Well tempered

The discussion between Johnny and Aaron regarding Well Temperaments is interesting to me, as I really don't have a lot of expertise in that department, other than knowing (sort of) what they are, and that they were used in Bach's era. So, who's right, and are there other theorists who may have yet another viewpoint? Can anybody really know, 100%, just how Bach (or anybody back then) tuned their axes, and another question is, did people use the same tuning all the time? Could Bach, for example, have tried different tunings for different works, for different effects? It seems there were many varieties of tuning systems back then; it also seems like they were fairly similar in purpose (?), to negotiate a 12 note system and be able to play in the major/minor keys with a minimum of wolflike howling.
I enjoy the discussion, but it's almost like different denominations of the Christian church; which is the true teaching, and can we ever know for sure? Keep it up, best...HHH
microstick.net

Neil,

Your point(s) is my point precisely. If I'm a member of any church, it's the
'no tuning religion' church that says Bach was a tuning polygamist.

As for the idea that Werck III is the definitive Bach tuning, hogwash. Johnny
has no *direct* evidence any more than anyone else who puts out their ideas.
(notice my emphasis on the word 'direct'). Johnny is speculating as much as
Brad Lehman, who ironically, he has dismissed outright. One can never stand
what one sees of oneself in others, perhaps? ;) Even in the sense that Brad
Lehman has done 'unverifiable' work, I think it is interesting and important
what he has done--it gives us all yet another potential choice for a bach
tuning, and that means it's 'valid'.

With all due respect to Johnny, in the absence of direct evidence, you get
religion, and so in Johnny's beliefs re: Werckmeister and Bach, we have the
religion of "Werckmeister III *is* Bach's tuning--done deal", in spite of his
protestations that he is not proposing just that!

To me what counts in any art is aesthetic truth and beauty; what is
compelling. By that I mean *even* if Bach used Werckmeister III, I think it
sounds better in plenty of other temperaments, so I see no point in chasing a
holy grail that most likely doesn't exist. I think even inventing a
neo-baroque temperament based on historical models is valid. It all boils
down to opinion. Johnny likes the sound of Werck III. I don't, even if Bach
did. If Bach ate shit, I would still refrain from eating shit. (And BTW, Carl
Lumma has the perfect right to love the radiant Gould 'Goldbergs' in
12-equal. It is simply one of the most important musical recordings of the
century, a potent artistic statement, authentic or not.)

Johnny, I see you are sticking to your guns about Werckmeister III. If that's
where you are going to stay, I hope it gives you utter bliss to chance that
dream to where it takes you! If you are utterly convinced you are right, far
be it for me to take that muse away. I also hope that you would open up and
explore other possibilities and not shut the door and some potent creative
exploration, because your own work shows just how capable you are at
exploring! Absolutism is the death of Art. But I guess sometimes, it gives
birth to art, in terms of an artist chasing a single theme or muse. (Maybe
the statement 'Absolutism is the death of Art' is too absolute, and I just
killed Art) ;) Who knows?! I don't always live comfortable with ambiguity,
but I know that my creative self depends on it, at least somewhat. My wife is
fond of quoting Rilke: "Live the questions"

....But it's just your opinion that Neidhardt I, for example, doesn't work for
Bach. Hogwash. As if Bach's music were that fragile. I think it's positively
radiant in it, as it is in most any temperament, because Bach's music really
is not so dependant on tuning in the same way that say, William Byrd is, as
much as you would like to argue that it is: it might bring out certain
special features, etc., but it's not going to lose it's essential beauty.
(Whereas Byrd's music just might) People have been listening to and loving
Bach for years in 12-equal, after all.

(BTW, I'm a fan of many, many, many pieces of 12-equal music. I'm here, like
most of you, to explore other possibilities, not to denegrate 12-equal.
Worshipping Werck-III for Bach to the exculsion of others seems as odd to me
as worshipping 12-equal to the exclusion of others)

But, this is just *my* opinion at the end of the day. As for what Bach wanted,
no one, not even the eminently respectable Johnny Reinhard can say for sure.

All best,
Aaron.

On Tuesday 16 August 2005 12:34 pm, Neil Haverstick wrote:
> The discussion between Johnny and Aaron regarding Well Temperaments is
> interesting to me, as I really don't have a lot of expertise in that
> department, other than knowing (sort of) what they are, and that they were
> used in Bach's era. So, who's right, and are there other theorists who may
> have yet another viewpoint? Can anybody really know, 100%, just how Bach
> (or anybody back then) tuned their axes, and another question is, did
> people use the same tuning all the time? Could Bach, for example, have
> tried different tunings for different works, for different effects? It
> seems there were many varieties of tuning systems back then; it also seems
> like they were fairly similar in purpose (?), to negotiate a 12 note system
> and be able to play in the major/minor keys with a minimum of wolflike
> howling.
> I enjoy the discussion, but it's almost like different denominations of
> the Christian church; which is the true teaching, and can we ever know for
> sure? Keep it up, best...HHH
> microstick.net
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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>
> Yahoo! Groups Links
>
>
>

Hi Aaron,

It is a bit rude to speak of me to another on the List, but okay.

Neil,

Your point(s) is my point precisely. If I'm a member of any church, it's the
'no tuning religion' church that says Bach was a tuning polygamist.

I am irreligious in all things. And I think, Aaron, you are misrepresenting
Bach's tuning intentions to others based on faulty connections.

As for the idea that Werck III is the definitive Bach tuning, hogwash. Johnny
has no *direct* evidence any more than anyone else who puts out their ideas.
(notice my emphasis on the word 'direct'). Johnny is speculating as much as
Brad Lehman, who ironically, he has dismissed outright. One can never stand
what one sees of oneself in others, perhaps? ;) Even in the sense that Brad
Lehman has done 'unverifiable' work, I think it is interesting and important
what he has done--it gives us all yet another potential choice for a bach
tuning, and that means it's 'valid'.

Sorry, can't get behind the "more the merrier idea" regarding Bach.

With all due respect to Johnny, in the absence of direct evidence, you get
religion, and so in Johnny's beliefs re: Werckmeister and Bach, we have the
religion of "Werckmeister III *is* Bach's tuning--done deal", in spite of his
protestations that he is not proposing just that!

This is really spin. To dismiss my active study of Bach's Tuning is base.
The case is still to be made that is circumstantial. Much of it has been
discussed on this List previously.

To me what counts in any art is aesthetic truth and beauty; what is
compelling. By that I mean *even* if Bach used Werckmeister III, I think it
sounds better in plenty of other temperaments, so I see no point in chasing a
holy grail that most likely doesn't exist. I think even inventing a
neo-baroque temperament based on historical models is valid. It all boils
down to opinion. Johnny likes the sound of Werck III. I don't, even if Bach
did. If Bach ate shit, I would still refrain from eating shit. (And BTW, Carl
Lumma has the perfect right to love the radiant Gould 'Goldbergs' in
12-equal. It is simply one of the most important musical recordings of the
century, a potent artistic statement, authentic or not.)

Well said, Aaron. I totally agree with the above depictions. I simply
disagree with you.

<snip>

....But it's just your opinion that Neidhardt I, for example, doesn't work
for
Bach.

Never said that. I said Bach works in everything because of the quality of
Bach. Any tuning works with Bach because Bach is that good. However, there is
an awesome power in using the right temperament.

Bradley is correct that an unequal temperament, of any kind, affects tempo,
phrasing, and other parameters. It is important not to misquote me or anyone
else when defending your ideas.

Worshipping Werck-III for Bach to the exculsion of others seems as odd to me
as worshipping 12-equal to the exclusion of others)

Why are you using religious terminology like "Worshipping"? I am simply (and
not so simply) making concerts and producing concerts of Bach in Werckmeister
III tuning. Once again, unless you really believe Neidhardt set the tuning
system for Bach's Brandenburg Concerti, what else could it be? Remember, this
is not a straight keyboard piece.

But, this is just *my* opinion at the end of the day. As for what Bach
wanted,
no one, not even the eminently respectable Johnny Reinhard can say for sure.

All best,
Aaron.

No, but it is easier to say what it is not.

best, Johnny

On Tuesday 16 August 2005 6:30 pm, Afmmjr@aol.com wrote:
> Hi Aaron,
>
> It is a bit rude to speak of me to another on the List, but okay.

Sorry, I just didn't want to be redundant. I didn't mean to offend...

BTW, can you please use qoute characters (>) when quoting me. It's so hard to
parse who said what, and you make me add them manually.

> > Neil,
> >
> > Your point(s) is my point precisely. If I'm a member of any church, it's
> > the 'no tuning religion' church that says Bach was a tuning polygamist.
> >
>
> I am irreligious in all things. And I think, Aaron, you are
> misrepresenting Bach's tuning intentions to others based on faulty
> connections.

Call it what you will, I call faith in anything with little hard evidence
'religion'.

I don't claim to know Bach's tuning. I just think several other options
besides Werckmeister III have more musical 'rightness'. These things are
subtle and more pertinant to the performer and tuners and musicians than to
the general audience, who might only get it at a subconscious level, if at
all.

> >
> > As for the idea that Werck III is the definitive Bach tuning, hogwash.
> > Johnny has no *direct* evidence any more than anyone else who puts out
> > their ideas. (notice my emphasis on the word 'direct'). Johnny is
> > speculating as much as Brad Lehman, who ironically, he has dismissed
> > outright. One can never stand what one sees of oneself in others, perhaps?
> > ;) Even in the sense that Brad Lehman has done 'unverifiable' work, I
think
> > it is interesting and important what he has done--it gives us all yet
> > another potential choice for a bach tuning, and that means it's 'valid'.
> >
> >

> Sorry, can't get behind the "more the merrier idea" regarding Bach.

If Bach cared so much what tuning was to be used for each and any piece, he
would have been explicit. Chances are, he thought any well-temperament
variety would do.

People invented new tunings to be creative, to push for new sonic resources. I
find it simply amazing that you think the mind of Bach was so rigid that he
stopped at Werckmeister III. It was far from the only game in town, we know
that much!

> > With all due respect to Johnny, in the absence of direct evidence, you get
> > religion, and so in Johnny's beliefs re: Werckmeister and Bach, we have
the
> > religion of "Werckmeister III *is* Bach's tuning--done deal", in spite of
> > his protestations that he is not proposing just that!
> >
>
> This is really spin. To dismiss my active study of Bach's Tuning is base.
> The case is still to be made that is circumstantial. Much of it has been
> discussed on this List previously.

Johnny, I was merely responding to the fact that by your own admission, you
hadn't really sonically explored many of the others.

> >
> > To me what counts in any art is aesthetic truth and beauty; what is
> > compelling. By that I mean *even* if Bach used Werckmeister III, I think
it
> > sounds better in plenty of other temperaments, so I see no point in
chasing
> > a holy grail that most likely doesn't exist. I think even inventing a
> > neo-baroque temperament based on historical models is valid. It all boils
> > down to opinion. Johnny likes the sound of Werck III. I don't, even if
Bach
> > did. If Bach ate shit, I would still refrain from eating shit. (And BTW,
> > Carl Lumma has the perfect right to love the radiant Gould 'Goldbergs' in
> > 12-equal. It is simply one of the most important musical recordings of the
> > century, a potent artistic statement, authentic or not.)
> >
>
> Well said, Aaron. I totally agree with the above depictions. I simply
> disagree with you.

