Yahoo Tuning Groups Ultimate Backup tuning COunterpoint books...

I asked for a review of...

> > Counterpoint : The Polyphonic Vocal Style of the Sixteenth Century
> > by Knud Jeppesen, Glen Haydon (Translator), Knud Jeppeson
>

...and saw (delayed by weeks, though the Yahoo change has hosed me more
than once) the following comments

> >
> > The Jeppeson book is a standard counterpoint text.
> >
> >
> > The *real* classic for this study, however, is _Gradus ad Parnassum_
> > by Johann Joseph Fux. It was published in Vienna in, IIRC, 1725.
> >
>
> > The book available almost anywhere in paperback, in the English
> > translation by Alfred Mann. ISBN # 0393002772.
> >
>
> Of course, Monz is right here... and the paperback is CONSIDERABLY
> less expensive than the Jeppesen, which Amazon.com lists as $89.00.
>

Hmmm, I saw the Jeppeson listed for $12. Also, I have Schoenbergs
counterpoint book, which I feel is sufficient for 'species tonal
18-th century' type counterpoint. I'm specifically interested in modal
and pre-tonal counterpoint. To that end, another book I saw is

Modal and Tonal Counterpoint : From Josquin to Stravinsky
by Harold Owen

which is supposed to be a brief history of everything (counterpoint
wise). Do any opinions exist on this one?

Bob Valentine

> ___________ ______ ______ _
> Joseph Pehrson
>

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

I am a newcomer to Western music. On enquiry, the librarian of a
local library recommended "Counterpoint" by Dr. Walter Piston.

Any advice on where to begin?

Haresh.

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> I asked for a review of...
>
> > > Counterpoint : The Polyphonic Vocal Style of the Sixteenth
Century
> > > by Knud Jeppesen, Glen Haydon (Translator), Knud Jeppeson
> >
>
> ...and saw (delayed by weeks, though the Yahoo change has hosed me
more
> than once) the following comments
>
> > >
> > > The Jeppeson book is a standard counterpoint text.
> > >
> > >
> > > The *real* classic for this study, however, is _Gradus ad
Parnassum_
> > > by Johann Joseph Fux. It was published in Vienna in, IIRC,
1725.
> > >
> >
> > > The book available almost anywhere in paperback, in the English
> > > translation by Alfred Mann. ISBN # 0393002772.
> > >
> >
> > Of course, Monz is right here... and the paperback is
CONSIDERABLY
> > less expensive than the Jeppesen, which Amazon.com lists as
$89.00.
> >
>
> Hmmm, I saw the Jeppeson listed for $12. Also, I have Schoenbergs
> counterpoint book, which I feel is sufficient for 'species tonal
> 18-th century' type counterpoint. I'm specifically interested in
modal
> and pre-tonal counterpoint. To that end, another book I saw is
>
> Modal and Tonal Counterpoint : From Josquin to Stravinsky
> by Harold Owen
>
> which is supposed to be a brief history of everything (counterpoint
> wise). Do any opinions exist on this one?
>
> Bob Valentine
>
> > ___________ ______ ______ _
> > Joseph Pehrson
> >

🔗Rosati <dante.interport@rcn.com>

I would recommend:

Counterpoint in Composition
by Felix Salzer and Carl Schachter
McGraw-Hill

not only teaches species counterpoint, but shows how it is used by Bach,
Beethoven, et al.

> -----Original Message-----
> From: Haresh BAKSHI [mailto:hareshbakshi@hotmail.com]
> Sent: Tuesday, March 27, 2001 7:56 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: COunterpoint books...
>
>
> I am a newcomer to Western music. On enquiry, the librarian of a
> local library recommended "Counterpoint" by Dr. Walter Piston.
>
> Any advice on where to begin?
>
> Haresh.
>
>
>
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
> >
> > I asked for a review of...
> >
> > > > Counterpoint : The Polyphonic Vocal Style of the Sixteenth
> Century
> > > > by Knud Jeppesen, Glen Haydon (Translator), Knud Jeppeson
> > >
> >
> > ...and saw (delayed by weeks, though the Yahoo change has hosed me
> more
> > than once) the following comments
> >
> > > >
> > > > The Jeppeson book is a standard counterpoint text.
> > > >
> > > >
> > > > The *real* classic for this study, however, is _Gradus ad
> Parnassum_
> > > > by Johann Joseph Fux. It was published in Vienna in, IIRC,
> 1725.
> > > >
> > >
> > > > The book available almost anywhere in paperback, in the English
> > > > translation by Alfred Mann. ISBN # 0393002772.
> > > >
> > >
> > > Of course, Monz is right here... and the paperback is
> CONSIDERABLY
> > > less expensive than the Jeppesen, which Amazon.com lists as
> $89.00.
> > >
> >
> > Hmmm, I saw the Jeppeson listed for $12. Also, I have Schoenbergs
> > counterpoint book, which I feel is sufficient for 'species tonal
> > 18-th century' type counterpoint. I'm specifically interested in
> modal
> > and pre-tonal counterpoint. To that end, another book I saw is
> >
> > Modal and Tonal Counterpoint : From Josquin to Stravinsky
> > by Harold Owen
> >
> > which is supposed to be a brief history of everything (counterpoint
> > wise). Do any opinions exist on this one?
> >
> > Bob Valentine
> >
> > > ___________ ______ ______ _
> > > Joseph Pehrson
> > >
>
>
>
> You do not need web access to participate. You may subscribe through
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>
>
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>
>

🔗jpehrson@rcn.com

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

/tuning/topicId_20459.html#20459

> >
> > Of course, Monz is right here... and the paperback is CONSIDERABLY
> > less expensive than the Jeppesen, which Amazon.com lists as
$89.00.
> >
>
> Hmmm, I saw the Jeppeson listed for $12.

Hi Bob!

You are right... I just saw that, too. It seems rather peculiar that
the harcover version is $89 and the paperback is $12... it must be
"abidged" somewhat. Anyway... I'm going to order it...

Also, I have Schoenbergs
> counterpoint book, which I feel is sufficient for 'species tonal
> 18-th century' type counterpoint.

I've always had trouble with Schoenberg as far as "introductory" books
on music subjects are concerned. His theoretical work is always
fascinating, but much too "ideosyncratic" in my view as an
introduction or overview of any subject...

And for Haresh...

I really wouldn't recommend Piston. I have his counterpoint book and
I've never read it. There are some nice examples, but the book is
quite short and not really presented systematically. I am also not a
great fan of his harmony text, although it was "forced" down our
throats in music school. His ORCHESTRATION book is quite fine,
though... the best of his efforts, and, of course, much of his own
music is fine.

I, personally would recommend the two paperbacks... the Fux, which
should be in the library of every serious student of Western music,
and the Jeppesen... which comes highly recommended...

_______ _____ ______ __
Joseph Pehrson

🔗Graham Breed <graham@microtonal.co.uk>

Joseph Pehrson wrote:

> > > Of course, Monz is right here... and the paperback is
CONSIDERABLY
> > > less expensive than the Jeppesen, which Amazon.com lists as
> $89.00.
> > >
> >
> > Hmmm, I saw the Jeppeson listed for $12.
>
> Hi Bob!
>
> You are right... I just saw that, too. It seems rather peculiar
that
> the harcover version is $89 and the paperback is $12... it must be
> "abidged" somewhat. Anyway... I'm going to order it...

I see it slightly cheaper again, and no hardcover. Are you including
postage, or are Amazon playing with selective pricing again? And it
comes under "entertainment" which is good, because I like entertaining
books.

Ships within 24 hours as well, whereas amazon.co.uk won't promise less
than a month. Same as with Fux and Vicentino. Grumble grumble.

> I really wouldn't recommend Piston. I have his counterpoint book
and
> I've never read it. There are some nice examples, but the book is
> quite short and not really presented systematically. I am also not
a
> great fan of his harmony text, although it was "forced" down our
> throats in music school. His ORCHESTRATION book is quite fine,
> though... the best of his efforts, and, of course, much of his own
> music is fine.

