Moroney on Unequal Temperament
Francis
Harpsichordist Davitt Moroney performing Bach's Well Tempered Clavier, the
Art of Fugue and the Musical Offering. In his CD-notes to the Well-Tempered
Clavier, Moroney writes:
"Owing to the coincidence between Werckmeister's description and the title
of Bach's great work, it has recently become fashionable to claim that Bach
intended 'Das Wohltemperierte Clavier' to be played on a harpsichord tuned
not in equal temperament, but rather in Werckmeister's system or some other
comparable kind of unequal temperament."
He goes on:
"However, the hypothesis that Bach might have composed pieces in all the
keys precisely because he wished to exploit the tonal characteristics of an
unequal temperament simply does not stand up to serious reasoning. This is
shown by the fact that he actually transposed some pieces from simple keys
(those most in tune with equal temperament) to difficult ones (those less in
tune): we know from some early versions that one piece originally in C major
ended up in C sharp major, while another went from F major to A flat major.
Such transpositions argue quite conclusively against Bach having composed
with particular key-characteristics in mind since these transpositions
alter, even destroy, any key-character which he might have exploited in an
unequal temperament."
So it appears yet another HIP-dogma is built on sand!
Regards
Charles
Inotmark
>Such transpositions argue quite conclusively against Bach having composed
>with particular key-characteristics in mind since these transpositions
>alter, even destroy, any key-character which he might have exploited in an
>unequal temperament."
>
>So it appears yet another HIP-dogma is built on sand!
this is not a sound argument.
it is not uncommon to work out a piece in one key and then transpose it into
another, and this can be seen in pieces where equal temperament was definitely
not intended. one example can be seen in Puccini's turandot. the finale to the
first act was sent to the publisher written in E minor and Puccini wrote a
letter to them specifically stating that he had forgot to tell them to
transpose that finale down to Eb minor. The fact that this section was always
intended to be in Eb minor can be seen from the key structure of the opera and
the characters as a whole. (See an article on this subject by Petty and Tuttle
in British Postgraduate Musicology Online appearing in February).
That equal temperament would not have been the norm in Bach's time is evident
from instrumental tutors written throughout the 19th and early 20th centuries,
which emphasize the use of small half steps (e.g. nicholson for the flute and
flesch for the violin).
Both Leopold Mozart and Quantz in their respective violin and flute methods
emphasize the nature of the large half-step between leading tone and tonic.
since mozart's treatise was written after bach died, we may reasonably question
the assumptions on which you base your conclusion on two counts:
1) Unequal temperament was recommended by later composers and pedagogues up
into the 20th century. (it can be heard on recordings by very famous
performers, including Heifetz, Oistrakh, etc.)
2) Transposition was a purely compositional practice unrelated to temperament.
Ian Kemmish
>"Owing to the coincidence between Werckmeister's description and the title
>of Bach's great work, it has recently become fashionable to claim that Bach
>intended 'Das Wohltemperierte Clavier' to be played on a harpsichord tuned
>not in equal temperament, but rather in Werckmeister's system or some other
>comparable kind of unequal temperament."
Whereas prior to `recently', it was merely the impracticality and lack of
musicality of equal temperament on the harpsichord which led to such opinions.
See Mersenne's comments and reporting of others opinions, writing 50 years
before Bach's birth, and therefore completely independent of Werckmeister.
While it may be true that Pythagoras rejected ET for purely mystical reasons,
in the Renaissance and Baroque, the reasons were purely pragmatic.
>unequal temperament simply does not stand up to serious reasoning. This is
>shown by the fact that he actually transposed some pieces from simple keys
>(those most in tune with equal temperament) to difficult ones (those less in
>tune): we know from some early versions that one piece originally in C major
>ended up in C sharp major, while another went from F major to A flat major.