I'm beginning to see that ;)

> <snip>
>
>
> > ....But it's just your opinion that Neidhardt I, for example, doesn't work
> > for
> > Bach.
> >

> Never said that. I said Bach works in everything because of the quality of
> Bach. Any tuning works with Bach because Bach is that good. However,
> there is an awesome power in using the right temperament.

I agree. I just don't think Werck III is at all gently resonant enough in the
distant keys, and a bit bumpy. Most of the thirds are a little too active for
me. It gives everything a 'coked-up' sound. (I suppose that's why I live in
Chicago, which is a bit mellower than New York, but has just the right amount
of edgyness for me.)

> Bradley is correct that an unequal temperament, of any kind, affects tempo,
> phrasing, and other parameters. It is important not to misquote me or
> anyone else when defending your ideas.

Fair enough. And I agree that these things are certainly in play with a tuning
choice.

> Worshipping Werck-III for Bach to the exculsion of others seems as odd to
> me as worshipping 12-equal to the exclusion of others)

> Why are you using religious terminology like "Worshipping"? I am simply
> (and not so simply) making concerts and producing concerts of Bach in
> Werckmeister III tuning.

Ok, worshipping goes too far. How about 'promoting as the only possible
candidate in spite of the lack of direct evidence'?

> Once again, unless you really believe Neidhardt
> set the tuning system for Bach's Brandenburg Concerti, what else could it
> be?

Well, um, any of the many other tunings that were floating around? A tuning
can exist in common practice prior to being published, as well.

> Remember, this is not a straight keyboard piece.

Nor an organ piece.

> But, this is just *my* opinion at the end of the day. As for what Bach
> wanted,
> no one, not even the eminently respectable Johnny Reinhard can say for
> sure.
>
> All best,
> Aaron.
>
> No, but it is easier to say what it is not.

Not really.

Best,
Aaron.

P.S. I've said enough on the subject. It's eating too much of my precious
time. You can have the last word if you must!

Hiya Neil,

> Can anybody really know, 100%, just how Bach (or anybody back
> then) tuned their axes, and another question is, did people use
> the same tuning all the time? Could Bach, for example, have
> tried different tunings for different works, for different
> effects?

Good question. To me, the fact that Bach didn't specify the
temperament any more exactly means that the particular well
temperament wasn't that important to him. And as is often
pointed out, he did not have the luxury of tuning the organs
he played, so he was at the mercy of the organ tech for that.

-Carl

Please visit my site, "Music of Sacred Temperament".
http://www.geocities.jp/imyfujita/index.html

In a message dated 8/16/2005 11:44:04 PM Eastern Standard Time,
aaron@akjmusic.com writes:
Call it what you will, I call faith in anything with little hard evidence
'religion'.

"While you may be innocent in this, I find someone declaring me 'religious'
offensive. Please find another metaphor. Besides, there is direct musical
evidence that can be interpreted differently, as we have both discovered."

If Bach cared so much what tuning was to be used for each and any piece, he
would have been explicit. Chances are, he thought any well-temperament
variety would do.

"Disagree. No one could tune to Bach's taste, according to his son CPE.
This smacks of a particular tuning to me."

People invented new tunings to be creative, to push for new sonic resources.
I
find it simply amazing that you think the mind of Bach was so rigid that he
stopped at Werckmeister III. It was far from the only game in town, we know
that much!

"Not true. Werckmeister was the only game in town for a superstar organist
in well temperament, at least as far as his Thuringian culture is concerned.
All the names you have given for alternatives came AFTER Bach began his
professional career. His best friend and relative (and author of the first
exhaustive encyclopaedia of music, J.G. Walther) was a proud student of Werckmeister's.
The organs built in Arnstadt and Muhlhausen were put into Werckmeister
tunnig by their builder, Wender. Even Kuhnau, attributed by Brad as
non-well-tempered, was a personal friend of Werckmeister's, and likely a utilizer of the
tuning in Leipzig, penultimate before the succession to Bach. And there are no
public records of Bach changing tunings upon his arrival in a new job."

Ok, worshipping goes too far. How about 'promoting as the only possible
candidate in spite of the lack of direct evidence'?

"If I was promoting, then I would have it say on the Early CD album cover 'In
Bach's authentic tuning, which I did not do."

> Once again, unless you really believe Neidhardt
> set the tuning system for Bach's Brandenburg Concerti, what else could it
> be?

Well, um, any of the many other tunings that were floating around? A tuning
can exist in common practice prior to being published, as well.

"In the practical performance of a Brandenburg Concerto, one tuning has to be
decided upon. If not Werckmeister III, what tuning would a modern like me
use to tune the orchestra? A flip answer will not solve this practical
situation."

P.S. I've said enough on the subject. It's eating too much of my precious
time. You can have the last word if you must!

"I hope the quotes worked out well this time. Thank you for your seriousness
on the issue. However, it is too diletantish for me to wishy-washy about
what I like and don't like, or to serve it up to a poll or commercial success. I
am afraid I will need more time to put this all together. However, my track
record is good in production, even if a bit later than I'd hope.

all best, Johnny Reinhard

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> Even Kuhnau, attributed by Brad as
> non-well-tempered, was a personal friend of Werckmeister's, and
likely a utilizer of the
> tuning in Leipzig, penultimate before the succession to Bach.

Wait a minute. "Attributed by Brad as non-well-tempered" where and
when? It doesn't do anybody any good to stick mistakenly imputed
ideas into my mouth and then shoot them down; it's straw-man
argumentation. I suspect you're misreading my material at the top of
page 6....

In fact, from playing through Kuhnau's "Biblical sonatas" myself many
years ago (and noting the musical/dramatic strokes in them, trying
various temperaments), I believe that he too used something that
allows modulation to almost all the keys. Clearly *not* regular
meantone of any tightness; and *at least* a modified-meantone along
_temperament ordinaire_ principles, in the usual French/Italian
manner. Maybe all the way to a circulating temp by Werckmeister or
Bendeler or somebody else, or maybe something home-grown in practice
(i.e. having nothing to do with publication) by adjusting until the
music sounds good.

In short, I believe that Kuhnau was a good and sensitive musician who
didn't stuff himself into a hole, constrained to use any particular
published temperament. If *he* had any firm preferences for a single
system, I trust it would have arisen from *his own* musical judgment/
experience doing all the regular jobs of a professional church
musician, and not simply because good-buddy W told him what he must
use.

Bradley Lehman

On Wednesday 17 August 2005 9:11 am, Brad Lehman wrote:
> Maybe all the way to a circulating temp by Werckmeister or
> Bendeler or somebody else, or maybe something home-grown in practice
> (i.e. having nothing to do with publication) by adjusting until the
> music sounds good.

A 'home-grown' tuning is something that is perhaps way more likely and common
in practice than some would be comfortable admitting. I think this must have
happened *all the time*

-Aaron.

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...>
wrote:
> ...
> As for the idea that Werck III is the definitive Bach tuning,
hogwash. ...
>
> To me what counts in any art is aesthetic truth and beauty; what is
> compelling. By that I mean *even* if Bach used Werckmeister III, I
think it
> sounds better in plenty of other temperaments, so I see no point in
chasing a
> holy grail that most likely doesn't exist. I think even inventing a
> neo-baroque temperament based on historical models is valid. It all
boils
> down to opinion. Johnny likes the sound of Werck III. I don't, even
if Bach
> did.

Aaron, I first investigated well-temperaments way back in 1964,
shortly after I began the study of alternative tunings. I tried a
few of those that I judged to be the most promising ones in Barbour's
_Tuning and Temperament_ on a retunable electronic organ, but I was
not satisfied with any of them.

I believe that in a well-temperament the major triads from Bb thru D
should have significantly better intonation than in 12-ET, and that
the error should increase progressively as one moves around the
circle of fifths toward F# or Gb. Werckmeister III is seriously
deficient in that the total error of the intervals in the G and D
major triads is the *same* as in 12-ET (!). Also, there is an equal
amount of error in the C and Bb major triads, while the lowest error
is in the F major triad.

To see a (bar-)graphic illustration of this, go to:
http://www.rollingball.com/TemperamentsFrames.htm
Click on "Well" at the top right and then on "Werckmeister (1691)" at
the left. (Note: In any well-temperament, you should find that the
total error of the intervals in any major triad will be twice the
error of its minor third, so you can easily evaluate the progression
of error by reading the top row of cents-deviation numbers, for the
minor third, in the table below the bar-graph.)

I've since found that recent attempts by others, such as "Jorgensen's
Prinz (2002)" (which you may click on at the lower left), are also
frequently biased with lower error in the keys having flats in the
key signature (e.g., the F major triad has less error than G, and Bb
has less error than D. Although Jorgensen described his "Idealized"
temperament as having "perfect harmonic balance for tonality", he
considered only the error of the major thirds in each triad, failing
to take into account the error of the fifths and minor thirds.

Thinking that I could do better than what I found in Barbour's book,
I devised my own neo-baroque well-temperament, but I didn't get it
completely right until 11 years later, when I could more easily test
and compare using a Scalatron. If you want to see what I came up
with, go to the above link and click on "Modern Well" at the top
right and then on "George Secor (1975)" at the bottom left. Observe
that the total error in the major triads is perfectly symmetrical as
one moves away from C in either direction through the circle of
fifths. (Note: This temperament should probably be in the "Well"
category, since it has a high contrast between its best and worst
triads.)

As for my alternative to temperaments in the Modified Meantone
category, click on "Modified Meantone" at the top, then on "Secor #3
(1975)" at the left to find a temperament with *no* fifths tempered
by more than 1/4-comma (in either direction) and only 4 major triads
with significantly greater total error than in 12-ET. (In this
category you can't evaluate total error of a triad by looking only at
the error of its minor third.) The widest major thirds are very
close to 11:14 (and they occur in triads with just fifths): rather
dissonant, but still usable; Margo Schulter observed that these work
very well for medieval or neo-medieval music, in response to my
remark that a (dissonant) dominant F# major triad resolving to a
(consonant) B minor triad sounds very effective.

It's open to debate whether one will do "better" in a performance of
Baroque music with an "authentic" well-temperament or with
an "inauthentic" modern tuning that optimizes the intent of those who
devised well-temperaments, but apart from that issue, I'd be
interested in your (and others') reactions to the above (if you could
be persuaded to come up with a few more "last" words).

Best,

--George

George,

Thanks for this post. I followed the link to the charts, which are great.
I will check out your temperaments--Iit sounds like you did some interesting
and pioneering explorations...

I did some spreadsheets on my recent variant of Neidhardt-I, and found problem
with it as far as well-temperaments go. Bb-D is a bit wider than even the F#
and Ab chords!. Nevertheless, it still sounds usable as a quasi-equal
temperament. Back to the drawing board!