I did see that (but no other counterpoint texts) in a few shops in
London village. It seems everybody reads it, but nobody likes it.

> I, personally would recommend the two paperbacks... the Fux, which
> should be in the library of every serious student of Western music,
> and the Jeppesen... which comes highly recommended...

Fux is in two volumes at amazon.co.uk. How interesting are Fugues?

Not being a serious student, I might make do with Vicentino's "Ancient
Music Adapted" and Palestrina's "Stabat Mater".

Graham

🔗jpehrson@rcn.com

--- In tuning@y..., "Graham Breed" <graham@m...> wrote:

/tuning/topicId_20459.html#20465

> I see it slightly cheaper again, and no hardcover. Are you
including postage, or are Amazon playing with selective pricing
again?
And it
> comes under "entertainment" which is good, because I like
entertaining
> books.
>

Counterpoint is, of course, always good for a "yuk.."

Here's what I get:

Counterpoint, The Polyphon Vocal Style
Of The Sixteenth Century (Music Book
Index)
by Knud Jeppesen (Library Binding -
January 1939)
Special Order
Our Price: $89.00

And the "paperback":

Counterpoint : The Polyphonic Vocal Style of the Sixteenth
Century
by Knud Jeppesen, et al (Paperback - April 1992)
Average Customer Review:
Usually ships in 24 hours

List Price: $12.95
Our Price: $10.36
You Save: $2.59 (20%)

So, the hardcover is $89.00 and the paperback is $10.36. This means
that the cover costs $78.64...

Must be nice and hard... good use to whack loquacious and
inattentive
concert goers...

_________ _____ _______
Joseph Pehrson

🔗Kraig Grady <kraiggrady@anaphoria.com>

I have always liked the 20 page
Modal Counterpoint
in the style of the 16th century
outline by Ernst Krenek
Boosey and Hawkes 1959

very composer friendly and oriented

jpehrson@rcn.com wrote:

> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> /tuning/topicId_20459.html#20459
>
> > >
> > > Of course, Monz is right here... and the paperback is CONSIDERABLY
> > > less expensive than the Jeppesen, which Amazon.com lists as
> $89.00.
> > >
> >
> > Hmmm, I saw the Jeppeson listed for $12.
>
> Hi Bob!
>
> You are right... I just saw that, too. It seems rather peculiar that
> the harcover version is $89 and the paperback is $12... it must be
> "abidged" somewhat. Anyway... I'm going to order it...
>
> Also, I have Schoenbergs
> > counterpoint book, which I feel is sufficient for 'species tonal
> > 18-th century' type counterpoint.
>
> I've always had trouble with Schoenberg as far as "introductory" books
> on music subjects are concerned. His theoretical work is always
> fascinating, but much too "ideosyncratic" in my view as an
> introduction or overview of any subject...
>
> And for Haresh...
>
> I really wouldn't recommend Piston. I have his counterpoint book and
> I've never read it. There are some nice examples, but the book is
> quite short and not really presented systematically. I am also not a
> great fan of his harmony text, although it was "forced" down our
> throats in music school. His ORCHESTRATION book is quite fine,
> though... the best of his efforts, and, of course, much of his own
> music is fine.
>
> I, personally would recommend the two paperbacks... the Fux, which
> should be in the library of every serious student of Western music,
> and the Jeppesen... which comes highly recommended...
>
> _______ _____ ______ __
> Joseph Pehrson
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗jpehrson@rcn.com

🔗monz <MONZ@JUNO.COM>

🔗Graham Breed <graham@microtonal.co.uk>

Joseph Pehrson wrote:

> Counterpoint, The Polyphon Vocal Style
> Of The Sixteenth Century (Music Book
> Index)
> by Knud Jeppesen (Library Binding -
> January 1939)
> Special Order
> Our Price: $89.00

That says "Library Binding" not "Hardcover". There may be a
difference. Yes, it isn't an Americanism, "Ancient Music Adapted" is
called "Hardcover" on amazon.com as well. Also happens to cost a bit
more than I paid, even after you take account of the exchange rate.

> And the "paperback":
>
> 5.
>
> Counterpoint : The Polyphonic Vocal Style of the Sixteenth
> Century
> by Knud Jeppesen, et al (Paperback - April 1992)
> Average Customer Review:
> Usually ships in 24 hours
>
> List Price: $12.95
> Our Price: $10.36
> You Save: $2.59 (20%)
>
>
> So, the hardcover is $89.00 and the paperback is $10.36. This means
> that the cover costs $78.64...

Worse than that, you get 18 extra pages in the paperback!

The two books don't seem to be equivalent at all. The library bound
volume is dated 1939, and from "Reprint Services Corp" whereas the
paperback is by "Dover Pubns". The latter is translated by Glen
Haydon whereas the former doesn't seem to have a translator. So if
you really want a reprint of the original edition, you'll have to pay
$89. Probably we'd all be happy with the modern translation.

I find it hard to believe that the two most expensive books are also
the best sellers, but that's what Amazon seem to be telling me.

I wonder why I couldn't see them both yesterday. Perhaps because the
titles are subtly different.

> Must be nice and hard... good use to whack loquacious and
> inattentive
> concert goers...

At least such usage shouldn't damage the book. Then again, a hard
cover may make a loud noise as it collides with the concert goer's
skull. Probably a heavy softback would be the thing.

Graham

🔗jpehrson@rcn.com

--- In tuning@y..., "monz" <MONZ@J...> wrote:

/tuning/topicId_20459.html#20482

>
> Since there have been so many different opinions on
> which counterpoint books to recommend, I'll just emphasize
> that the Fux book really is great.
>
> If you work your way thru it seriously, one step at a time
> (which is exactly what the original title "Gradus ad Parnassum"
> indicates you should do), you'll have a mastery of Fux's
> 18th Century view of Palestrinian counterpoint.
>
> Supplement that with Kneppeson's book, AND STUDY RENAISSANCE
> SCORES, and that should be all you really need.
>
>

Just one more comment on the "Point Counter Point" discussion (famous
Aldous Huxley novel!)

[And Dan Stearns, I don't want to hear about "counterpoint-
smounterpoint again... Actually "smounterpoint" sounds pretty
interesting... perhaps a new piece title...]

I had forgotten that, while the PISTON counterpoint book is kind of
"self evident" in most of the examples in the first part of the book,
the chapter on INVERTIBLE counterpoint is invaluble. I noticed that
I had scribbled all over that, since I had to master that technique
in order to pass my prelims...

And, again, the Fux book is actually ENTERTAINING. It consists of a
dialog between Josephus (named after ME, of course) the perennial
student, and Aloys (from Karamazov??) the teacher, and there are many
humorous "interactions." The writing is practically as entertaining
as Berlioz... I had forgotten about it. The examples are also quite
clear and systematic... And, it's "cheap" in paperback... probably a
good addition to any composer/theorist's library, if it isn't there
already...

_______ ____ ______ _____
Joseph Pehrson

🔗monz <monz@attglobal.net>

hello all,

we've discussed Fux's _Gradus ad Parnassum_ before, for example:

/tuning/topicId_20459.html#20488

but i don't recall ever finding out for sure what tuning
Fux had in mind when he wrote this work. can anyone help?

unfortunately, Mann's popular English translation of part of
_Gradus_, _The Study of Counterpoint_, doesn't say a thing
about tuning other than to demonstrate the different types
of proportions (arithmetic, geometric, and harmonic), but
i suspect that earlier portions of the text which were not
included in Mann's version *do* discuss tuning.

the Thesarum Musicarum Latinarum only goes as far as
the 17th century, and _Gradus_ was published in 1725, so
i can't get the full Latin text there.

Fux's categorization of intervals, with their equivalents
one 8ve greater:

consonant perfect: unison, 5th, 8ve;
consonant imperfect: 3rds and 6ths;
dissonant: 2nds, 4th, diminished-5th, tritone, 7ths

seems to me to imply 5-limit JI or meantone.

