, the same size as in
conventional equal temperament. Two cents, or a schisma, is the discrete tool that
best depicts what is otherwise a very general suggestion to get people going in
tuning without too much undue pain, providing some small insurance that they
will achieve a listenable success. A further direction, “almost purely” is
taken as a 701 cent fifth, mathematically almost a full single cent flat in
comparing the G-sharp to its tonic D-sharp fifth. For the fifths that are to
be tuned “a little high,” I chose 704 cents, a schisma higher pure fifth.
Werckmeister treats the final F to C fifth as a flexible buffer zone, leaving
open the possibility for most any size fifth. My numbers gave a one cent
sharp fourth at 499 cents, which works out quite well. The eventual scale, in
comparison with the primary tuning of Musicalische Temperatur (1691), or
Werckmeister III tuning, demonstrates they sound much alike with no more than six
cents difference, and on only one note, A. The other distances are much
less.
Werckmeister Tuning(1698)
C C# D Eb E F
F# G G# A Bb B
0 88 196 293 392 499
590 698 789 894 997 1092
Werckmeister Tuning (1681)
C C# D Eb E F
F# G G# A Bb B

0 90 192 294 390 498
588 696 792 888 996 1092
However, comparing Werckmeister’s 1698 tuning to the cents figures of the
increasingly practicable sixth comma meantone movement may indicate that
Werckmeister was a pioneer in that direction as well. The sixth comma fifth, major
second, major third, and major sixth in the scale are core to Werckmeister
1698. This means they have the same notes in common on C, D, E, F (because
Werckmeister left this as a flexible buffer zone), G, and A. The biggest
discrepancy is the minor third of C, where Werckmeister chose to be 10 cents lower
than sixth comma meantone. Werckmeister (1698) relished the need to be
moodier at times since he was an active improviser readily called upon to express
different sentiments. C-sharp, F-sharp, and B-natural are each within 2
cents of the other, G-sharp is 5 cents apart, and B-flats are within 7 cents of
the other.
Werckmeister Tuning (1698)
C C# D Eb E F
F# G G# A Bb B
0 88 196 293 392 499
590 698 789 894 997 1092
Sixth Comma Meantone (1681)
C C# D Eb E F
F# G G# A Bb B

0 86 196 306 392 502
588 698 784 894 1004 1090

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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Hi Tunas! Following up on Paul Poletti's discussions of what we
could even
> call Werckmeister VII tuning (unless I missed one along the way).
I have
> deduced its identity using a translation by Ellen J. Archambault
from her PhD
> dissertation at Florida State University's School of Music in 1999.
Let me
> hear your thoughts. Johnny

Paul Poletti gave a fine written analysis of that 1698 harpsichord
temperament at least four or five years ago, allotting it a whole page
of commentary in his "T4D.pdf" (available from his web site). That
is, he deduced its identity -- or its range of possibilities for the
spread of its downtown naturals -- a long time ago already.

Brad Lehman

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Hi Tunas! Following up on Paul Poletti's discussions of what we
could even
> call Werckmeister VII tuning (unless I missed one along the way).

I wouldn't. If anything other than what it is -Werckmeister's continuo
temperament- I would call it "Werckmeister's Ordinaire".

> I have
> deduced its identity using a translation by Ellen J. Archambault
from her PhD
> dissertation at Florida State University's School of Music in 1999.
Let me
> hear your thoughts. Johnny

My first thought is, if you want to "deduce" it's structure, why don't
you just sit down and tune it according to Werckmeister's quite clear
instructions, rather than relying on some modern mislead
interpretation? Doing so will in fact demonstrate precisely how
mislead said interpretation is.

Failing that, you can always download the spreadsheet I made which
allows one to tweak things around without straying off the fairly
narrow though by no means inflexible path W. described:

http://polettipiano.com/Media/Werckmeister1698.xls

(BTW, just noticed this link was broken, now it's fixed again)
>
------------------------------------------------------------------------------
> -------------------------------------------------
> This new 1698 tuning was not included
> on the published copper-plate monochord, and it was distinguished
from its
> predecessors for being easier to tune, and without having to split
commas.

This is absolute Bullkrap! The continuo temperament is far more
difficult to tune than WIII!! Any idiot can tune WIII with one ear
tied behind his back; one starts with a series of pure fifths from C
left around the circle to E, which pushes the comma into the zone C-E.
Using these two notes as extremes, you then simply temper the four
fifths more or less the same, and once you've got 'em, you retune
A-E-B as pure, pushing the last tempered fifth out to B-F#. Done.
Finshed!! In Continuo there are many more fifths which must be
tempered all by exactly the same amount (at the very least, C<->G#),
plus a couple fifths which must be tempered WIDER than pure. Depending
on the mix you end up with, there are either NO pure fifths or one to
two (MAX!) pure fifths. You only find out if it all works when you get
to the very end of the whole process, and if it doesn't, you have to
go back through a whole chain, adjusting and hoping yo get it right
the second time. How is this easier?!