I think I can solve this by making my C-E smaller, and then tempering it into
fifth as usual (noe D will be lower where it 'should' be) or still having the
equal beating scheme, but temper E-B-F#-C#-G#-Eb-Bb-F. Or just, adjust the Bb
higher a tad.

I'm now considering on a temperament very close to 12-ET, but using an equal
beating augmented triad skeleton, and breaking those into 4 equal beating
5ths....This gets out of 'well-temperament' territory, but has interesting
shimmer and resonance properties which are subtely more attractive than
12-equal, even though the audible result is almost indistinguishable from
12-equal.

Best,
Aaron.

On Wednesday 17 August 2005 3:16 pm, George D. Secor wrote:
> Aaron, I first investigated well-temperaments way back in 1964,
> shortly after I began the study of alternative tunings. I tried a
> few of those that I judged to be the most promising ones in Barbour's
> _Tuning and Temperament_ on a retunable electronic organ, but I was
> not satisfied with any of them.
>
> I believe that in a well-temperament the major triads from Bb thru D
> should have significantly better intonation than in 12-ET, and that
> the error should increase progressively as one moves around the
> circle of fifths toward F# or Gb. Werckmeister III is seriously
> deficient in that the total error of the intervals in the G and D
> major triads is the *same* as in 12-ET (!). Also, there is an equal
> amount of error in the C and Bb major triads, while the lowest error
> is in the F major triad.
>
> To see a (bar-)graphic illustration of this, go to:
> http://www.rollingball.com/TemperamentsFrames.htm
> Click on "Well" at the top right and then on "Werckmeister (1691)" at
> the left. (Note: In any well-temperament, you should find that the
> total error of the intervals in any major triad will be twice the
> error of its minor third, so you can easily evaluate the progression
> of error by reading the top row of cents-deviation numbers, for the
> minor third, in the table below the bar-graph.)
>
> I've since found that recent attempts by others, such as "Jorgensen's
> Prinz (2002)" (which you may click on at the lower left), are also
> frequently biased with lower error in the keys having flats in the
> key signature (e.g., the F major triad has less error than G, and Bb
> has less error than D. Although Jorgensen described his "Idealized"
> temperament as having "perfect harmonic balance for tonality", he
> considered only the error of the major thirds in each triad, failing
> to take into account the error of the fifths and minor thirds.
>
> Thinking that I could do better than what I found in Barbour's book,
> I devised my own neo-baroque well-temperament, but I didn't get it
> completely right until 11 years later, when I could more easily test
> and compare using a Scalatron. If you want to see what I came up
> with, go to the above link and click on "Modern Well" at the top
> right and then on "George Secor (1975)" at the bottom left. Observe
> that the total error in the major triads is perfectly symmetrical as
> one moves away from C in either direction through the circle of
> fifths. (Note: This temperament should probably be in the "Well"
> category, since it has a high contrast between its best and worst
> triads.)
>
> As for my alternative to temperaments in the Modified Meantone
> category, click on "Modified Meantone" at the top, then on "Secor #3
> (1975)" at the left to find a temperament with *no* fifths tempered
> by more than 1/4-comma (in either direction) and only 4 major triads
> with significantly greater total error than in 12-ET. (In this
> category you can't evaluate total error of a triad by looking only at
> the error of its minor third.) The widest major thirds are very
> close to 11:14 (and they occur in triads with just fifths): rather
> dissonant, but still usable; Margo Schulter observed that these work
> very well for medieval or neo-medieval music, in response to my
> remark that a (dissonant) dominant F# major triad resolving to a
> (consonant) B minor triad sounds very effective.
>
> It's open to debate whether one will do "better" in a performance of
> Baroque music with an "authentic" well-temperament or with
> an "inauthentic" modern tuning that optimizes the intent of those who
> devised well-temperaments, but apart from that issue, I'd be
> interested in your (and others') reactions to the above (if you could
> be persuaded to come up with a few more "last" words).
>
> Best,
>
> --George

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...>
wrote:
>
> George,
>
> Thanks for this post. I followed the link to the charts, which are
great.
> I will check out your temperaments--Iit sounds like you did some
interesting
> and pioneering explorations...

I kept the #2 tuning on my (acoustic) piano for several years (till
1979, when I sold it just prior to moving). After a very short time
I found that, as I became accustomed to the differences in intonation
in the various keys, I tended to hear the "remote" pythagorean triads
as having a different "mood" rather than being unacceptably out of
tune. I might compare my first reaction to swimming in cold water:
initially shocking, but ultimately invigorating.

For your convenience, here is the .scl file content for the two
tunings:

! secor12_2.scl
!
George Secor's 12-tone well-temperament #2, with 7 just fifths
12
!
256/243
194.86828
32/27
388.02514
4/3
1024/729
698.28985
128/81
891.44671
16/9
4096/2187
2/1

! secor12_3.scl
!
George Secor's 12-tone temperament #3 with 5 meantone, 3 just, and 2
wide fifths
12
!
83.13700
193.15686
292.42357
5/4
501.71015
581.18200
696.57843
785.09200
889.73529
999.75514
1082.89214
2/1

> I did some spreadsheets on my recent variant of Neidhardt-I, and
found problem
> with it as far as well-temperaments go. Bb-D is a bit wider than
even the F#
> and Ab chords!. Nevertheless, it still sounds usable as a quasi-
equal
> temperament. Back to the drawing board!

I've found that a major triad with a just 5th and major 3rd 1/4-comma
wide sounds about as consonant as a 1/4-comma meantone triad (because
the minor 3rds are the same size). In a well-temperament, the sizes
of the 3 fifths separating the 3rd and 5th of a major triad will
therefore determine the consonance of that triad, and the size of the
fifth built on the tonic will be *irrelevant* (as long as no major
3rd in the temperament is tempered narrow and no minor 3rd or 5th is
tempered wide). You might want to try playing around with the minor
(instead of the major) 3rds to see where that takes you.

> I think I can solve this by making my C-E smaller, and then
tempering it into
> fifth as usual (noe D will be lower where it 'should' be) or still
having the
> equal beating scheme, but temper E-B-F#-C#-G#-Eb-Bb-F. Or just,
adjust the Bb
> higher a tad.
>
> I'm now considering on a temperament very close to 12-ET, but using
an equal
> beating augmented triad skeleton, and breaking those into 4 equal
beating
> 5ths....This gets out of 'well-temperament' territory, but has
interesting
> shimmer and resonance properties which are subtely more attractive
than
> 12-equal, even though the audible result is almost
indistinguishable from
> 12-equal.

Sounds intruiging -- I'll be interested to see how this works out.

Best,

--George

--- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...> wrote:

> So, who's right, and are there other theorists who may
> have yet another viewpoint?

I'm pig ignorant save for two things--I've actually done a lot of
tuning experiments, and have studied well-temperaments.

Can anybody really know, 100%, just how Bach (or
> anybody back then) tuned their axes, and another question is, did
people use
> the same tuning all the time? Could Bach, for example, have tried
different
> tunings for different works, for different effects?

Dang. That's what *I've* been wondering about. Of course I'm not even
convinced that Bach didn't use meantone, or something close to it, for
WTC I, since as yet no one has put forward a historical argument that
he couldn't have.

In a message dated 8/18/2005 10:48:46 PM Eastern Standard Time,
gwsmith@svpal.org writes:
Could Bach, for example, have tried
different
> tunings for different works, for different effects?
Well, yes, Bach did sometimes have the use of meantone in mind, as he did
when he wrote the Orgelubungen works for W.F. Bach, his oldest son. Telemann was
the sixth comma meantone balance to the use of 12unET of Bach.

Telemann was W.F.'s godfather. And W.F. would work in Halle and Dresden
(Quantz's origin) were ensconsed in meantone tuning.

They two tunings sort of mirror each other, fascinating because Werckmeister
spoke only of the quarter comma variant of meantone and never the later
prominent sixth comma. Below is from a book I am writing:

It is to J. Murray Barbour to explain that the falsities of modern
conclusions about which keys sound better or worse cannot be based on sustained
harmonies as pertains to Bach. For, “except at a final cadence, Bach usually
avoids sustained triads. Even subsidiary cadences are often arpeggiated or
contain suspensions or other dissonances” (Barbour, Bach, p. 81).

Barbour hammers home the conclusion that well temperament is evident for all
organ works using the most conservative of those as prime evidence. “Even in
the Orgelbüchlein, which contains the highest proportion of Bach organ works
with simple compass, the latter are far outweighed by others which could be
sharply dissonant in meantone tunings.” Barbour measured the compass of Bach’s
organ works as a whole to be Ebb-Cx for a total of 25 degrees (Barbour, Bach,
p. 84).

These organ works are pedagogical, written for his son while living in
Anhalt-Cothen, to develop as a Dresden and Halle organist, likely in meantone.
Heinrich Schütz (1585-1672) referenced Dresden, Merseburg, and Halle as cities
that had adopted his Psalter, wherein listeners like to follow along the texts in
their psalm-books, and even sing along by ear. This is a meantone-based
population, unworried about lost chromaticism. Praetorius worked in Dresden and
Madgeburg (the city ravished by the 30 Years War and birthplace of
meantone-based Telemann). Was not Halle birthplace and home to Handel, possessor of a
subsemitonium organ keyboard? Wilhelm Friedemann Bach worked almost exclusively
in the meantone cities of Dresden, Merseburg, and Halle. Friedemann studied
at 15 with Graun in Merseburg. Perhaps this is why his father utilized so many
organ works in the Orgelbüchlein reduced to the meantone compass of notes
(e.g., Eb-G#).

As we turn to the organ literature, we find that of the 148 works examined,
only 15 lie completely within the E flat to G sharp compass, 12 of these being
chorale preludes in the Orgelbüchlein. Only one in ten would be playable on
the conventionally tuned organ, or only one in thirty-four if we exclude the
Orgelbüchlein! This is an astounding result, not wholly unexpected to an
organist who is familiar with the entire Bach literature, but still remarkable in
the observed ratio (Barbour, Bach, p. 81).

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...> wrote:

> I'm now considering on a temperament very close to 12-ET, but using
an equal
> beating augmented triad skeleton, and breaking those into 4 equal
beating
> 5ths....This gets out of 'well-temperament' territory, but has
interesting
> shimmer and resonance properties which are subtely more attractive than
> 12-equal, even though the audible result is almost indistinguishable
from
> 12-equal.

You might be interested in the Wendell well temperaments:

! wendell1.scl
!
Robert Wendell's Natural Synchronous well-temperament (2003)
12
!
94.16800
198.17100
298.07800
393.68000
4/3
597.59000
699.49200
796.12300
895.75700
1000.03300
1095.63500
2/1

! wendell2.scl
!
Robert Wendell's Very Mild Synchronous well-temperament (2003)
12
!
94.93100
198.79700
298.84100
394.11360
498.44500
598.02400
700.05800
796.88600
895.75900
1000.79600
1096.06900
2/1

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...>
wrote:

> ... Of course I'm not even convinced that Bach didn't
> use meantone, or something close to it, for WTC I,
> since as yet no one has put forward a historical argument
> that he couldn't have.

Have you ever tried to play anything in Db-major in
a 1/4-meantone chain-of-5ths tuned from Eb to G#?