Fux's method was based on his 18th-century interpretation of
the style of Palestrina, which would arguably indicate 5-limit JI
or some form of adaptive-JI based on that. but at that late
date (1725), he very well could have had meantone or even
a well-temperament or 12edo in mind.

-monz

🔗Leonardo Perretti <dombedos@tiscalinet.it>

🔗monz <monz@attglobal.net>

🔗Leonardo Perretti <dombedos@tiscalinet.it>

Hi all,

I have got Fux's book today, and gave it a quick look.
Tuning related issues are discussed in the Book 1, which wasn't translated by Mann (according to the table of contents I saw on Amazon site); I don't know what Mann reported in his introduction.

In Book 1, Fux goes through the math fundamentals of music, starting with the definition of Music and sound (Chap. I-II), then he defines the usual classification of proportions (Chap. III-VIII). The Chap. IX, X and XI are devoted to the three kinds of division (arithmetic, harmonic, and geometric), then he describes the operations on ratios (Chap. XII-XIV), and the intervals (XV-XXI), that are resumed in a table, while the Chap. XXII describes the compound intervals. Finally, the Last (XXIII) Chapter is devoted to "Today's system of music", where he describes the Diatonic and Chromatic scales and the intervals and consonances.
Fux does not describe any kind of temperament with mathematical accuracy; in Chap. XXII and XXIII he makes some comments about the scale in use at his times, from which it clearly appears that 12edo or some sort of circular system was currently in use (no wonder), while organs were still tuned in meantone or the like, perhaps because they carried the tuning they were given when they had been built. Fux states he does not condemn the current usage ("because in everything one must adapt to his times"), but he warns composers to use only the diatonic scale when the organ is required for accompaniment.
He appears to have no robust knowledge of the math concepts underlying the temperaments, according to the way he describes "today's system of music". In addition, his evaluation of the consonance of intervals appears to be based rather on their traditional use and their artistic function within the piece, then on the actual consonance, as intended in the physical sense.

I will translate the relevant parts regarding tuning, and post them later.

Regards
Leonardo

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Leonardo Perretti <dombedos@t...>

/tuning/topicId_20459.html#46837

wrote:
> Hi all,
>
> I have got Fux's book today, and gave it a quick look.
> Tuning related issues are discussed in the Book 1, which wasn't
> translated by Mann (according to the table of contents I saw on
> Amazon site); I don't know what Mann reported in his introduction.
>
> In Book 1, Fux goes through the math fundamentals of music,
starting
> with the definition of Music and sound (Chap. I-II), then he
defines
> the usual classification of proportions (Chap. III-VIII). The Chap.
> IX, X and XI are devoted to the three kinds of division
(arithmetic,
> harmonic, and geometric), then he describes the operations on
ratios
> (Chap. XII-XIV), and the intervals (XV-XXI), that are resumed in a
> table, while the Chap. XXII describes the compound intervals.
> Finally, the Last (XXIII) Chapter is devoted to "Today's system of
> music", where he describes the Diatonic and Chromatic scales and
the
> intervals and consonances.
> Fux does not describe any kind of temperament with mathematical
> accuracy; in Chap. XXII and XXIII he makes some comments about the
> scale in use at his times, from which it clearly appears that 12edo
> or some sort of circular system was currently in use (no wonder),
> while organs were still tuned in meantone or the like, perhaps
> because they carried the tuning they were given when they had been
> built. Fux states he does not condemn the current usage ("because
in
> everything one must adapt to his times"), but he warns composers to
> use only the diatonic scale when the organ is required for
> accompaniment.
> He appears to have no robust knowledge of the math concepts
> underlying the temperaments, according to the way he describes
> "today's system of music". In addition, his evaluation of the
> consonance of intervals appears to be based rather on their
> traditional use and their artistic function within the piece, then
on
> the actual consonance, as intended in the physical sense.
>
> I will translate the relevant parts regarding tuning, and post them
later.
>
> Regards
> Leonardo

***Well, this is pretty amazing. I had no idea there were additional
parts to Fux "Gradus ad Parnassum..." I guess I'm seeing now this
statement by translator Alfred Mann: "The complete text of the
_Gradus_ begins with an explanation of the nature of intervals and
scales and ends with comments on various stylistic trends of Fux's
time..."

To bad the *complete* work isn't the one in general circulation...

Joseph Pehrson

🔗monz <monz@attglobal.net>

hi Leonardo,

thanks for working on this! Fux explicitly states that his
counterpoint method is based on Palestrina's usage, and i
belive that Fux primarily had in mind vocal composition,
which would indicate JI or adaptive-JI. but if his methods
are meant to be applicable to instruments as well, then
another tuning (meantone or well-temperament/12edo) would
be likely as well.

unfortunately, his classification of consonances and
dissonances is not necessarily the same across all of
these different tuning systems, hence my interest in
determining what he had most in mind.

Mann's English translation includes only very small portions
of Book 1, dealing with consonant/dissonant intervals as
a parenthetical comment near the beginning of the main text,
and explaining the 3 different proportions in an appendix.

i very much appreciate your work on this!!

-monz

--- In tuning@yahoogroups.com, Leonardo Perretti <dombedos@t...>
wrote:
> Hi all,
>
> I have got Fux's book today, and gave it a quick look.
> Tuning related issues are discussed in the Book 1, which wasn't
> translated by Mann (according to the table of contents I saw on
> Amazon site); I don't know what Mann reported in his introduction.
>
> <snip>

🔗Leonardo Perretti <dombedos@tiscalinet.it>

hi all,

as I promised, here is the translation of some parts of Fux's treatise, in which he speaks about tuning. They are the second half of the Chapter 22, and the beginning of the Chap. 23, that he calls "The Last Chapter", of the Book One.
I have tried to translate as literally as possible; I hope it is clear enough.

begin translation (the first part of the Chap.22 talks about compound intervals)
------------------------------------------------------------

.......
So, who is the man who doesn't know how, because of the new system introduced in today's music, the ancient one was changed, and those three Greek genera, Diatonic, Chromatic, and Enharmonic, with their tetrachords, are decayed? from which it derived, that many intervals in the music, consisting of their own rational proportions, rather are founded on ear's judgment, than on that of the reason. And what? , maybe someone will oppose, So nowadays' music, lacking of sure, never fallacious principles, and just relying on the misleading judgment of the ear, will be undeserving the name of science. To which I reply, that this does not compromise the dignity, and the infallibility of our Music at all. As if to the one, and to the other of the major and minor tones, to the one, and the other, of the major and minor semitones, and to some intervals likewise minor, to each of them in particular one still poses its own clef, which many expert Musicians, both ancient and modern, showed with their various kinds of clefs, which they invented, as of today one would surely have all of the usual intervals, chiefly according to the division of Ptolemy, consisting in their rational proportions. Having then known, that the use of different clefs is full of difficulties, and still desiring to put a remedy to the scarcity of intervals, being applied to the amplification [multiplication] of them, and to gain the imperfect consonances, they tried to divide the tone, and the semitone in two equal parts. But since they discovered, that this could not be made by the numbers only, they called the judgment of the ear for help, taking away from one interval a certain, almost imperceptible quantity, and adding it to the other, by which operation, having put away the difficulty of the position of the clefs, they managed in such a way that our Music, from the shortage of intervals, as escaping from the prison, today can widely run through the vast field of modulation: but the Composers, and the Organists should maintain themselves within the limits of the reason, so that because of ignorance, and avidity for transporting, going out of the right path, they wouldn't go too licentiously wandering through the chromatic intervals, especially in the organ. Should that happen, it could hardly be avoided, that instead of a pleasant, and agreeable concert, a highly harsh and unpleasant howl wouldn't come to hurt the ear. Then, I have no doubt, that all that has been added to the Music, in utility and splendor, and how much praiseworthy the first Author is (whose glory is rightly ascribed to the ancient philosopher Aristoxenus) is well known to whoever has even a light dye of Music. Although those things, that I will say below, rather appear to belong to the second Book, that is to the practice, nevertheless, in order to begin the following Book immediately with the lessons to be prescribed, I judged it more opportune to put them at the end of this one.