That observation only stands up if, firstly, we know with absolute certainty
the tuning system which Bach used (which presupposes that there was only one
during his entire career, which supposition is obviously false), and secondly,
can demonstrate that the transpositions which occurred (discounting those
which had to do with tessitura and/or fingering) have a completely random
effect on the emotional impact of the pieces.
Such a statistical analysis has already been done, and far from favoring modern
equal temperament, led to the development of John Barnes' temperament.
And of course it's simply not true to assert that in any of the great
temperaments of the past C major is '`most in tune with equal temperament'; as
the object of these temperaments is to *remove* the discordant triads of ET,
and the commoner keys are the one in which you strive for the *best* triads,
not the worst! This is an astonishingly ignorant assertion to make.
>So it appears yet another HIP-dogma is built on sand!
That depends on who you think is trying to be hip here, people contiuning a
centuries old tradition, or someone trying to find a gimmick with which to flog
CDs in a crowded marketplace;-)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Ian Kemmish 18 Durham Close, Biggleswade, Beds SG18 8HZ, UK
i...@jawssytems.com Tel: +44 1767 601 361
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Behind every successful organisation stands one person who knows the secret
of how to keep the managers away from anything truly important.
Michael
[snip]
>1) Unequal temperament was recommended by later composers and pedagogues up
>into the 20th century. (it can be heard on recordings by very famous
>performers, including Heifetz, Oistrakh, etc.)
[snip]
To and through the 20th century, if we're talking about non-keyboard
instruments. I'm a flutist, and some of my teachers taught me just
intonation with great emphasis (e.g. Albert Tipton); I now teach this
to my students. We play intervals and listen to get the correct
difference tone. When you get the correct difference tone, the
interval is perfectly in tune, i.e. justly tuned (NOT tempered).
Michael
To reply by email, please eliminate "NOSPAM" from my address. Personal messages only!
Michael Zapf
Kemmish) schreibt:
> it has recently become fashionable to claim that Bach
>>intended 'Das Wohltemperierte Clavier' to be played on a harpsichord tuned
>>not in equal temperament, but rather in Werckmeister's system or some other
>>comparable kind of unequal temperament
I ran into a mathematician-tuner yesterday who has won the golden tuning fork
of the German tuners' association for discovering that the 12 interwoven
squiggles on top of the WTC1 autograph front page represent Bach's well
temperament. This must be the man Moroney is referring to, because the theory
was represented last autumn in a Koethen symposium which I unfortunately could
not attend. I immediately offered him to proofread his soon-to-appear book on
the subject, and I will record a summary to this newsgroup. The discovery was
printed in a 1998 (!) mathematical yearbook over here, and musicological
circles seem to have overlooked it. Such squiggles were a common memory aid for
organists and organ builders, and Werckmeister describes and uses them himself
in his treatise.
Michael
Deutsche Clavichord Societaet
http://members.aol.com/dcsdd/
Rob Potharst
"Michael Zapf" <clavi...@aol.comnojunk> schreef in bericht
news:20010118035548...@nso-fk.aol.com...
> I ran into a mathematician-tuner yesterday who has won the golden tuning
fork
> of the German tuners' association for discovering that the 12 interwoven
> squiggles on top of the WTC1 autograph front page represent Bach's well
> temperament. This must be the man Moroney is referring to, because the
theory
> was represented last autumn in a Koethen symposium which I unfortunately
could
> not attend. I immediately offered him to proofread his soon-to-appear book
on
> the subject, and I will record a summary to this newsgroup. The discovery
was
> printed in a 1998 (!) mathematical yearbook over here, and musicological
> circles seem to have overlooked it. Such squiggles were a common memory
aid for
> organists and organ builders, and Werckmeister describes and uses them
himself
> in his treatise.
> Michael
I just looked up the squiggles in the New Bach Reader, and I found them on
page
96!! Could you give details about the mathematical yearbook?
But I wonder how such squiggles can be a memory aid for anyone...
Cheers, Rob
Michael Zapf
schreibt:
> Could you give details about the mathematical yearbook?