I have, and i'd rather listen to a pack of howling wolves
than to that. Doesn't work, plain and simple -- and
WTC I most definitely has pieces in Db-major.

Now, admittedly, a milder version of meantone wouldn't
be as bad ... but for the stronger versions, forget it.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi again Gene,

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

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > ... Of course I'm not even convinced that Bach didn't
> > use meantone, or something close to it, for WTC I,
> > since as yet no one has put forward a historical argument
> > that he couldn't have.
>
>
>
> Have you ever tried to play anything in Db-major in
> a 1/4-meantone chain-of-5ths tuned from Eb to G#?
>
> I have, and i'd rather listen to a pack of howling wolves
> than to that. Doesn't work, plain and simple -- and
> WTC I most definitely has pieces in Db-major.
>
> Now, admittedly, a milder version of meantone wouldn't
> be as bad ... but for the stronger versions, forget it.

Ah, i see from your very next post that you must
be talking about *extended* meantone, and not the
Eb-to-G# version ... but on any typical _Klavier_,
the meantone can only be extended if the performer
retunes some notes between performances of pieces
in different keys. So the 12-tone version is the one
we really should be discussing for the case of trying
to determine Bach's actual keyboard tuning.

For the purposes of experimenting with retuning of
Bach's pieces today, sure, i say go for it! I'm a
big fan of following the notation and using extended
meantone. In fact i'm totally convinced that that's
exactly what Mahler had in mind.

Using Tonescape, i've made what i think is a gorgeous
version of Beethoven's "Cavatina" (from the late Bb quartet)
in a 15-tone 1/6-comma meantone which has 3 pairs of
"enharmonically equivalent" notes Fb/E, Cb/B, and Gb/F#.
I mentioned it here before, but i've done more work on
it and it sounds much better now:

http://tonalsoft.com/music/free/beethoven-cavatina-1-6cmt.mid

(In fact, Gene, i was going to ask you if you could
make lovely sounding .ogg and .mp3 versions of this.)

-monz
http://tonalsoft.com
Tonescape microtonal music software

>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> Hi Gene,
>
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> > ... Of course I'm not even convinced that Bach didn't
> > use meantone, or something close to it, for WTC I,
> > since as yet no one has put forward a historical argument
> > that he couldn't have.

> Have you ever tried to play anything in Db-major in
> a 1/4-meantone chain-of-5ths tuned from Eb to G#?

The question is not really relevant. The point at issue is, could Bach
sometimes have retuned his harpsichord to fit the character of a
particular piece? Unlike an organ, or even a piano, a harpsichord is
readily tunable.

> I have, and i'd rather listen to a pack of howling wolves
> than to that. Doesn't work, plain and simple -- and
> WTC I most definitely has pieces in Db-major.

Which could mean that those pieces were to be played on a keyboard
tuned to Db minor. Do we have some reason to think this is not
possible? What evidence do we possess?

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> ! secor12_2.scl
> !
> George Secor's 12-tone well-temperament #2, with 7 just fifths

The cycle of fifths goes 698.290 696.578 696.578 696.578 698.290
followed by seven just fifths. Pretty close to Parizek's rational well
temperament #3.

> ! secor12_3.scl

Cycle of fifths:

698.290 696.578 696.578 696.578 696.578 696.578 698.290
701.955 701.955 707.332 707.332 701.955

This is temperament ordinaire territory; here is bifrost by way of a
comparison:

696.578 696.578 696.578 696.578 696.578 696.578
701.955 701.955 706.355 706.355 701.955 701.955

<The point at issue is, could Bach
sometimes have retuned his harpsichord to fit the
character of a
particular piece? Unlike an organ, or even a piano, a
harpsichord is
readily tunable.>

As I stated in another reply, there were instruments
like the baroque transverse flutes who had an 18-note
octave ("white keys" plus all the flats plus all the
sharps plus a separate fingering for B#). And I am
utterly convinced that Bach, when playing a flute cum
harpsichord piece would adjust the temperament on his
harpsichord to fit the flute.
One of my harpsichords has split d#/eb and g#/ab keys
which I tune rigidly meantone, and it is the only one
which I use for accompanying flutes, simply because
the sound is so much better. And I am no Bach.
Michael

___________________________________________________________
Yahoo! Messenger - NEW crystal clear PC to PC calling worldwide with voicemail http://uk.messenger.yahoo.com

In a message dated 8/17/2005 10:13:17 AM Eastern Standard Time, bpl@umich.edu
writes:
--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> Even Kuhnau, attributed by Brad as
> non-well-tempered, was a personal friend of Werckmeister's, and
likely a utilizer of the
> tuning in Leipzig, penultimate before the succession to Bach.

Wait a minute. "Attributed by Brad as non-well-tempered" where and
when? It doesn't do anybody any good to stick mistakenly imputed
ideas into my mouth and then shoot them down; it's straw-man
argumentation. I suspect you're misreading my material at the top of
page 6....

In fact, from playing through Kuhnau's "Biblical sonatas" myself many

Hi Brad and All,

I got the idea for the above from your Early Music article, part 1 on page 6.
And I quote you:

"Bach's emphasis here is the assertion that he will surpass the revered
incumbent Kuhnau by handling all the ut re mi and re mi fa keys, not just most of
them. Bach here demonstrates the complete flexibility he will bing as a
candidate for Kuhnau's job in Leipzig."

How did I misread this? It also reads as if Kuhnau was alive which is creepy.

Johnny Reinhard

Let me second this -- Aaron, if you are looking for well-temperaments
with subtle shimmer properties -- actually, a wealth of synchronized
beatings -- you might not be able to do any better than these two.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...>
wrote:
>
> > I'm now considering on a temperament very close to 12-ET, but
using
> an equal
> > beating augmented triad skeleton, and breaking those into 4 equal
> beating
> > 5ths....This gets out of 'well-temperament' territory, but has
> interesting
> > shimmer and resonance properties which are subtely more
attractive than
> > 12-equal, even though the audible result is almost
indistinguishable
> from
> > 12-equal.
>
> You might be interested in the Wendell well temperaments:
>
> ! wendell1.scl
> !
> Robert Wendell's Natural Synchronous well-temperament (2003)
> 12
> !
> 94.16800
> 198.17100
> 298.07800
> 393.68000
> 4/3
> 597.59000
> 699.49200
> 796.12300
> 895.75700
> 1000.03300
> 1095.63500
> 2/1
>
> ! wendell2.scl
> !
> Robert Wendell's Very Mild Synchronous well-temperament (2003)
> 12
> !
> 94.93100
> 198.79700
> 298.84100
> 394.11360
> 498.44500
> 598.02400
> 700.05800
> 796.88600
> 895.75900
> 1000.79600
> 1096.06900
> 2/1

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> Hi Gene,
>
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Neil Haverstick"
<microstick@m...>
> wrote:
>
>
> > ... Of course I'm not even convinced that Bach didn't
> > use meantone, or something close to it, for WTC I,
> > since as yet no one has put forward a historical argument
> > that he couldn't have.
>
>
>
> Have you ever tried to play anything in Db-major in
> a 1/4-meantone chain-of-5ths tuned from Eb to G#?

Clearly you haven't read the relevant discussion on WTC I that
occured on this list, Monz. The rule that was found to work for WTC
is to use a 12-note meantone compass that includes the 7 notes of the
stated key signature, 1 more on the flat side, and 4 more on the
sharp side. One has to retune the clavier for each piece, of course,
but that was common practice throughout the meantone era.

> I have, and i'd rather listen to a pack of howling wolves
> than to that. Doesn't work, plain and simple -- and
> WTC I most definitely has pieces in Db-major.

Obviously. Gene has done so much work in this area that, if I were
Gene, I'd probably find this remark to be an insult to my
intelligence. But I'd also try to smile about it :)

> Now, admittedly, a milder version of meantone wouldn't
> be as bad ... but for the stronger versions, forget it.

Now, why did you choose to interpret Gene's remark as implying a 1/4-
meantone chain-of-5ths tuned from Eb to G#, when you yourself have
primarily interpreted and implemented meantone in a more general and
flexible manner?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > ! secor12_2.scl
> > !
> > George Secor's 12-tone well-temperament #2, with 7 just fifths
>
> The cycle of fifths goes 698.290 696.578 696.578 696.578 698.290
> followed by seven just fifths. Pretty close to Parizek's rational
well
> temperament #3.
>
> > ! secor12_3.scl
>
> Cycle of fifths:
>
> 698.290 696.578 696.578 696.578 696.578 696.578 698.290
> 701.955 701.955 707.332 707.332 701.955

The first fifth listed is above would be F-C, not C-G. If you
intended to list it beginning with C-G, then that should be :

696.578 696.578 696.578 696.578 696.578 698.290
701.955 701.955 707.332 707.332 701.955 698.290

> This is temperament ordinaire territory;

Yep!

> here is bifrost by way of a
> comparison:
>
> 696.578 696.578 696.578 696.578 696.578 696.578
> 701.955 701.955 706.355 706.355 701.955 701.955

Okay, in order to confirm that you're also listing F-C first, I found
it here:

http://66.98.148.43/~xenharmo/bifrost.html

They're very similar. We both found that it's not difficult to
banish the wolf fifth from a temperament ordinaire. It's only a
question of how much you're willing to temper the thirds, and we seem
to be in general agreement about that.

Bifrost has one more meantone and pythagorean fifth than my #3, for
which I substituted 698-cent fifths. My wide fifths are about a cent
wider than yours, making my widest major 3rds about a cent wider than
11:14.

You have 4 major triads with the same total error as 1/4-comma
meantone, from Bb to G (flat-biased), whereas I have 3, from F to G.
I also have two more (Bb and D) that are almost as good. My
intention was to have the (5) best triads centered on C.

You have at least 4 triads (E, B, F#, Db) with significantly worse
intonation than 12-ET (and possibly a 5th one, Ab, which I would have
hear before judging), whereas I have clearly have only 4 (B, F#, Db,
Ab). As was noted below, the major 3rds of the worst triads of both
temperaments are close to 11:14, but I see that your minor 3rds are
closer to 11:13 than mine.

Another indication of your favoring the flat keys is that your Eb and
Ab major triads have less total error than A and E, respectively In
my 7 worst triads I favored the intonation in the sharp direction by
giving the Eb and E major an equal amount of total error and B
slightly less error than Ab. This was done for two reasons:

1) To reduce the error in the dominant triads in the keys of D, A,
and E minor;
2) To avoid intonation significantly worse than 12-ET for any of the
8 usable triads of the Eb-to-G# meantone tuning.

I spent a lot of time back in '75 testing and fine-tuning my #2 and
#3 temperaments by ear on my Scalatron, making instantaneous back-and-
forth comparisons between slightly different versions of each, so I
went quite bit beyond evaluating the numbers. I treated them as
works of art that I considered unfinished until I had reached the
point where I could find no further way to improve them.