THE LAST CHAPTER

About today's system of Music.

I informed above how, taken away the disparity of the tones, and semitones, the three Greek genera were abolished, and it will be useful to have it remembered: because from it, of necessity, a different system has been introduced, and those three genera were narrowed to two, that is the Diatonic, and the Chromatic, which substituted the Greek ones, and which now I will present in the following express range:

[three rows of pentagram follow, showing the diatonic scale, three octaves from C to c'' (C to e in the tenor clef, f to e' in the soprano clef, f' to c'' in the violin clef), and the chromatic scale, the same compass and notation. The chromatic notes are all represented as sharps of the preceding diatonic note]

Although the insatiable cupidity of the man has been satisfied, always ready to the variety, and novelty around the use of the one, and the other of those genera, the Composers have been used to employ them untidily in their Compositions, so that nowadays the mixed genus is in use, which (because in everything one must adapt to his times) I don't condemn, nevertheless the Composers be warned, that in this mixed genus, in the a cappella compositions that are used to be sung, they don't use the Organ; otherwise they can be sure, that they will never reach the craved aim. As nothing else can serve to this style, then the pure Diatonic genus: and, based on the long practice I have for the long use, and experience, I wish that everybody had this very important warning to hearth. Now, assumed the equality of the Tones, and Semitones, let us go to the intervals, that are in use today, beginning with
About the Unison
........

-----------------------------------------------------------------

(a description of the intervals follows) end translation

Some comments.
By the flowery language of his times, Fux appears to state two main things, as far as I have understood it:
first, the equal or at least circular tuning was well known and fairly widely spread at his time, and,
second, the organs were still tuned by some sort of unequal temperament. It cannot be understood here whether organs were tuned that way because they still carried their original tuning, as possibly they were built before the diffusion of ET, or they were still built and tuned with some sort of non-circulating temperament at Fux's times.

Further comments?

Regards
Leonardo

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz <monz@attglobal.net>

Hi Joe and Leonardo,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, Leonardo Perretti <dombedos@t...>
>
> /tuning/topicId_20459.html#47107
> >
> > Further comments?
> >
> > Regards
> > Leonardo
>
>
> ***Thanks so much for this research.

yes, and a BIG thank you from me too, Leonardo!

> My only comment is my regret that "popular" texts, such
> as the Fux _Gradus ad Parnassum_ aren't reprinted in
> their *entire* rather than selecting what the editors
> feel is the "important" stuff, tuning, obviously, not
> being regarded in that category...
>
> J. Pehrson

i would say that i agree with you 100%, Joe ... except
that for me the emotional response is turned up a few
notches, from "regret" to outright anger. it's offensive
to me that translators and editors take it upon themselves
to decide for "posterity" what is important and what is not.

if their purpose is to bring an old but still very useful
piece of scholarship to a new audience, they should be
presenting the entire work and not their own idea of what's
valuable from it.

veering a bit off topic, i was angered in the same way
when Antony Beaumont translated *portions* of Alma Mahler's
diary, whereas the German editon was published complete.

needless to say, i found English translations of Alma's
diary to be a goldmine of information in my Mahler research.

unfortunately, it probably would also be a goldmine of
information in my Schoenberg research too ... except that
there is precious little in the published version which
discusses Schoenberg. but this book chronicles the period
in Alma's life when she fell in love with Zemlinsky (who
became Schoenberg's brother-in-law when S. married his sister),
and i have little doubt that Alma wrote much more about
S. than what appears in the English version.

OK, back to tuning ... if anyone wants to follow up on
this, change the subject line and send it to metatuning ...

-monz

🔗Aaron K. Johnson <akj@rcn.com>

On Sunday 21 September 2003 12:13 pm, Leonardo Perretti wrote:

> Some comments.
> By the flowery language of his times, Fux appears to state two main
> things, as far as I have understood it:
> first, the equal or at least circular tuning was well known and
> fairly widely spread at his time,

Surely this was true --- Fux's lifespan was 1660-1741. Neidhardt's 'IV' tuning
is ET as we know it, published in 1724. Not to mention that fretted
instruments ike gambas are scaled to ET.

> and, second, the organs were still tuned by some sort of unequal
> temperament. It cannot be understood here whether organs were tuned
> that way because they still carried their original tuning, as
> possibly they were built before the diffusion of ET, or they were
> still built and tuned with some sort of non-circulating temperament
> at Fux's times.

Yes, organs are in a class by themselves for practical reasons, when
considering tuning and temperament...We know that organs in particular had a
tradition of being tuned to meantone, and because a large pipe organ had so
many ranks, a well-temperament like Werkmeister would work well to shorten
the labor of switching from meantone to well-temperament, because only a few
notes would be altered in the bearing from meantone; indeed, Werkmeister's
temperament was a practical tuning for organs, not a baroque-wide tuning for
all instruments, as is commonly misuunderstood, and not even considered a
great tuning by Werkmeister himself--again, he was being practical.

(BTW, Kirnbergers' tuning was also considered of low-quality by and large by
the musicians of the time-and it is. It's 20th-century early-music success is
partly due to encyclopedia entries, etc., and the Korg electronic tuners.
Tunings similar to Neidhardts were considered better alternatives by
contemporary commentators, and rough variations of this were probably the
basic idea of where the 18th century harpsichord/pianoforte/clavichord
mindset was......)

We forget that the harpsichord is what we are really talking about when we
thinkabout these tunings....strings bend freely, and like singers use a
quasi-just intonation when playing by themselves; winds are scaled to a
temperament, but flexible; and fretted instruments have been theoretically ET
for a long time....that is, fixed fretted instruments.

-Aaron.

🔗Aaron K. Johnson <akj@rcn.com>

Wanted to add one more thing about Neidhardt--his "small city" tuning is
beautiful, and its qualites bar far outshine Kirnberger, Werkmeister, and the
ubiquitous Valotti/Young...try it out -- here is the bearing plan:

First, we tackle tempering the thirds to handle getting rid of the diesis.....

C-E, E beating slighty sharp, about 2+ beats per second in the tenor range.
(C below middle C)

E-G# and G#-C divide the remainder of the diesis comma between them, with g#-c
beating slightly faster (rougher).

Now to tempering the fifths..........

Divide the C-E(slightly sharp) between C-G-D-A-E a la meantone.....

Now we do the decending fifths C-F-Bb pure, then Bb-Eb-G# equally dividing the
comma (don't touch the G# you already set)

Do the same for the next four fifths: G#-C#-F# pure, F#-B-E equally dividing
the comma (don't touch the E you already set)

Now play some WTC, and you'll love this tuning!!! It's beats the pants off any
other Baroque tuning I've heard for its beauty and ease of remembering the
bearing plan.....it sounds great for Mozart and Beethoven and Chopin, too!!!

Best,
Aaron.

🔗monz <monz@attglobal.net>

hi Aaron,

thanks for posting this! i found it very interesting.
specific (and very detailed) comments:

(use "Expand Messages" format to view tables correctly if
viewing on the Yahoo website)

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akj@r...> wrote:
>
> Wanted to add one more thing about Neidhardt--his
>"small city" tuning is beautiful, and its qualites bar
> far outshine Kirnberger, Werkmeister, and the ubiquitous
> Valotti/Young...try it out -- here is the bearing plan:
>
> First, we tackle tempering the thirds to handle getting
> rid of the diesis.....
>
> C-E, E beating slighty sharp, about 2+ beats per second
> in the tenor range. (C below middle C)

i believe that the "C" in the "tenor range" is indeed
"middle-C". that's the "C" which lies right near the center
of the tenor clef, which is what anyone singing a
tenor part would have been reading in Niedhardt's day.

also, i went thru the method on a spreadsheet and found
that starting from "middle-C" gives a tuning which is very
close to 12edo, whereas starting from the C an 8ve lower
right off the bat gives a Pythagorean 81:64 "E"! i don't
think that's what Niedhardt wanted.

so, i started with "middle-C", which i defined as 256 Hz
(i.e., 2^8 Hz, my own personal favorite tuning for "C").

the 5/4 above this is 320 Hz, so i just kept things simple
and let "E" beat 2 times per second, setting it to 322 Hz.
that's ~397.1002537 cents.