> Essentially, it is simpler language for getting started.

Bollocks!

> In following the Werckmeister’s directions, it is possible to
make some
> basic assumptions as to what constitutes Werckmeister 1698. Since
Werckmeister
> rails against the “horrible” 696 cent fifth of quarter comma
meantone as “
> lame,” and admittedly, four keys in Werckmeister III tuning have
the same
> lameness, the direction given this time is to detune a pure fifth
“a little bit
> lower,” I will take to mean a 698 cent fifth. This is the same
fifth as in
> sixth sixth comma meantone.

1/6 Syn. comma is but one of the tempered fifths that will work. It
could be anything from about 1/5 Syntonic to 1/7 Pythagorean and still
work.

> It is likely a nod by Werckmeister to the realities
> on the ground.

It is much more likely to be a nod by this modern author to the
current fad for thinking that 1/6th comma meantone is some sort of
default late 17th/early 18th century temperament.

That much said, I will say that the WHOLE APPROACH "is likely a nod by
Werckmeister to the realities on the ground", i.e. the widespread use
of modified meantones.

> It provides a reasonable alternative to the straight
> meantone.

Indeed it does, as does any of the other modified meantones, including
the French "ordinaire".

> The audience for this new tuning is would not be expected to
understand
> the intricacies to tune any other way.

I don't understand this sentence. None of Werkcmeister's 3
rationalized circulating temperaments given in the 1691 copperplate
are "intricate", neither in structure nor application. You can both
remember their structures and set them by ear precisely far more
rapidly than you can the Continuo temperament. If anything, they are
considerably simpler.

> Besides, they would need the odder
> intervals for improvisation that Buxtehude, Werckmeister, and Bach
needed.

I suppose they is a typo for "they woundN'T need". Bullkrap again. It
is quite easy to push the Contiunuo scheme to a point where it is
actually BETTER than WWIII in providing distant keys; in it's mildest
version, it only has ONE Pythagorean major third, whereas WIII has
three. Ugh!

> They
> might not rally around depicting gloomy sentiments.

Cute but pointless.

> The eventual scale, in
> comparison with the primary tuning of Musicalische Temperatur
(1691), or
> Werckmeister III tuning, demonstrates they sound much alike with no
more than six
> cents difference, and on only one note, A. The other distances are
much
> less.

This is where this author shows her real ignorance. One does not
compare historical temperaments by how much the individual notes of
their "scales" differ, but rather by how much the major and minor
TRIADS differ. WIII and any stripe of W Continuo do NOT sound "much
alike". One wonders if she even actually compared how they SOUND, or
did she just play with some numbers?

> However, comparing Werckmeister’s 1698 tuning to the cents figures

Here we go again!

> of the
> increasingly practicable sixth comma meantone movement

Here we go with THAT myth again!

> may indicate that
> Werckmeister was a pioneer in that direction as well.

Oh. First he was giving a nod to what was "happening on the ground",
now he is a "pioneer". She sounds like Hillary Clinton trying to
justify why the Michigan primary was "fair" and should be counted.

> The sixth comma fifth, major
> second, major third, and major sixth in the scale are core to
Werckmeister
> 1698.

How do we know that? Pure invention on her part. Could just as well be
1/5th or 1/7th.

What follows is naught but empty speculation about Werckmeister's
desires and practices based on HER single interpretation.

I think it is shocking that in relatively recent times somebody can
submit a doctoral thesis on Historical Temperaments and compare them
in the outmoded and uniformation manner of Barbour's 1950's methodology.

Me 'umble opinee.

Ciao,

P

(Is the discussion text Johnny gave his own, or Archambault's? I would
guess the former.)

What is the 'identity' of a tuning for which no mathematical
specification was ever given? Seems to me we need a slightly wider
vocabulary than Barbour's beloved cent tables, to avoid losing sight
of practical / historical reality - by which no two people may have
produced the same intervals, to say nothing of the musical effects,
starting from the one set of instructions.

We need to distinguish two historical creatures. One is an instruction
for tuning a keyboard, telling the tuner what needs to be done in what
order, and what to listen for and how one can know if it is correct.
I.e. a bearing plan.
The second is a mathematical specification of a set of ratios, which
may be approximated by frequency ratios of actual keyboard notes under
certain conditions. I will call this a temperament scheme.

The two are quite distinct and different concepts and widely different
in their musical applicability and the historical information they
give us.