--George

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> Hi again Gene,
>
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> >
> > > ... Of course I'm not even convinced that Bach didn't
> > > use meantone, or something close to it, for WTC I,
> > > since as yet no one has put forward a historical argument
> > > that he couldn't have.
> >
> >
> >
> > Have you ever tried to play anything in Db-major in
> > a 1/4-meantone chain-of-5ths tuned from Eb to G#?
> >
> > I have, and i'd rather listen to a pack of howling wolves
> > than to that. Doesn't work, plain and simple -- and
> > WTC I most definitely has pieces in Db-major.
> >
> > Now, admittedly, a milder version of meantone wouldn't
> > be as bad ... but for the stronger versions, forget it.
>
>
>
> Ah, i see from your very next post that you must
> be talking about *extended* meantone, and not the
> Eb-to-G# version ...

Nope -- Gene is talking about a different 12-note meantone compass
for each piece.

> but on any typical _Klavier_,
> the meantone can only be extended if the performer
> retunes some notes between performances of pieces
> in different keys.

Well, I'd think of "extended meantone" as implying more than 12
pitches in a particular piece.

> So the 12-tone version is the one
> we really should be discussing for the case of trying
> to determine Bach's actual keyboard tuning.

Why would you assume there was *one* keyboard tuning when it was
common practice at the time to retune between pieces? This is an
assumption that others here have made, and it may be true, but there
was no need to pin this assumption behind Gene's posts, which had
nothing to do with it.

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > Have you ever tried to play anything in Db-major in
> > a 1/4-meantone chain-of-5ths tuned from Eb to G#?
>
> Clearly you haven't read the relevant discussion on WTC I
> that occured on this list, Monz. The rule that was found
> to work for WTC is to use a 12-note meantone compass that
> includes the 7 notes of the stated key signature, 1 more
> on the flat side, and 4 more on the sharp side. One has
> to retune the clavier for each piece, of course, but that
> was common practice throughout the meantone era.

I've read almost every post in this discussion, some in
more depth than others. I thought the topic i was addressing
here was the effort to uncover which fixed 12-tone tuning
would have been favored by Bach.

> > I have, and i'd rather listen to a pack of howling wolves
> > than to that. Doesn't work, plain and simple -- and
> > WTC I most definitely has pieces in Db-major.
>
> Obviously. Gene has done so much work in this area that,
> if I were Gene, I'd probably find this remark to be an
> insult to my intelligence.

Sheesh, Paul ... please, lighten up. I'm just putting
in my 2 cents, and not trying to criticize anyone else's
work or intelligence. Anyway ...

> But I'd also try to smile about it :)

OK, that's better.

> > Now, admittedly, a milder version of meantone wouldn't
> > be as bad ... but for the stronger versions, forget it.
>
> Now, why did you choose to interpret Gene's remark as
> implying a 1/4-meantone chain-of-5ths tuned from Eb to G#,
> when you yourself have primarily interpreted and
> implemented meantone in a more general and flexible manner?

I should have written more in my post. It just so
happens that one of my adult students has had his piano
tuned in 1/4-comma meantone for a few months, and at
his lesson yesterday i was talking about the last
movement of Mahler's 9th Symphony, which is in Db-major,
and i tried to play the opening of it for him ... but
of course, on his piano, as soon as i play the first
Db chord it sounded horrible.

:-)

The moral of the story is: i should just stay out of
discussions on this list if i'm not in a "tuning list
addiction" phase. My mind and time are too preoccupied
right now with Tonescape and our new website.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > So the 12-tone version is the one
> > we really should be discussing for the case of trying
> > to determine Bach's actual keyboard tuning.
>
> Why would you assume there was *one* keyboard tuning
> when it was common practice at the time to retune between
> pieces? This is an assumption that others here have made,
> and it may be true, but there was no need to pin this
> assumption behind Gene's posts, which had nothing to do
> with it.

OK, thanks for the clarifications. I didn't realize that
we're going under the assumption now that keyboard players
did that much retuning while performing, so i stand corrected.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> Hi Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > >
> > > So the 12-tone version is the one
> > > we really should be discussing for the case of trying
> > > to determine Bach's actual keyboard tuning.
> >
> > Why would you assume there was *one* keyboard tuning
> > when it was common practice at the time to retune between
> > pieces? This is an assumption that others here have made,
> > and it may be true, but there was no need to pin this
> > assumption behind Gene's posts, which had nothing to do
> > with it.
>
>
> OK, thanks for the clarifications. I didn't realize that
> we're going under the assumption now that keyboard players
> did that much retuning while performing, so i stand corrected.

We're not going under that assumption now -- it's just that not
everyone here has made the opposite assumption (that the tuning was
utterly fixed and never changed).

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> Clearly you haven't read the relevant discussion on WTC I that
> occured on this list, Monz. The rule that was found to work for WTC
> is to use a 12-note meantone compass that includes the 7 notes of
the
> stated key signature, 1 more on the flat side, and 4 more on the
> sharp side. One has to retune the clavier for each piece, of
course,
> but that was common practice throughout the meantone era.

"Rule that was found to work for WTC" how? The C# minor fugue of
book 1 has at least 14 different notes in it. G, D, A, E, B, F#, C#,
G#, D#, A#, E#, B#, Fx, and Cx. Each time we come around 12 notes in
any 12-note temperament we've got a Pythagorean comma to gain or
lose, whether gracefully or clunkily. (See pp214-218 of my article,
part 2, for more thorough discussion of this....)

Or if we venture out to the inventions/sinfonias: the E major
invention has 13 notes from D to Cx. The A minor has both G# and Ab.
The D minor sinfonia has both D# and Eb. The E minor sinfonia has 14
notes from Eb-Bb up to D#-A#. The F minor sinfonia has 15, from Bbb-
Fb up to A-E-B.

And the first Duetto (BWV 802) makes a virtue of shifting enharmonics
within its main theme, smacking us in the face variously with A#-Bb,
E#-F, C#-Db, and G#-Ab as the piece goes along. If the instrument's
not set up to handle all that stuff gracefully, or the other weird
stuff thrown at it by the other three Duetti, it's not fit to play
the rest of the book (Clavieruebung III) either.

My file explaining that, including scores of all four of those:
http://em.oxfordjournals.org/cgi/content/full/33/2/211/DC1
(I hope to get a new link to that *outside* the subscription area
soon!)

Brad Lehman

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@u...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> >
> > Clearly you haven't read the relevant discussion on WTC I that
> > occured on this list, Monz. The rule that was found to work for
WTC
> > is to use a 12-note meantone compass that includes the 7 notes of
> the
> > stated key signature, 1 more on the flat side, and 4 more on the
> > sharp side. One has to retune the clavier for each piece, of
> course,
> > but that was common practice throughout the meantone era.
>
>
> "Rule that was found to work for WTC" how?

Only for WTC I, and only according to two people. Everett Hafner, in:

Hafner, Everett. "The Forty-Eight Revisited in Thirty-One", Well
Tempered Notes, November 1974, Motorola Scalatron Inc.

and Gene Ward Smith, who corroborated these findings. I remain
agnostic.

> The C# minor fugue of
> book 1 has at least 14 different notes in it. G, D, A, E, B, F#,
C#,
> G#, D#, A#, E#, B#, Fx, and Cx.

Yes, Hafner and Smith are claiming that if you follow the particular
strategy in question of matching the 12-note compass to the key
signature, the "incorrect" notes (the ones that would be tuned
differently if one had an extended-meantone instrument) occur only in
passing, and their mistuning is not disturbing.

> Each time we come around 12 notes in
> any 12-note temperament we've got a Pythagorean comma to gain or
> lose, whether gracefully or clunkily.

I'm well aware of this, but thanks! Bach's music, unlike Beethoven's,
doesn't appear to make use of the ability to go all the way around
the circle of 12 fifths (or any equivalent enharmonic modulation) in
a single piece, though. While a circulating well-temperament was
certainly essential to render most of Bach's music on a 12-note
keyboard, I don't think any of it is impossible in a sufficiently
extended meantone -- while Beethoven's certainly is (unless you're
happy with the Appassionata starting in F minor and ending in a key
of Abbbb minor! :))

> Or if we venture out to the inventions/sinfonias:

This was *only* intended to apply to WTC I, nothing else.

> the E major
> invention has 13 notes from D to Cx. The A minor has both G# and
Ab.
> The D minor sinfonia has both D# and Eb. The E minor sinfonia has
14
> notes from Eb-Bb up to D#-A#. The F minor sinfonia has 15, from
Bbb-
> Fb up to A-E-B.

I think all of these would be possible in extended meantone, with
enough pitches per octave to distinguish all these notes. The exact
equivalence of what we call "enharmonic equivalents" today would have
been a practical necessity on 12-note keyboards, but wasn't a
*musical* necessity until abour the time of Beethoven.

> And the first Duetto (BWV 802) makes a virtue of shifting
enharmonics
> within its main theme, smacking us in the face variously with A#-
Bb,
> E#-F, C#-Db, and G#-Ab as the piece goes along. If the
instrument's
> not set up to handle all that stuff gracefully, or the other weird
> stuff thrown at it by the other three Duetti, it's not fit to play
> the rest of the book (Clavieruebung III) either.

The Hafner idea is that the keyboard would be retuned for each piece,
at least for WTC I.

> Each time we come around 12 notes in
> any 12-note temperament we've got a Pythagorean comma to gain or
> lose, whether gracefully or clunkily.

p.s. One other nifty piece of Bach's not to neglect: the modulation
canon of the Musical Offering. Each time it's played it has the
canonic theme enter in two different minor keys, moving up the spiral
of 5ths. If we play it merely six times, i.e. using 12 different
minor scales along the way, we've already moved from the beginning C
minor all the way up to B# minor; and it can keep going as long as we
like.

Arguably, there should also be some steady progression of character--
something smooth rather than jumpy, if there's a change at all--from
each minor scale to the next as its tonic moves up the spiral of 5ths
to the next position. [If there's variety, gentle/smooth variety
with some logical flow to it; or if there's no variety, why bother
modulating at all?]

Given that each scale shares most of its notes with the next one, the
simplest way to make a gradual and logical change is to have the new
note that's coming in be slightly more pure or impure than the one
that is dropping out of the set. Pure/impure in the context of the
remaining six notes, melodically.... It's all relative proportions
on this rotating thingy where we can lay down a tonic, and then see
where the other six notes of the diatonic scale are vis-a-vis the
slope of their positions in a *regular* ("meantone") generation of
the notes. Are they pure or impure off that context of regularity,
and in which direction, and how much?

Hence my graph at
http://www-personal.umich.edu/~bpl/larips/enharmonic.html
where you can make a little overlay card with a window in it, as wide
as seven positions. Slide it side to side and look at the shape of
the graph, being different at all 12 positions before it starts to
repeat itself (one Pythagorean comma away, in either direction).

Brad Lehman

> > The C# minor fugue of
> > book 1 has at least 14 different notes in it. G, D, A, E, B, F#,
> C#,
> > G#, D#, A#, E#, B#, Fx, and Cx.
>
> Yes, Hafner and Smith are claiming that if you follow the
particular
> strategy in question of matching the 12-note compass to the key
> signature, the "incorrect" notes (the ones that would be tuned
> differently if one had an extended-meantone instrument) occur only
in
> passing, and their mistuning is not disturbing.