> E-G# and G#-C divide the remainder of the diesis comma
> between them, with g#-c beating slightly faster (rougher).

the best division i could find here to both give a perfect
1200-cent 8ve for the next higher "C" and to have "G#-C"
beating slightly faster, was to make "E-G#" beat at 3.5 times
per second and "G#-C" at 4.5 times.

the 5/4 above "E" 322 Hz is G# 402.5 Hz; sharpening the "G#"
to make it beat 3.5 times per second gives "G#" 406 Hz, which
is ~798.4031006 cents.

the 5/4 above "G#" 406 Hz is B# 507.5 Hz; sharpening the "B#"
to make it beat 4.5 times per second and make it the perfect
8ve of "C" gives "C" 512 Hz (exactly 1200 cents).

> Now to tempering the fifths..........
>
> Divide the C-E(slightly sharp) between C-G-D-A-E
> a la meantone.....

adding 2 8ves to the "E" and then dividing it by 4 gives
a "5th" size of ~699.2750634 cents. this results in the
chain:

note ~cents
C 0
G 699.2750634
D 198.5501269
A 897.8251903
E 397.1002537

> Now we do the decending fifths C-F-Bb pure,

note ~cents
C 0
F 498.0449991
Bb 996.0899983

> then Bb-Eb-G# equally dividing the comma (don't touch
> the G# you already set)

the interval between "Bb" and "G#" is ~197.6868976 cents.
adding 1200 cents to that and dividing by 2 gives a "5th"
of ~698.8434488 cents, so:

note ~cents
Bb 996.0899983
Eb 297.2465494
G# 798.4031006

> Do the same for the next four fifths: G#-C#-F# pure,

note ~cents
G# 798.4031006
C# 96.44809976
F# 594.4930989

> F#-B-E equally dividing the comma (don't touch the E you
> already set)

the interval between "F#" and "E" is ~197.3928452 cents.
adding 1200 cents to that and dividing by 2 gives a "5th"
of ~698.6964226 cents, so:

note ~cents
F# 594.4930989
B 1095.796676
E 397.1002537

that completes the tuning.

> Now play some WTC, and you'll love this tuning!!! It's
> beats the pants off any other Baroque tuning I've heard
> for its beauty and ease of remembering the bearing plan.....
> it sounds great for Mozart and Beethoven and Chopin, too!!!

essentially what i got here is a chain of "5ths" in which
four are tuned to a "pure" 3:2 ratio, four are very close
to 1/8-comma meantone, and four are near 1/7-comma meantone:

G#/Ab
> pure 3:2
C#
> pure 3:2
F#
> 1/7-comma meantone
B
> 1/7-comma meantone
E
> 1/8-comma meantone
A
> 1/8-comma meantone
D
> 1/8-comma meantone
G
> 1/8-comma meantone
C
> pure 3:2
F
> pure 3:2
Bb
> 1/7-comma meantone
Eb
> 1/7-comma meantone
Ab/G#

here is the scale i derived, in descending order:

note ~cents
B 1095.796676
Bb 996.0899983
A 897.8251903
G# 798.4031006
G 699.2750634
F# 594.4930989
F 498.0449991
E 397.1002537
Eb 297.2465494
D 198.5501269
C# 96.44809976
C 0

-monz

🔗monz <monz@attglobal.net>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <akj@r...> wrote:
> >
> > Wanted to add one more thing about Neidhardt--his
> >"small city" tuning is beautiful, and its qualites bar
> > far outshine Kirnberger, Werkmeister, and the ubiquitous
> > Valotti/Young...try it out -- here is the bearing plan:

Neidhardt changed his recommendations over various publications,
so that the tuning he proposed for "small city" in 1724
became the one for "big city" in 1732, and the one proposed
for "village" in 1724 became the one for "small city" in 1732.

> <huge snip>
>
> [me, monz:]
> essentially what i got here is a chain of "5ths" in which
> four are tuned to a "pure" 3:2 ratio, four are very close
> to 1/8-comma meantone, and four are near 1/7-comma meantone:
>
>
> G#/Ab
> > pure 3:2
> C#
> > pure 3:2
> F#
> > 1/7-comma meantone
> B
> > 1/7-comma meantone
> E
> > 1/8-comma meantone
> A
> > 1/8-comma meantone
> D
> > 1/8-comma meantone
> G
> > 1/8-comma meantone
> C
> > pure 3:2
> F
> > pure 3:2
> Bb
> > 1/7-comma meantone
> Eb
> > 1/7-comma meantone
> Ab/G#

i found the following in Paul Poletti's excellent paper:
http://ourworld.compuserve.com/homepages/paulpoletti/T4D.PDF

(it's at almost exactly halfway thru the paper, with a
nifty "radar" graph too)

of the two conflicting "small city" tunings, this
is the one which matches the tuning method given
by Aaron and followed by me.

Neidhardt 1724 "Village", 1732 "Small City"

G#/Ab
> pure 3:2
C#
> pure 3:2
F#
> 3:2 / 1/12-Pythagorean comma
B
> 3:2 / 1/12-Pythagorean comma
E
> 3:2 / 1/6-Pythagorean comma
A
> 3:2 / 1/6-Pythagorean comma
D
> 3:2 / 1/6-Pythagorean comma
G
> 3:2 / 1/6-Pythagorean comma
C
> pure 3:2
F
> pure 3:2
Bb
> 3:2 / 1/12-Pythagorean comma
Eb
> 3:2 / 1/12-Pythagorean commane
Ab/G#

so everywhere that i had determined 1/8-comma "5ths",
they should be 1/6-comma, and everywhere that i had
determined 1/7-comma, they should be 1/12-comma.

actually, i had suspected that Neidhardt was dealing
primarily with 1/6-comma, and that was what i originally
put into the table in my post ... but then i adjusted
the fraction-of-a-comma amounts to agree better with
the cents values i had obtained from following the bearing
method given by Aaron.

also note that i was thinking in terms of tempering by
fractions of a *syntonic* comma, but Neidhardt used
fractions of a Pythagorean comma. of course, a "5th"
narrowed by 1/12-Pythagorean-comma is our familiar old
12edo "5th".

the crucial variable in following the bearing method
is in determining just how sharp to tune the "G#" --
everything else depends on that. had i plugged in the
right relationships for the beating of C:E, E:G#, and
G#:C, i would have ended up exactly with Neidhardt's tuning.

> here is the scale i derived, in descending order:
>
> note ~cents
> B 1095.796676
> Bb 996.0899983
> A 897.8251903
> G# 798.4031006
> G 699.2750634
> F# 594.4930989
> F 498.0449991
> E 397.1002537
> Eb 297.2465494
> D 198.5501269
> C# 96.44809976
> C 0

here is the actual scale according to Neidhardt's published
fraction-of-a-comma values:

C 1200
B 1092.179997
Bb 996.0899983
A 894.1349974
G# 796.0899983
G 698.0449991
F# 592.1799965
F 498.0449991
E 392.1799965
Eb 296.0899983
D 196.0899983
C# 94.1349974
C 0

-monz

🔗Afmmjr@aol.com

🔗Aaron K. Johnson <akj@rcn.com>

On Sunday 21 September 2003 08:46 pm, Afmmjr@aol.com wrote:
> In a message dated 9/21/03 3:16:09 PM Eastern Daylight Time, akj@rcn.com
>
> writes:
> > ; indeed, Werkmeister's
> > temperament was a practical tuning for organs, not a baroque-wide tuning
> > for
> >
> > all instruments, as is commonly misuunderstood, and not even considered a
> > great tuning by Werkmeister himself--again, he was being practical.
>
> I must disagree with these statements. There is nothing to conclude that
> either Werckmeister's tuning was inappropriate for non-organ keyboards, or
> that it was widespread in Thuringia, the Harz region, and the Saxon
> regions, let alone Prussian and other regions of Germany.