A bearing plan need not have any mathematical content at all in terms
of commas, divisions thereof, integer ratios, etc. etc. The
specification of the quality of intervals and chords may be simply
that they are tolerable, or good, or as flat as the ear can support,
or as pure as possible. These are all more or less subjective
indications that can be directly evaluated by ear.

On the other hand, such a bearing plan *must* give indications that
are adequate to produce a musically satisfactory result. That is, at
the end of the process the tuner must have been able to adjust all the
musically useful intervals and chords so that they sound good enough.
The musical judgement and experience of the tuner, particularly the
ability to compare intervals having different amounts of temperament,
may be directly called upon.

Of course, this doesn't mean that the result could just be anything.
The structure of the bearing plan and the remarks that go along with
it almost always allow us to deduce what kind of result was expected.

By contrast, a mathematical temperament scheme may or may not be
applicable directly by ear to a keyboard instrument. It depends
strongly on the prior expertise that the tuner brings to the task of
translating mathematical entities into real sounding notes.
Whether or not the result of such a process sounds good depends first,
on whether the author of the scheme knew what he was doing; second, on
whether the tuner is technically competent to produce a mathematically
good approximation; third, on whether the inevitable *deviations* of
the actual notes from the mathematical scheme are handled attentively
and with musical judgement - or just at random.

For instance it is quite difficult to tune an *exact* pure fifth by
ear on some instruments - eg pipe organ. A small deviation from the
'correct' mathematical ratio can exist, even if the interval sounds
pure. Now 'Werckmeister III' uses no fewer than 8 pure fifths. What
then happens if the tuner's technique is such that it leaves them a
tiny bit wide? Say +1 cent error on just half of them... that leaves
the 4 flat fifths to take up 28 cents of temperament in total - each
of which is then virtually 1/3 syntonic comma flat! Almost nothing
will sound good with such a tuning, but Werckmeister's text gives no
inkling of how this could happen, or what to do about it.
On the other hand if one sets the bearings slightly differently and
allows for the 'pure' fifths to err on the narrow side, while the
'flat' ones are more like 1/4 syntonic, the result will be much more
tolerable.

This illustrates the major weakness of the mathematically specified
temperament schemes. They don't tell the tuner what to do if things go
a bit awry, which is inevitable in practice; how to prevent, diagnose
and correct, or allow for, or even take advantage of, imprecision in
setting the temperament. In short, they say almost nothing about the
art and craft of tuning.

If good tuners did (try to) use such schemes, they still had to apply
a set of practical procedures to make the result sound good - which
were not mentioned in the sources where the schemes are.

The subjective bearing plan, by contrast, honestly and directly allows
for tuners to hear and choose for themselves what interval qualities
are musically more or less acceptable. It does not refer to an ideal
of setting up mathematical entities on an instrument; rather, it
privileges the musical experience and judgment of the practitioner.

The essential step in such plans is balancing one tempered interval
against another.
If it's meantone, this can mean balancing the flatness of F-C-G
against the sharpness of A-D-G. Or the sharpness of C-E against the
flatness of C-G-D-A-E. (And not necessarily an equal balance!)
If it's modified meantone or ordinaire, it can mean balancing E-G#
against Eb-Ab, or against F-Ab, or B-D# against Eb-G, or Eb-Bb against
Bb-F.
If it's a circulating 'good' temperament, it can mean starting off by
balancing F-A against A-C# and C#-F... etc. etc.

None of this requires any calculations of fractions of commas or
worrying about whether the circle is going to be closed at the end.
But it does require that the tuner checks the right thirds, fifths,
major and minor triads at the appropriate moments throughout the
process. This is the practical way to prevent mistakes and surprises:
check early and check often. For example in the Werckmeister
instructions one has to check C-E before proceeding further. Once one
gets to G# one can try constructing a chord of F minor to see how if
it is tolerable. One step further it is implied to check that Eb has
been sharpened such that both B-D# and Eb-G are tolerable. Then the Bb
must be sharpened so that Bb-D is OK. By this point it is basically
impossible for the circle not to be closable. Simply because one has
already listened to all the musically used thirds and fifths in doing
the temperament, the result will *by construction* always sound good
enough in musical application.

In short: the musical 'identity' of a historical tuning consists not
of a table of comma fractions or cent values regardless of the
competence or taste of their execution.
The tuning's identity is given by the questions: What intervals or
chords must the tuner listen to? In which order? What acoustic or
musical qualities or conditions must they be adjusted to fulfil?

Any supposed historical tuning that consists only of a row of
comma-fractions to be applied to fifths and fourths, or of monochord
values, without any indication of a bearing plan or of checks, cannot
contain any useful information about how keyboards were actually
tuned. Because no good tuning can be set just by tempering fifths and
fourths found the circle, or by monochord.
~~~T~~~