The G, D, Fx, and Cx occur in accented *thematic* positions in this
piece...anything but passing-note situations! This fugue has real
entrances of its subject in SIX different keys. And it gives us all
of the following diminished 4ths in melodic contexts: B#-E, Fx-B, E#-
A, Cx-F#, D#-G, A#-D.

Brad Lehman

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

> > > The C# minor fugue of
> > > book 1 has at least 14 different notes in it. G, D, A, E, B,
F#,
> > C#,
> > > G#, D#, A#, E#, B#, Fx, and Cx.
> >
> > Yes, Hafner and Smith are claiming that if you follow the
> particular
> > strategy in question of matching the 12-note compass to the key
> > signature, the "incorrect" notes (the ones that would be tuned
> > differently if one had an extended-meantone instrument) occur
only
> in
> > passing, and their mistuning is not disturbing.
>
>
> The G, D, Fx, and Cx occur in accented *thematic* positions in this
> piece...anything but passing-note situations!

Well, I'll leave it to Gene to try to rebut this, since he was the
one who seemed to defend or support Hafner's thesis.

P.S. My aim here is not to pit list member against list member; it's
to encourage dialogue and debate toward the end of mutual
enlighenment and enlightenment of the readership of the list.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> I think all of these would be possible in extended meantone,
> with enough pitches per octave to distinguish all these
> notes. The exact equivalence of what we call "enharmonic
> equivalents" today would have been a practical necessity
> on 12-note keyboards, but wasn't a *musical* necessity
> until abour the time of Beethoven.

And as i'm finding out, it's generally only a necessity
for Beethoven with his piano music.

I've been making Tonescape files of quite a bit of his
string quartet music, and have been very surprised to
find that Beethoven's notation keeps using a 15-tone
chain-of-5ths, generators -5 ... +9, with 3 pairs of
"enharmonically-equivalent" notes.

I'm rendering these pieces in 1/6-comma meantone,
so that these are actually 3 pairs of notes which are
close but not the same -- the flats are ~19.55256881
cents higher than the sharps.

I found it *very* interesting that while the keys of
three pieces i've worked on are very different --
namely, Eb-major, Bb-minor, and E-major -- when the
tonic of each key is used as the origin (1/1),
the *structure* of the lattice is exactly the same
in each case!

That's a discovery which might not have ever been made
without Tonescape, which makes *me* feel real good!

-monz
http://tonalsoft.com
Tonescape microtonal music software

Thirded.

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> Let me second this -- Aaron, if you are looking for well-
> temperaments with subtle shimmer properties -- actually, a
> wealth of synchronized beatings -- you might not be able to
> do any better than these two.

//
> >
> > You might be interested in the Wendell well temperaments:
> >
> > ! wendell1.scl
> > !
> > Robert Wendell's Natural Synchronous well-temperament (2003)
> > 12
> > !
> > 94.16800
> > 198.17100
> > 298.07800
> > 393.68000
> > 4/3
> > 597.59000
> > 699.49200
> > 796.12300
> > 895.75700
> > 1000.03300
> > 1095.63500
> > 2/1
> >
> > ! wendell2.scl
> > !
> > Robert Wendell's Very Mild Synchronous well-temperament (2003)
> > 12
> > !
> > 94.93100
> > 198.79700
> > 298.84100
> > 394.11360
> > 498.44500
> > 598.02400
> > 700.05800
> > 796.88600
> > 895.75900
> > 1000.79600
> > 1096.06900
> > 2/1

> > Yes, Hafner and Smith are claiming that if you follow the
> > particular strategy in question of matching the 12-note
> > compass to the key signature, the "incorrect" notes (the
> > ones that would be tuned differently if one had an extended-
> > meantone instrument) occur only in passing, and their
> > mistuning is not disturbing.
>
>
> The G, D, Fx, and Cx occur in accented *thematic* positions in this
> piece...anything but passing-note situations! This fugue has real
> entrances of its subject in SIX different keys. And it gives us all
> of the following diminished 4ths in melodic contexts: B#-E, Fx-B, E#-
> A, Cx-F#, D#-G, A#-D.
>
>
> Brad Lehman

I thought Gene's meantone WTC renderings sounded wrong. Again,
that's subjective, but why would Bach call the work the
Well Tempered Clavier if he intended it to be played in meantone?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> I thought Gene's meantone WTC renderings sounded wrong.

They did the first time I listened, but he said he had dome something
wrong, and I haven't done a full listening of the subsequent corrected
versions.

> Again,
> that's subjective,

It's also subjective that Bach was one of the greatest composers of all
time. The appreciation of music is itself a very subjective thing. And
there's no truer test of the success or failure of a particular musical
choice than its subjective effect on a listener in the relevant musical
context. The only bit of "objectivity" that we can reach here is if
different listeners happen to agree with one another.

> but why would Bach call the work the
> Well Tempered Clavier if he intended it to be played in meantone?

Good question -- I don't know, but rememeber for one thing that
meantone wasn't called "meantone" at the time . . .

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> I thought Gene's meantone WTC renderings sounded wrong.

What do you think of my extended meantone rendering of BWV 803? I've
put it in tuning files, under files/31 equal. If I wasn't following
the suggested tuning for WTC I, I would have made a few changes.

Again,
> that's subjective, but why would Bach call the work the
> Well Tempered Clavier if he intended it to be played in meantone?

I don't think we know what Bach meant by "well-tempered", do we? For
all I know, at any rate, he meant "appropriately tuned". Can any of
the music history mavens tell us what, if anything, is known about
what Bach meant by the phrase?

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

> And as i'm finding out, it's generally only a necessity
> for Beethoven with his piano music.

What would be an example of where you thought it necessary? It seems
to be that the difficulties of transcribing music to extended meantone
have been exaggerated, because people fail to realize how often the
problems can be solved by a willingness to occasionally use a subminor
third in place of a minor one, or even (especially in fast passages) a
supermajor third in place of a major one.

> That's a discovery which might not have ever been made
> without Tonescape, which makes *me* feel real good!

Tonescape is great for musical discoveries of that sort.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> Well, I'll leave it to Gene to try to rebut this, since he was the
> one who seemed to defend or support Hafner's thesis.

I thought Hafner's thesis was very interesting and possibly correct, but
if I was going to do a meantone version of WTC I I would not always
have tuned it his way.

In a message dated 8/19/2005 6:14:34 PM Eastern Standard Time,
gwsmith@svpal.org writes:
Can any of
the music history mavens tell us what, if anything, is known about
what Bach meant by the phrase?

"Wohl-temperirt"? Maybe you missed it, but it is wholly and fully a term
used by Werckmeister in publishing his tunings. Bach MUST have known that it
meant "good enough" to transverse all the keys of the Halberstadt keyboard.
Remember also, Werckmeister was chosen by the city of Halberstadt to work there
for the last 10 years of his life.

Johnny

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > And as i'm finding out, it's generally only a necessity
> > for Beethoven with his piano music.
>
> What would be an example of where you thought it necessary?
> It seems to be that the difficulties of transcribing music
> to extended meantone have been exaggerated, because people
> fail to realize how often the problems can be solved by a
> willingness to occasionally use a subminor third in place
> of a minor one, or even (especially in fast passages) a
> supermajor third in place of a major one.

There are cases in Beethoven's music (and Mozart's) where,
for example, a G# occurs in one measure and is tied to
an Ab in the next measure.

I wouldn't rule out "comma shifts" where those are two
different pitches (in extended meantone) ... but where
notes are tied, we should probably assume that the
composer intends for them to be the same pitch.

> > That's a discovery which might not have ever been made
> > without Tonescape, which makes *me* feel real good!
>
> Tonescape is great for musical discoveries of that sort.

Thanks. It's also great for *composing* microtonal music
... but i have yet to convince *you* of that. (But i will!
Just give me some more time ...)

-monz
http://tonalsoft.com
Tonescape microtonal music software

> It's also subjective that Bach was one of the greatest composers
> of all time. The appreciation of music is itself a very subjective
> thing. And there's no truer test of the success or failure of a
> particular musical choice than its subjective effect on a listener
> in the relevant musical context. The only bit of "objectivity" that
> we can reach here is if different listeners happen to agree with
> one another.

Now that's a good idea. I'd also be open to revisiting a
Barnes-like statistical approach.

> > but why would Bach call the work the
> > Well Tempered Clavier if he intended it to be played in meantone?
>
> Good question -- I don't know, but rememeber for one thing that
> meantone wasn't called "meantone" at the time . . .

Clearly Bach was referring to a non-meantone tuning in which the
entire work was playable.

-Carl

> > I thought Gene's meantone WTC renderings sounded wrong.
>
> What do you think of my extended meantone rendering of BWV 803?
> I've put it in tuning files, under files/31 equal. If I wasn't
> following the suggested tuning for WTC I, I would have made a few
> changes.

I don't hear the kind of melodic problems I did when you first
produced these tests, though this piece is hardly the acid test
of this approach.

How many notes in the scale here?

> > Again, that's subjective, but why would Bach call the work
> > the Well Tempered Clavier if he intended it to be played in
> > meantone?
>
> I don't think we know what Bach meant by "well-tempered", do we?
> For all I know, at any rate, he meant "appropriately tuned". Can
> any of the music history mavens tell us what, if anything, is
> known about what Bach meant by the phrase?

The overwhelming consensus among Bach biographers I have read
is that he was one (not the only one) champion of circulating
temperaments around this time. Whether or not all this could
have been fabricated by biographers over time is a question I'm
not qualified to answer.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > Well, I'll leave it to Gene to try to rebut this, since he was the
> > one who seemed to defend or support Hafner's thesis.
>
> I thought Hafner's thesis was very interesting and possibly correct,
but
> if I was going to do a meantone version of WTC I I would not always
> have tuned it his way.

Well, I'd still like to see some more detail on what happens in the C#
minor prelude that came up here if we are to accept that Hafner's
thesis is "possibly correct". Perhaps the "wrong" notes only occur
against other "wrong" notes so all the harmonies actually turn out
right?

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> Hi Gene,
>
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > > And as i'm finding out, it's generally only a necessity
> > > for Beethoven with his piano music.
> >
> > What would be an example of where you thought it necessary?
> > It seems to be that the difficulties of transcribing music
> > to extended meantone have been exaggerated, because people
> > fail to realize how often the problems can be solved by a
> > willingness to occasionally use a subminor third in place
> > of a minor one, or even (especially in fast passages) a
> > supermajor third in place of a major one.

To me that's almost like saying the difficulties of arthritis have
been exaggerated because people fail to realize how often the
problems can be solved by a willingness to occasionally amputate a
limb :)

> There are cases in Beethoven's music (and Mozart's) where,
> for example, a G# occurs in one measure and is tied to
> an Ab in the next measure.

More starkly, in Beethoven's writing, there are examples of
enharmonic modulation, where the entire key signature is abruptly re-
interpreted from one with a lot of sharps to one with a lot of flats,
and generally some notes are tied across the change. Beethoven's
Appasionata Sonata would end in a key 24 steps flatter on the chain
of fifths than it began if we assumed that the music was truly in
meantone and the enharmonic modulations were purely for notational
convenience. Since composers at the time always ended in the same key
as they began, such an assumption seems pretty outlandish to me.