I don't mean to say that it is 'inappropriate', just that Neidhardts tunings
were widely regarded by contemporaries as a sort of high point in
well-temperment, and the early music scene is, in general, largely stuck in
Valotti/Young, Kirnberger, and Werckmeister land....

> While not
> baroque-wide throughout all of Europe, it may be more widespread than
> commonly appreciated.

And for all we know, it could be less so....there are no real strong, hard
truths about this subject.

> Werckmeister III is easily applied to all
> instruments.

What does that prove? So is meantone, Kirnberger, and...more to the point, so
is the Neidhardt tuning I described, and it has more modulation ability
without the harsher thirds of Werck III, and the era was starting to really
like that kind of thing. To these ears, Neidhardts' tuning IS more beautiful
than Werckmeisters', but then were not arguing facts. To see what I mean,
tune your keyboard instrument to it and listen to it. The rest is useless
sophistry. It's all about delighting the ear, no? To the past generations as
much as to us....why wouldn't they use a more 'rich tuning' like Neidhardt
when they had a choice (i.e., they weren't on an organ)

> And Werckmeister was instrumental (pardon the pun) in
> bringing other instruments into the church to make music with the organ.

I'm not sure I follow what you mean.....

> Also, what makes you think Werckmeister self-deprecates his circular
> chromatic temperaments? I haven't seen anything of this kind anywhere and
> I am on the look out.
>

I was mistakenly giving the wrong impression. Not some much
'self-deprication', but a healthy sense of what works in a given practical
setting, and what is best, even if it's not 'your own tuning'....plus, there
was a common practice tuning that defied specific mathematical description,
i.e., one used one's ears and 'guess-timated'. In other words, no one 'owned'
the 'ordinary temperament' of the 18th century, because its description was
not as mathematically precise as we now are. They didn't use cents. They used
their ears! Just like no good piano tuner ever tunes every piano the same
EXACT way. See the quote below....

from http://ourworld.compuserve.com/homepages/paulpoletti/T4D.PDF .....

"......Proof that Werckmeister would have used a completely different type of
temperament for harpsichords, especially when used in a chamber music
setting, is given by his brief description of a harpsichord (Clavier)
tempering scheme in his 1698 treatise on realizing figured bass.
Werckmeister's description is somewhat imprecise, but there can be little
doubt that it describes yet another "meantone modification". He probably
started from a 1/5 or 1/6th Syntonic comma Meantone, but then deviated from
the basic logic by adjusting G#, D#, and Bb toward their enharmonic
equivalents, allowing them to be tolerable if not perfect when used for both
harmonic functions. This is essentially the same sort of "bending" of the
basic meantone logic found in the temperaments of Rameau, Couperin, and
Schlick, and is probably much more representative of common practice among
harpsichordists in the late-17th and early-18th centuries than is a primitive
"economy-class" 1/4 Pythagorean comma well-temperament like "Werckmeister
III". Although this description was perhaps the first published unequal
temperament description of the entire modern "original instrument" movement
(being summarized in 1931 by F. T. Arnold), much like its French
counterparts, it has been completely ignored by modern keyboard players...."

I hope that clarifies what I was driving at.....yes, this is very based on
subjective opinion, and I could be wrong, but we'll never know. I guess I
just find Paul Poletti's reasoning compelling and accurate. It jives with my
experience as a musician and with all the musicians I've known.

Best,
Aaron.

--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

🔗Aaron K. Johnson <akj@rcn.com>

🔗monz <monz@attglobal.net>

hi Aaron,

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akj@r...> wrote:

> On Sunday 21 September 2003 06:23 pm, monz wrote:
> >
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > Neidhardt changed his recommendations over various publications,
> > so that the tuning he proposed for "small city" in 1724
> > became the one for "big city" in 1732, and the one proposed
> > for "village" in 1724 became the one for "small city" in 1732.
> >
>
> monz and all tuning friends,
>
> Isn't that weird? What makes a tuning appropriate, exactly,
> for a given place? It seems like such a foreign sentiment to me,
> I guess.

i didn't have my copy of Barbour's _Tuning and Temperament_
handy, so i was searching the 'net for specific data on
Neidhardt's tunings. (aside from the source works themselves,
Barbour is one of the best compendia of data on tunings.)

during one of the searches, probably in Poletti's paper,
i read something about Neidhardt's feelings that the
relatively unsophisticated (for lack of a better way of
putting it) instruments, playing technique, and repertoire
of village musicians was best suited to a circulating
temperament leaning more towards JI and meantone; those
for a small city leaned closer to 12edo; those for a
big city even more towards 12edo; and those for the court
still more so.

... but his ideas about it changed between the 1723 and 1734
publications, and the later trend shifted all situations
by one degree to what Poletti and i see as favoring meantone/JI.
it's interesting to look at a tabulation of these changes:

( ... on the Yahoo web interface, use "Expand Messages" mode
to view properly ... "pure" means the 3:2 ratio, and fractions
refer to tempering of a "5th" by fraction-of-a-Pythagorean-comma;
thus "1/12" means 12edo.)

1724 1732

village E:B, F#:C#, G#:Eb:Bb, F:C pure (5)
D:A:E 1/4 (2)
G:D 1/6 (1)
C:G, B:F#, C#:G#, Bb:F 1/12 (4)

village small city F#:C#:G#, Bb:F:C pure (4)
C:G:D:A:E 1/6 (4)
E:B:F#, G#:Eb:Bb 1/12 (4)

small city big city E:B, G#:Eb:Bb pure (3)
C:G:D:A 1/6 (3)
A:E, B:F#:C#:G#, Bb:F:C 1/12 (6)

big city E:B, G#:Eb, F:C pure (3)
C:G 1/4 (1)
D:A 1/6 (1)
G:D, A:E, B:F#:C#:G#, Eb:Bb:F 1/12 (7)

> Thanks for all the interesting mathematical details, Monz!

you're welcome. ... something i seem to really love ...

> BTW, tommorow, I'm going to check you[r] findings against what
> Scala says about Neidhardt. But I gotta get to beddy-bye now...

i'm sure that Scala has good data on Neidhardt. Manuel
(Scala's author) is very familiar with quite a lot of the
tuning literature, especially works published in the
Netherlands (home of Diapason Press, which published
new editions of two of Neidhardt's tuning treatises).

-monz

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Afmmjr@aol.com

Hi Aaron,

> I don't mean to say that it is 'inappropriate', just that Neidhardts
> tunings
> were widely regarded by contemporaries as a sort of high point in
> well-temperment, and the early music scene is, in general, largely stuck in
> Valotti/Young, Kirnberger, and Werckmeister land....

I agree that the early music scene has not spent much time with Neidhardt's
tunings. His influence is also still yet undetermined.

> >Werckmeister III is easily applied to all
> >instruments.
>
> What does that prove? So is meantone, Kirnberger, and...more to the point,
> so
> is the Neidhardt tuning I described, and it has more modulation ability
> without the harsher thirds of Werck III, and the era was starting to really
> like that kind of thing.

I though you were saying Werckmeister III was more an "organ tuning" and I
just wanted to say that it is rather easy to perform on winds and strings, let
alone harpsichord. And it modulates just as easily as the other well
temepraments. The "harsher" thirds are not harsh at all if they are used melodically,
as was the custom through JS Bach.

To these ears, Neidhardts' tuning IS more beautiful
> than Werckmeisters', but then were not arguing facts. To see what I mean,
> tune your keyboard instrument to it and listen to it. The rest is useless
> sophistry. It's all about delighting the ear, no?

Sorry to be a curmudgeon, but my ears love Werckmeister as beautiful. Modern
ears are not the issue, though. For example, many modern ears care little
for the microtonal interals that tickle so many on this List.