I will have the article by next week.
>But I wonder how such squiggles can be a memory aid for anyone...
>
If you look at them closely, they have little loops which go
Start-1-1-1-0-0-0-2-2-2-2-2-End
Now once you know that Bach tuned in fifths, and if you assume the "Start" and
"End" to be "A", and knowing you have to flatten the fifths, you only have to
ponder what the zeros and ones and twos means. Bear with me, I will be back on
this.
Francis
> Such a statistical analysis has already been done, and far
> from favoring modern equal temperament, led to the development
> of John Barnes' temperament.
Interesting! I once selected a few random pieces from the WTC to compare
Werkmeister III, Kellner and Barnes' temperaments. At the time I felt that
Barnes' gave best results in the sense of best reflecting the mood (Affekt?)
of each piece. But perhaps this is just because Barnes' is the "closest" to
Equal Temperament and adds the least colouration? Personally, I like to keep
my piano in Werkmeister III (its been tuned that way for years) and use
Barnes and Equal Temperament with electronic keyboards.
I heard mention of "statistical analysis" in relation to the Barnes
temperament. Could you perhaps say a little more about John Barnes'
rationale, and especially the statistical method?
Regards,
Charles
Rob Potharst
You wrote:
>
> I will have the article by next week.
Please, send me (or the bach ng) the name and issue of the journal or
proceedings to find the article.
I am very interested in this. (I am a mathematician and Bach-lover).
> If you look at them closely, they have little loops which go
> Start-1-1-1-0-0-0-2-2-2-2-2-End
> Now once you know that Bach tuned in fifths, and if you assume the "Start"
and
> "End" to be "A", and knowing you have to flatten the fifths, you only have
to
> ponder what the zeros and ones and twos means. Bear with me, I will be
back on
> this.
So it is some kind of encoding of the tuning...
It makes me all very curious to get to know the details of all this...
Cheers,
Rob
"Michael Zapf" <clavi...@aol.comnojunk> schreef in bericht
news:20010118113435...@nso-bh.aol.com...
Michael Zapf
a speech last year for which he earned the golden tuning fork of the German
tuners' association. The abstracts of the speech are published in "Deutsche
Mathematiker Vereinigung Jahrestagung 1999", Mainz 1999. He discovered that the
squiggles on top of the autograph page of the WTC 1 of 1722 conform to a
memory-aid-for-tunings practice which also Werckmeister discusses in his
treatise. That is the good news, and all my instincts tell me the man is right.
I have created a folder in both the harpsichord and clavichord e-groups files
area where people who have no acces to a print of the autograph front page can
have a look at them.
The bad news is that imo Mr. Sparschuh's deductions are unrealistic. He thinks
that the little loops within the squiggles which read
Start-1-1-1-0-0-0-2-2-2-2-2-End mean
1. octaves, i.e. 0 for the small octave, 1 for the octave beginning with middle
C, and that
2. the beginning of the sequence of fiths is A.
I will spare you the details of a long discussion which we had publicly. Tuning
the second octave makes no sense, and no known Baroque tuning instruction works
that way, and outside of one medieval source and the Praetorius all the
practicians started with C, which was the beginning of the old meantone tuning
In my opinion, the squiggles mean seconds per beat, and you have to start from
C, and you have to tune the small octave like all preceding tutors would, i.e.
the oactave-down-fifth-up range of C0 to F#1. Thus, you will have equal-beating
fifths (1 bps) C-G-D-A, pure fifths A-E-B-F#, and equal-beating fifths (0.5
bps) F#-C#-G#-Eb-Bb-F. The residual fifth F-C will beat 0.9 (say 1).
I have also put the spreadsheet into the files area of both the e-groups.
The resulting temperament has memories of Werckmeister (from C to b the basic
design is identical, i.e. three flat fifths and two pure ones), but the
narrowing of the Werckmeister's B-F# fifth is spread amongst other fifths. This
improves the B-tonalities which Werckmeister "neglects", at a slight expense of
Dmaj in particular. This is just a sketchy and draft opinion of mine, but I
wanted to get this out into the open right away.