Not too long ago, someone here brought up an orchestral score where
different (transposing) instruments would be playing 12 steps apart
on the chain of fifths in several sections of the music if one
interpreted the score literally in extended meantone. I hope this
person will speak up and contribute again. By the 19th century, I
think it's hard to find a significant orchestral score where this
*doesn't* happen.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> More starkly, in Beethoven's writing, there are examples of
> enharmonic modulation, where the entire key signature is abruptly re-
> interpreted from one with a lot of sharps to one with a lot of flats,
> and generally some notes are tied across the change. Beethoven's
> Appasionata Sonata would end in a key 24 steps flatter on the chain
> of fifths than it began if we assumed that the music was truly in
> meantone and the enharmonic modulations were purely for notational
> convenience. Since composers at the time always ended in the same key
> as they began, such an assumption seems pretty outlandish to me.

Is that the third movement? It might be interesting to see if the
Appasionata could be plausibly put into meantone. My point is not that
it always works, but that it can seemingly be done more often than not
in common practice music. Did you think my recent extended meantone
versions of Wagner and Brahms made sense?

> Not too long ago, someone here brought up an orchestral score where
> different (transposing) instruments would be playing 12 steps apart
> on the chain of fifths in several sections of the music if one
> interpreted the score literally in extended meantone.

As I pointed out in the discussion of the Mozart quintet, there's no
reason to think you *should* always interpret the score literally.

I hope this
> person will speak up and contribute again. By the 19th century, I
> think it's hard to find a significant orchestral score where this
> *doesn't* happen.

And when it does, how often does it matter?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> How many notes in the scale here?

WWV 803 ranges from Gb to D# in my version; the Brahms quartet
movement from Cb to D#.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Did you think my recent extended meantone
> versions of Wagner and Brahms made sense?

I just listened to the latest Brahms, and the intonation was very
beautiful except for a few brief moments (which is what happens with
good human ensembles anyway), but on my computer the music sounded like
it was recorded backwards -- that is, the envelopes seemed to be
reversed. So it was hard to get "into" the music.

Anyway, I think late Schubert (is it Quartet #15 with the relentless
major-third modulations) might be a far tougher test than any Brahms.

I'll have to check out the Wagner some other time.

> > Not too long ago, someone here brought up an orchestral score where
> > different (transposing) instruments would be playing 12 steps apart
> > on the chain of fifths in several sections of the music if one
> > interpreted the score literally in extended meantone.
>
> As I pointed out in the discussion of the Mozart quintet, there's no
> reason to think you *should* always interpret the score literally.

But in the context of enharmonic modulations, you have an enharmonic
shift that has to occur somewhere -- if you change the score to
eliminate it from one place, it'll have to pop up somewhere else, or
else the music would have to end 12 or 24 or some other number of
fifths away from where it began.

> I hope this
> > person will speak up and contribute again. By the 19th century, I
> > think it's hard to find a significant orchestral score where this
> > *doesn't* happen.
>
> And when it does, how often does it matter?

It often matters, because *all* the instruments are undergoing
enharmonic modulation, but these enharmonic modulations aren't
typically notated in the same place in the score for each instrument
because (I'm claiming) enharmonic modulation is meant to be inaudible
and the notation is chosen purely for convenience. In meantone, it
would be quite audible where you put the enharmonic shift, and I don't
believe many of the composers in question would have approved of the
sound of such a shift.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> I just listened to the latest Brahms, and the intonation was very
> beautiful except for a few brief moments (which is what happens with
> good human ensembles anyway), but on my computer the music sounded like
> it was recorded backwards -- that is, the envelopes seemed to be
> reversed. So it was hard to get "into" the music.

Hmmm...maybe I'd better see if I can improve it. Does anyone have any
ideas about this?

> Anyway, I think late Schubert (is it Quartet #15 with the relentless
> major-third modulations) might be a far tougher test than any Brahms.

The last few Schubert quartets are great stuff, and you could be
right. Schubert loved relationships of a major third, which are more
of a problem in meantone that fifths.

> > How many notes in the scale here?
>
> WWV 803 ranges from Gb to D# in my version;

So 16 notes? That's not consistent with Hafner's thesis,
is it?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > > How many notes in the scale here?
> >
> > WWV 803 ranges from Gb to D# in my version;
>
> So 16 notes? That's not consistent with Hafner's thesis,
> is it?

His thesis is only about WTC, Book I.

> > > > How many notes in the scale here?
> > >
> > > WWV 803 ranges from Gb to D# in my version;
> >
> > So 16 notes? That's not consistent with Hafner's thesis,
> > is it?
>
> His thesis is only about WTC, Book I.

Ok, but it breaks authenticity. It's still a great project
as far as hearing these works in a more consonant tuning.
Bach would probably have approved.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> Ok, but it breaks authenticity. It's still a great project
> as far as hearing these works in a more consonant tuning.
> Bach would probably have approved.

Authenticity is what I was thinking about with my question about
chamber music. It's pretty hard to argue, before Schoenberg, that to
be authentic a string quartet has to be in 12 equal.

> > Ok, but it breaks authenticity. It's still a great project
> > as far as hearing these works in a more consonant tuning.
> > Bach would probably have approved.
>
> Authenticity is what I was thinking about with my question
> about chamber music. It's pretty hard to argue, before
> Schoenberg, that to be authentic a string quartet has to be
> in 12 equal.

No 'fixed scale' (where notes in the score map to one or only
a few notes in the scale) is authentic for string quartets,
since it isn't known how string quartets tend to play, or
indeed if they tend to play a certain way at all.

My own feeling is that adaptive JI is a good model, except
that intonation does change while "notes" (stringed instruments
don't even play notes in the same sense that keyboards do)
are sounding and the ability to hit JI is generally not very
good (compared to a computer) and probably scales with the
length of the chord (as research posted here by Manuel years
ago suggested).

Of course, just because so few string quartets have anywhere
near a computer's skill at hitting pure intervals doesn't
mean we should make our computer renditions farther from
pure -- authenticity and listener enjoyment aren't necessarily
the same thing. Though the main improvement to be made in
computer reditions of string music, in both enjoyment and
authenticity departments, isn't tuning at all, but what
happens at note boundaries and transitions -- the demos at
www.synful.com convinced me of that.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> No 'fixed scale' (where notes in the score map to one or only
> a few notes in the scale) is authentic for string quartets,
> since it isn't known how string quartets tend to play, or
> indeed if they tend to play a certain way at all.

This just says no system, including adaptive JI, is authentic. Isn't
it more reasonable to say both 12 equal and extended meantone can
count as authentic?

> Of course, just because so few string quartets have anywhere
> near a computer's skill at hitting pure intervals doesn't
> mean we should make our computer renditions farther from
> pure -- authenticity and listener enjoyment aren't necessarily
> the same thing. Though the main improvement to be made in
> computer reditions of string music, in both enjoyment and
> authenticity departments, isn't tuning at all, but what
> happens at note boundaries and transitions -- the demos at
> www.synful.com convinced me of that.

So how can that be translated to midi?

> > No 'fixed scale' (where notes in the score map to one or only
> > a few notes in the scale) is authentic for string quartets,
> > since it isn't known how string quartets tend to play, or
> > indeed if they tend to play a certain way at all.
>
> This just says no system, including adaptive JI, is authentic.

Right.

> Isn't it more reasonable to say both 12 equal and extended
> meantone can count as authentic?

I don't think so.

> > Of course, just because so few string quartets have anywhere
> > near a computer's skill at hitting pure intervals doesn't
> > mean we should make our computer renditions farther from
> > pure -- authenticity and listener enjoyment aren't necessarily
> > the same thing. Though the main improvement to be made in
> > computer reditions of string music, in both enjoyment and
> > authenticity departments, isn't tuning at all, but what
> > happens at note boundaries and transitions -- the demos at
> > www.synful.com convinced me of that.
>
> So how can that be translated to midi?

Not easily, since MIDI wasn't designed to capture string
articulations. The thing that Eric's done is translate MIDI
to it.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Though the main improvement to be made in
> computer reditions of string music, in both enjoyment and
> authenticity departments, isn't tuning at all, but what
> happens at note boundaries and transitions -- the demos at
> www.synful.com convinced me of that.

Carl, thanks for pointing out that product (I think you've mentioned
it before?) - it really *is* remarkable. When I finishing mixing and
deliver my current project, I'm going to install the demo and see how
hard it would be to do microtonal stuff with it. Do you have any
contact/connection with the dev, in that we might find an ear for
adding native tuning support?

In the last 12-18 months I've seen a noticeable uptick in interest,
support, and use of non-12 in the soft instrument community. Somewhere
there will be a tipping point.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:

> Carl, thanks for pointing out that product (I think you've mentioned
> it before?) - it really *is* remarkable. When I finishing mixing and
> deliver my current project, I'm going to install the demo and see how
> hard it would be to do microtonal stuff with it.

Note you need at least 256 meg of memory, and 1/2 gig is probably
better. Then, you still have to figure out how to get it to work. It
might be worth upgrading my computer if I was confident I could make
the damn thing work.

Do you have any
> contact/connection with the dev, in that we might find an ear for
> adding native tuning support?

I think it can render a pitch-bended midi file; maybe Carl can tell us.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Note you need at least 256 meg of memory, and 1/2 gig is probably
> better.

I've got 2g, and virtually all the current soft instruments, samplers,
etc, need at least 512mb. Memory is cheap these days, at least the
silicon kind.

> Then, you still have to figure out how to get it to work.

Nothing new there! :) I've been digging into Sonar a lot on my current
project, and it is great to have a semi-commissioned piece that I can
also use as a big learning project. I love having 3 or 4 instruments,
all in non12 tunings, playing realtime simultaneously. Compared to
what I've had to do in the past, today is a dream world by comparison.

> It might be worth upgrading my computer if I was confident I could
> make the damn thing work.

I don't ever pretend to know an individual's personal financial
situations, but I'd bet its worth upgrading your computer no matter
what. Most of the slaps to my forehead came when realizing, after some
upgrade, just how hindered I had caused myself to be.

> I think it can render a pitch-bended midi file; maybe Carl can tell us.

Too bad. Pitch bend isn't a route that works for me.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
>
> > Ok, but it breaks authenticity. It's still a great project
> > as far as hearing these works in a more consonant tuning.
> > Bach would probably have approved.
>
> Authenticity is what I was thinking about with my question
> about chamber music. It's pretty hard to argue, before
> Schoenberg, that to be authentic a string quartet has to be
> in 12 equal.