To the past generations as >
> much as to us....why wouldn't they use a more 'rich tuning' like Neidhardt
> when they had a choice (i.e., they weren't on an organ)
>

There are many reasons. Inertia of a previous tuning (as Werckmeister
predates Neidhardt), different compositional choices (as melodic versus harmonic
interest), relevance to other prominent tunings (such as a significant meantone
match to a well-temperament), and ease and speed of tuning (Werckmeister is
rapid in comparison to the "paper" temperaments of Neidhardt).

> >And Werckmeister was instrumental (pardon the pun) in
> >bringing other instruments into the church to make music with the organ.
>
> I'm not sure I follow what you mean.....
>

Just that. Werckmeister made an early pitch (pardon the pun again) for
instruments to be allowed into the church to make music with the organ. It was more
usual at the time for there to be a segregation of the organ with the other
instruments.

> >Also, what makes you think Werckmeister self-deprecates his circular
> >chromatic temperaments? I haven't seen anything of this kind anywhere and
> >I am on the look out.
> >
>
> I was mistakenly giving the wrong impression. Not some much
> 'self-deprication', but a healthy sense of what works in a given practical
> setting, and what is best, even if it's not 'your own tuning'....plus, there
>
> was a common practice tuning that defied specific mathematical description,
> i.e., one used one's ears and 'guess-timated'. In other words, no one
> 'owned'
> the 'ordinary temperament' of the 18th century, because its description was
> not as mathematically precise as we now are. They didn't use cents. They
> used
> their ears!

Yes, but ears are trained. They are not given a sense of musical temperament
perfection at birth. The ears are best judges when there are specific and
exact intervals that they are measuring against, for example pure fifths and
octaves.

As you may know a young Neidhardt was in a contest in 1706 in Jena with an
elder Bach. He lost the contest of tuning the organ because the Bach tuning was
considered by all listening to be more singable. It is likely that Neidhardt
was tuning to the equal temperament he first promoted. The Bach, eldest son
of Johann Christoph Bach (Uncle to J.S.) was certainly unequal at this time
(and likely Werckmeister III in my estimation). This is a tuning duel,
essentially, and ET lost.

Neidhardt obviously thought differently after this, relegating ET to the
fourth of four temperaments. ET was for the High Court now. J.S. Bach was not,
however, Hight Court. CPE Bach was.

best,

Johnny Reinhard

🔗Aaron K. Johnson <akj@rcn.com>

Hey Johnny,

My responses are inter-mixed below....

On Monday 22 September 2003 11:36 am, Afmmjr@aol.com wrote:
> Hi Aaron,
>
> > I don't mean to say that it is 'inappropriate', just that Neidhardts
> > tunings
> > were widely regarded by contemporaries as a sort of high point in
> > well-temperment, and the early music scene is, in general, largely stuck
> > in Valotti/Young, Kirnberger, and Werckmeister land....
>
> I agree that the early music scene has not spent much time with Neidhardt's
> tunings. His influence is also still yet undetermined.
>
> > >Werckmeister III is easily applied to all
> > >instruments.
> >
> > What does that prove? So is meantone, Kirnberger, and...more to the
> > point, so
> > is the Neidhardt tuning I described, and it has more modulation ability
> > without the harsher thirds of Werck III, and the era was starting to
> > really like that kind of thing.
>
> I though you were saying Werckmeister III was more an "organ tuning" and I
> just wanted to say that it is rather easy to perform on winds and strings,
> let alone harpsichord. And it modulates just as easily as the other well
> temepraments. The "harsher" thirds are not harsh at all if they are used
> melodically, as was the custom through JS Bach.

I was wondering what you made of the quote from Paul Poletti's article, where
he talked about Werckmeisters approach to tuning the harpsichord note being
based on Werck III, but on a rough 1/6 comma meantone starting point...the
evidence is apparantly from Werckmeister's own work. Yes it's not conclusive,
but it does suggest something about the use of different tuning based on
whether it was an organ setting or not.

>
> >To these ears, Neidhardts' tuning IS more beautiful
> > than Werckmeisters', but then were not arguing facts. To see what I mean,
> > tune your keyboard instrument to it and listen to it. The rest is useless
> > sophistry. It's all about delighting the ear, no?
>
> Sorry to be a curmudgeon, but my ears love Werckmeister as beautiful.
> Modern ears are not the issue, though. For example, many modern ears care
> little for the microtonal interals that tickle so many on this List.

True enough...although I'd say that the intervals are not as much the problem
as how they are used...as a small example, I can see an audience being turned
off by 11:8 ratios when used in the low bass register as a bare dyad---then
being delighted by the same when reinforced by a full five voice 4:5:6:7:9
underneath......and rightly so!

> To the past generations as >
>
> > much as to us....why wouldn't they use a more 'rich tuning' like
> > Neidhardt when they had a choice (i.e., they weren't on an organ)
>
> There are many reasons. Inertia of a previous tuning (as Werckmeister
> predates Neidhardt), different compositional choices (as melodic versus
> harmonic interest), relevance to other prominent tunings (such as a
> significant meantone match to a well-temperament), and ease and speed of
> tuning (Werckmeister is rapid in comparison to the "paper" temperaments of
> Neidhardt).

I don't buy it. In fact, the Neidhardt tuning I described is about the same
effort as Werck III, less just fifths notwithstanding. You could, I suppose,
only advance your argument against Neidhardt IV (ET), but that was really
never what I was ever referring to....

Besides, 'inertia' and 'ease and speed' seem to have not worked against the
onslaught of ET anyway !!! If that argument held, we would still be doing 1/4
comma meantone in an ubiquitous way today.....(it would be nice for pop music
and folk music, I think, and have always thought--I've even written
progressive folk-rock tunes in meantone!)

>
> > >And Werckmeister was instrumental (pardon the pun) in
> > >bringing other instruments into the church to make music with the organ.
> >
> > I'm not sure I follow what you mean.....
>
> Just that. Werckmeister made an early pitch (pardon the pun again) for
> instruments to be allowed into the church to make music with the organ. It
> was more usual at the time for there to be a segregation of the organ with
> the other instruments.

Off-kilter humor: He probably said to the priests, "listen, I can get you more
young boys to molest if you allow more instrumentalists to play here."

> > >Also, what makes you think Werckmeister self-deprecates his circular
> > >chromatic temperaments? I haven't seen anything of this kind anywhere
> > > and I am on the look out.
> >
> > I was mistakenly giving the wrong impression. Not some much
> > 'self-deprication', but a healthy sense of what works in a given
> > practical setting, and what is best, even if it's not 'your own
> > tuning'....plus, there
> >
> > was a common practice tuning that defied specific mathematical
> > description, i.e., one used one's ears and 'guess-timated'. In other
> > words, no one 'owned'
> > the 'ordinary temperament' of the 18th century, because its description
> > was not as mathematically precise as we now are. They didn't use cents.
> > They used
> > their ears!
>
> Yes, but ears are trained. They are not given a sense of musical
> temperament perfection at birth. The ears are best judges when there are
> specific and exact intervals that they are measuring against, for example
> pure fifths and octaves.

So we agree!?

> As you may know a young Neidhardt was in a contest in 1706 in Jena with an
> elder Bach. He lost the contest of tuning the organ because the Bach
> tuning was considered by all listening to be more singable. It is likely
> that Neidhardt was tuning to the equal temperament he first promoted. The
> Bach, eldest son of Johann Christoph Bach (Uncle to J.S.) was certainly
> unequal at this time (and likely Werckmeister III in my estimation). This
> is a tuning duel, essentially, and ET lost.

Where is the source for this interesting story. How do you know it was ET?
Neidhardt has at least 4 tuning we know of.....

The statement that it was likely Werckmeister III is purely speculative.
Kellner tried to reconstruct Bach's tuning, but his ideas are also
speculative. This is history, an impure science, like astronomy. Are there
Black holes for sure? We think so. But history, without written records, is
even fuzzier. Again, Bach left nothing on the subject to my knowledge.

Best,
Aaron.