Francis
news:20010124124334...@nso-bd.aol.com...
> ... That is the good news, and all my instincts tell me the man is right.
The squiggles certainly add little to the look of the cover page! But
perhaps one of Bach's children was responsible?
> The bad news is that imo Mr. Sparschuh's deductions are unrealistic. He
thinks
> that the little loops within the squiggles which read
> Start-1-1-1-0-0-0-2-2-2-2-2-End mean
> 1. octaves, i.e. 0 for the small octave, 1 for the octave beginning with
middle
> C, and that
> 2. the beginning of the sequence of fiths is A.
What on earth is a "small octave"?
> In my opinion, the squiggles mean seconds per beat, and you have to start
from
> C, and you have to tune the small octave like all preceding tutors would,
i.e.
> the oactave-down-fifth-up range of C0 to F#1. Thus, you will have
equal-beating
> fifths (1 bps) C-G-D-A, pure fifths A-E-B-F#, and equal-beating fifths
(0.5
> bps) F#-C#-G#-Eb-Bb-F. The residual fifth F-C will beat 0.9 (say 1).
I must say when I read your initial article, I found the idea of starting
from "A" a bit strange. I also assumed the squigles had something to do with
beats and seconds. Presumably, beats per second doesn't work, while seconds
per beat is plausible. But before rushing off in this direction, do we know
if was it actually possible to measure a second in Bach's day? What
equipment (e.g. a clock) would Bach need and would it be available to him?
In another discussion group, there was a long debate about tempo (beats per
minute) and one of the issues was whether or not Bach would have a device
that could measure a minute accurately. Now measusing a second is another
problem.
> I have also put the spreadsheet into the files area of both the e-groups.
> The resulting temperament has memories of Werckmeister (from C to b the
basic
> design is identical, i.e. three flat fifths and two pure ones), but the
> narrowing of the Werckmeister's B-F# fifth is spread amongst other fifths.
This
> improves the B-tonalities which Werckmeister "neglects", at a slight
expense of
> Dmaj in particular. This is just a sketchy and draft opinion of mine, but
I
> wanted to get this out into the open right away.
> Michael
What are the formulas you use for relating "seconds per beat" to frequency?
Regards
Charles
Unknown
is that the majority of composers liked the way in which dissonant fifths,
thirds and the like sounded; for this reason, meantone remained popular
across Europe until well into the 1800s (especially in England), despite
equal temperament being known from as early as the 1540s. John Barnes was
quite wrong to try to look at the intervals and work backwards, especially
when one considers that the majority of WTC I were transpositions of already
extant works. The simple answer is that like harpsichordists today, Bach had
his own unequal temperament that he preferred. Probably this was based on
1/6 comma meantone (e.g. Silbermann), but if there was an interval did sound
terrible, the tuning would have been re-tuned. This is the whole idea behind
tempering.
J
"Francis" <Fra...@datacomm.ch> wrote in message
news:3a67...@news.datacomm.ch...
Michael Zapf
schreibt:
>What on earth is a "small octave"?
>
Please, bear with me, I am German, and my English has its quirks. In German,
the octave below middle c is called the "kleine" (small) octave.
On the whole subject, we have been having an intense discussion in the
clavichord e-groups - I will be back here, with whatever century's thinking
(what is so 21st in my presentation?).
They knew what beating intervals were (Italian vox humanas, German
"Flötenschwebungen" are beating organ registers with identical pipes which are
mistuned against each other), they knew what a second was (hell, even I know
without looking at the watch, it is slightly slower than my pulse, and for
practical tuning purposes this is quite sufficient), so measuring beats per
second was no problem - again, for practical, not theoretical matters. Mersenne
specifically mentions that the tempered fifth (strictly: the d-a fifth) should
beat once per second.