🔗Afmmjr@aol.com

Hi Aaron,

Thought I'd get back to your recent points. Some of my support material is
in a different location, but my memory should be okay. (These are subject
areas dear to my heart.)

Re the Paul Poletti reasoning: I don't think you can rely on his
interpretation. First off, Werckmeister never ever mentioned sixth comma meantone (let
alone fifth comma). All Werckmeister's work is based on quarter comma meantone
(which is Werckmeister II tuning). The fact that sixth comma works to mirror
some of WIII is more of an after the fact that before the fact situation.

Also, Poletti is referring ot something that has been fully translated into
English now, the directions for the harpsichord tuning attached to the 1698
treatise on the Figured Bass treatise, and it smells more like ET than any
meantone-derived tuning. Poletti says the "somewhat imprecise" instructions are
with little doubt another "meantone modification." This is simply untrue,
unless ET is considered in fact a meantone modification as well.

Besides, descriptions like "primitive economy-class" is too biased for me to
take seriously. I have performing Brandenburg Concerti in this "primitive
econmy class tuning" of Werckmeister III to grand effect.

Regarding some of your points:
When I listed reasons for using a tuning other than the apparent modern sense
of richness, I was being very general, not specific to either Werckmeister or
Neidhardt. And I can think of still more reasons. Werckmeister III can be
tuned in 15 minutes according to Werckmeister, and Bach was reputed to do
likewise. Neidhardt is likely more labor intensive, no?

But yes, ease and speed did not help ET. And so we have the guild of piano
tuners taking over.

As to Werckmeister and little boys...well, I'd hate to sully his reputation,
once again, based on moderns of a different Christian denomination.

Finally, the story of Neidhardt and a Bach in competition of tunings at Jena
is quite famous. Look for it in the Mendel/David source material on J.S.
Bach. I only provided the info on who the Bach actually was. Also, Neidhardt's
first published tuning was ET, so any tuning duel as early as 1706 would likely
be with this as his ammunition.

best, Johnny Reinhard

🔗Aaron K. Johnson <akj@rcn.com>

On Tuesday 23 September 2003 09:21 am, Afmmjr@aol.com wrote:
> Hi Aaron,
>
> Thought I'd get back to your recent points. Some of my support material is
> in a different location, but my memory should be okay. (These are subject
> areas dear to my heart.)
>
> Re the Paul Poletti reasoning: I don't think you can rely on his
> interpretation. First off, Werckmeister never ever mentioned sixth comma
> meantone (let alone fifth comma). All Werckmeister's work is based on
> quarter comma meantone (which is Werckmeister II tuning). The fact that
> sixth comma works to mirror some of WIII is more of an after the fact that
> before the fact situation.

Ok-doke, I'll buy that. But I still don't get the feeling, having tried
WerckIII for Bach WTC, that this was Bach's tuning. I think something in
general like Poletti described, ie a 'common 18th century well-temperament'
with the rough outlines of WerckIII, but perhaps a wider C-E and a less wide
E-G# and G#-C work better for those Bach pieces in remote keys from C, or the
mannerist modulatory stuff......

> Also, Poletti is referring ot something that has been fully translated into
> English now, the directions for the harpsichord tuning attached to the 1698
> treatise on the Figured Bass treatise, and it smells more like ET than any
> meantone-derived tuning. Poletti says the "somewhat imprecise"
> instructions are with little doubt another "meantone modification." This
> is simply untrue, unless ET is considered in fact a meantone modification
> as well.
>
> Besides, descriptions like "primitive economy-class" is too biased for me
> to take seriously. I have performing Brandenburg Concerti in this
> "primitive econmy class tuning" of Werckmeister III to grand effect.

Yes, this is a subjective opinion, and should be taken as such. I relate,
however, to his critique of the narrow, automatic myopia that takes over when
the eary music scene wraps its jaws around something, like "lets use this
tuning EVERYWHERE, because it's easy to use, who cares if its the most
appropriate!!!" (Valotti/Young syndrome)

> Regarding some of your points:
> When I listed reasons for using a tuning other than the apparent modern
> sense of richness, I was being very general, not specific to either
> Werckmeister or Neidhardt. And I can think of still more reasons.
> Werckmeister III can be tuned in 15 minutes according to Werckmeister, and
> Bach was reputed to do likewise. Neidhardt is likely more labor intensive,
> no?

Try it....'small city' is as quick as Werck III...

> But yes, ease and speed did not help ET. And so we have the guild of piano
> tuners taking over.
>
> As to Werckmeister and little boys...well, I'd hate to sully his
> reputation, once again, based on moderns of a different Christian
> denomination.

hehe....true, but do we really think this is a Catholic only phenomena? (even
though they take 90% of the cake.) It was only a joke. Don't take my quip
seriously...

> Finally, the story of Neidhardt and a Bach in competition of tunings at
> Jena is quite famous. Look for it in the Mendel/David source material on
> J.S. Bach. I only provided the info on who the Bach actually was. Also,
> Neidhardt's first published tuning was ET, so any tuning duel as early as
> 1706 would likely be with this as his ammunition.

Fair 'nuff....I read the 'Bach Reader' years ago (in my teens!!!). The story
was probably in there, but it didn't stand out or ring a bell for me.
Sometimes, one has to read something several times to remember all the
details! (or be older and interested in a particular area of study like
tuning...)

great talking to you Johnny....I'm moving, and really should be packing right
now, but I took 10 minutes to answer this. If I ignore you for a week, it's
not personal, but I have to keep my wife happy that I'm slaving on these
boxes!

All best,
Aaron.

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz <monz@attglobal.net>

hi Joe,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_20459.html#47125
>
> > during one of the searches, probably in Poletti's paper,
> > i read something about Neidhardt's feelings that the
> > relatively unsophisticated (for lack of a better way of
> > putting it) instruments, playing technique, and repertoire
> > of village musicians was best suited to a circulating
> > temperament leaning more towards JI and meantone; those
> > for a small city leaned closer to 12edo; those for a
> > big city even more towards 12edo; and those for the court
> > still more so.
> >
>
> ***Thanks, Monz. This answered the question I posed in
> the previous query...

but note the post Manuel sent regarding this, which appeared
right after mine:

/tuning/topicId_20459.html#47126

>> Neidhardt meant this in a metaphorical sense, not literally.
>> These places like Dorf, Stadt and Hof represent the
>> continuum from traditional music to progressive music.
>> And with "court" he means the highest kind of music like
>> Bach's.
>>
>> By the way, I found this misunderstanding also in
>> Isacoff's book about temperament

-monz

COunterpoint books...

🔗Robert C Valentine <BVAL@IIL.INTEL.COM>

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗Rosati <dante.interport@rcn.com>

🔗jpehrson@rcn.com

🔗Graham Breed <graham@microtonal.co.uk>

🔗jpehrson@rcn.com

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗jpehrson@rcn.com

🔗monz <MONZ@JUNO.COM>

🔗monz <MONZ@JUNO.COM>

🔗monz <MONZ@JUNO.COM>

🔗Graham Breed <graham@microtonal.co.uk>

🔗jpehrson@rcn.com

🔗monz <monz@attglobal.net>

🔗Leonardo Perretti <dombedos@tiscalinet.it>

🔗monz <monz@attglobal.net>

🔗Leonardo Perretti <dombedos@tiscalinet.it>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz <monz@attglobal.net>

🔗Leonardo Perretti <dombedos@tiscalinet.it>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz <monz@attglobal.net>

🔗Aaron K. Johnson <akj@rcn.com>

🔗Aaron K. Johnson <akj@rcn.com>

🔗monz <monz@attglobal.net>

🔗monz <monz@attglobal.net>

🔗Afmmjr@aol.com

🔗Aaron K. Johnson <akj@rcn.com>

🔗Aaron K. Johnson <akj@rcn.com>

🔗monz <monz@attglobal.net>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Afmmjr@aol.com

🔗Aaron K. Johnson <akj@rcn.com>

🔗Afmmjr@aol.com

🔗Aaron K. Johnson <akj@rcn.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz <monz@attglobal.net>