I'm fairly certain that Schoenberg was the first composer
to insist that a string quartet tune to 12-edo. Peter Yates
witnessed rehearsals, and wrote that it cast a strange patina
over the music ... that's an image i like for comparing
12-edo to JI. (just to substantiate what you wrote)

-monz

> > Though the main improvement to be made in
> > computer reditions of string music, in both enjoyment and
> > authenticity departments, isn't tuning at all, but what
> > happens at note boundaries and transitions -- the demos at
> > www.synful.com convinced me of that.
>
> Carl, thanks for pointing out that product (I think you've
> mentioned it before?) - it really *is* remarkable. When I
> finishing mixing and deliver my current project, I'm going
> to install the demo and see how hard it would be to do
> microtonal stuff with it. Do you have any contact/connection
> with the dev, in that we might find an ear for adding native
> tuning support?
>
> In the last 12-18 months I've seen a noticeable uptick in
> interest, support, and use of non-12 in the soft instrument
> community. Somewhere there will be a tipping point.

Eric and I had fairly extensive discussions about tuning support
over lunch one day. He's interested, and he basically agreed to
implement .tun support in the next version. Since I left
Keyboard (big mistake, that) I haven't kept up... don't even
know if it isn't already implemented! He's got lots of other
very cool features in mind too. We also talked about adaptive
tuning, and he was interested.

-Carl

> > It might be worth upgrading my computer if I was confident I
> > could make the damn thing work.
>
> I don't ever pretend to know an individual's personal financial
> situations, but I'd bet its worth upgrading your computer no matter
> what. Most of the slaps to my forehead came when realizing, after
> some upgrade, just how hindered I had caused myself to be.

Jon's right, Gene. You can get the kind of firepower you need (plus
a flat panel monitor to save your eyes) for $700 or so from Dell.

> > I think it can render a pitch-bended midi file; maybe Carl can
> > tell us.

Actually it might not, since it interprets MIDI events in a very
special way.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Eric and I had fairly extensive discussions about tuning support
> over lunch one day. He's interested, and he basically agreed to
> implement .tun support in the next version. Since I left
> Keyboard (big mistake, that) I haven't kept up... don't even
> know if it isn't already implemented! He's got lots of other
> very cool features in mind too. We also talked about adaptive
> tuning, and he was interested.

One of the aspects that is very interesting about this is that,
because of their technology, the program is geared towards single
instruments (with a promise of sections to come). But most of the
people who are writing microtonal music to eventually be played by
traditional acoustic musicians are primarily writing chamber music
(i.e. there aren't a lot of 'us' writing full orchestral symphonies or
whatever). And Synful could really portray those chamber pieces in a
very, very convincing fashion. For instance, I can imagine Joe Pehrson
working on his piece for cello and electronics this way.

As I said before, I'll try to check out the demo, and I'll see if
there is any mention in there about .tun or other micro. But being
that it *isn't* sample based, it is going to be a _heck_ of a lot
easier for him to implement it!

Cheers,
Jon

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> Eric and I had fairly extensive discussions about tuning support
> over lunch one day. He's interested, and he basically agreed to
> implement .tun support in the next version. Since I left
> Keyboard (big mistake, that) I haven't kept up... don't even
> know if it isn't already implemented! He's got lots of other
> very cool features in mind too. We also talked about adaptive
> tuning, and he was interested.

If you could convince him to support both pitch bend and MTS it would
be great. Not to mention, it would be nice if the program simply
installed, and then worked.

> > Eric and I had fairly extensive discussions about tuning support
> > over lunch one day. He's interested, and he basically agreed to
> > implement .tun support in the next version. Since I left
> > Keyboard (big mistake, that) I haven't kept up... don't even
> > know if it isn't already implemented! He's got lots of other
> > very cool features in mind too. We also talked about adaptive
> > tuning, and he was interested.
>
> One of the aspects that is very interesting about this is that,
> because of their technology, the program is geared towards single
> instruments (with a promise of sections to come).

Note that one can create entire orchestras of single intruments
as easily (processing power aside) as chamber groups with the
software as it is.

-Carl

> > Eric and I had fairly extensive discussions about tuning support
> > over lunch one day. He's interested, and he basically agreed to
> > implement .tun support in the next version. Since I left
> > Keyboard (big mistake, that) I haven't kept up... don't even
> > know if it isn't already implemented! He's got lots of other
> > very cool features in mind too. We also talked about adaptive
> > tuning, and he was interested.
>
> If you could convince him to support both pitch bend and MTS it
> would be great.

Because of the way he has to interpret pitch bends, that might
never work if it doesn't currently. MTS would be ideal.

> Not to mention, it would be nice if the program simply installed,
> and then worked.

I'm not sure what kind of problems you're having.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Note that one can create entire orchestras of single intruments
> as easily (processing power aside) as chamber groups with the
> software as it is.

Not easily. And processing power can't be set 'aside'. Stacking 16
tracks of first (solo) violins is never going to be as easy as calling
up a section patch.

Jon

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> I'm not sure what kind of problems you're having.

In the first place, I need a computer upgrade to run it. Synful requires
1/3 gig of memory, and wants a gig of CPU speed, though if you aren't
worried about realtime that probably doesn't matter. However, even if
you've got a powerful enough computer, Synful will not run. It isn't a
stand-alone program. "Synful Orchestra is a plugin program that cannot
run by itself." So it seems to me you could pay $1000 for a new
computer and still not get it to work. You'd have to futz around
buying even more stuff until you found what would make it work,
presuming you are lucky.

It would be nice if the thing just ran, or if there was some clearcut
way of getting it run. It would also be nice if it wasn't so
demanding, given that not everyone is going to care about realtime.

> In the first place, I need a computer upgrade to run it. Synful
> requires 1/3 gig of memory, and wants a gig of CPU speed,

Well get with the times... this kind of PC was standard-issue
five years ago.

> However, even if you've got a powerful enough computer, Synful
> will not run. It isn't a stand-alone program. "Synful Orchestra
> is a plugin program that cannot run by itself."

This is a very standard way to distribute software synthesizers
these days.

> So it seems to me you could pay $1000 for a new computer and
> still not get it to work.

There are plenty of free VST hosts... I sent you a list of
them and never heard back from you.

> It would be nice if the thing just ran,

I agree, I don't like the VST architecture either. But it's
the way of things.

-Carl

Carl, basically agreeing with all your points, with amplification...

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Well get with the times... this kind of PC was standard-issue
> five years ago.

Yep. And the freeing up of your personal time as things get rendered,
etc, so quickly is really hard to measure in the few $$ it takes.

> > However, even if you've got a powerful enough computer, Synful
> > will not run. It isn't a stand-alone program. "Synful Orchestra
> > is a plugin program that cannot run by itself."
>
> This is a very standard way to distribute software synthesizers
> these days.

Not only is it standard, but who wants to have a bunch of separate
applications? One host that handles all the sequencing and audio
chores, and then a nice set of plugins that give you a great variety
of musical resources. Standalone programs are from another time,
unless you can actually pipe stuff between them (Rewire or something
else), and even then it doesn't make much sense conceptually.

> There are plenty of free VST hosts... I sent you a list of
> them and never heard back from you.

They are getting better all the time, and because so many are from
small devs, the interactive nature of support and communication allows
you to influence the development of the product. I've seen very cool
things happen over at KVR, where the pool of users works in tandem
with the dev to really get new features debugged, etc.

And speaking of hosts, I'm becoming quite impressed with energyXT, all
for a paltry $50. Completely saved my ass on a project the other night
when a VST wouldn't run properly, and I simply wrapped it in eXT and
it was magic all over again.

> > It would be nice if the thing just ran,
>
> I agree, I don't like the VST architecture either. But it's
> the way of things.

I can very easily live with the VST arch., and it *is* the way of
things. I haven't been this happy about non-acoustic music since...
ever, I guess. My last step into the unknown will be if I can get
AudioMulch to work inside of Sonar, or something similar. Now _that_
would really be something!

Cheers,
Jon

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> There are plenty of free VST hosts... I sent you a list of
> them and never heard back from you.

Because they didn't work, and even if they did work, I probably need a
new computer.

> > It would be nice if the thing just ran,
>
> I agree, I don't like the VST architecture either. But it's
> the way of things.

It's selling crippleware, isn't it? What if a prospective customer
isn't interested in realtime synthesis?

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:

> Not only is it standard, but who wants to have a bunch of separate
> applications? One host that handles all the sequencing and audio
> chores, and then a nice set of plugins that give you a great variety
> of musical resources.

I don't *want* a program to do that.

> They are getting better all the time, and because so many are from
> small devs, the interactive nature of support and communication allows
> you to influence the development of the product. I've seen very cool
> things happen over at KVR, where the pool of users works in tandem
> with the dev to really get new features debugged, etc.

I couldn't even get them to work. At all.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Because they didn't work, and even if they did work, I probably need a
> new computer.

If they didn't work for you (not know exactly what "they" were), then
you probably didn't have the right computer/sound card setup. You
can't blame the software when the hardware platform is at fault.

> It's selling crippleware, isn't it?

No, it isn't. It is selling software that works for a particular purpose.

> What if a prospective customer isn't interested in realtime synthesis?

Options:
1. Start working with Csound.
2. Consider that you are a niche, and can't reasonably expect much to
come your way.
3. Consider altering some of your work/composition strategies to be
more in line with the tools that are coming available.

Just some thoughts.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I don't *want* a program to do that.

Fine, your choice. But painting yourself into a corner has to be
recognized for just that.

> I couldn't even get them to work. At all.

"Them"? No way at all to know what you mean, but there are thousands
and thousands of people using this particular protocol/technology to
make music, and many of them who have problems initially are helped
out by the user communities. It can be done, I see it day in and day
out. You either have inadequate computing resources, need for a
quality ASIO-supporting audio card, or maybe just some time to study
how this is all done and then follow the guidelines.

It may be that you'll never be able to adapt your approach to the way
the majority of computer musicians do their work, but if that is the
case, you can't complain that what is out there doesn't work or is
crippled in some way. You just haven't met them at least half way.

Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:

> If they didn't work for you (not know exactly what "they" were), then
> you probably didn't have the right computer/sound card setup. You
> can't blame the software when the hardware platform is at fault.

That was my impression. However, if I wasn't dealing with stupidware,
it wouldn't *matter*, because my computer/sound card setup ought to be
irrelevant to the problem of creating a wav file.

> > It's selling crippleware, isn't it?
>
> No, it isn't. It is selling software that works for a particular
purpose.

It's selling software which, when installed, won't work.

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:

> "Them"? No way at all to know what you mean, but there are thousands
> and thousands of people using this particular protocol/technology to
> make music, and many of them who have problems initially are helped
> out by the user communities. It can be done, I see it day in and day
> out.

Fine. Why don't you or Carl offer suggestions, then?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> That was my impression. However, if I wasn't dealing with stupidware,
> it wouldn't *matter*, because my computer/sound card setup ought to be
> irrelevant to the problem of creating a wav file.

I notice you're giving exactly zero information as to what software
didn't work for you. Besides that, if the software is meant to do
something other than, or - more importantly - very much in addition to
"creating a wav file", then there are plenty of good reasons why your
hardware wasn't up to the task.

> It's selling software which, when installed, won't work.

Since there are no exact examples that you've specified, I have to be
generic. But you give a distinct impression that you don't understand
the basic principle of "system requirements", as I'm sure most or all
of the software (the mystery software) will work if given the proper
hardware and software environment to do it's job. If you aren't
willing to make that investment, then you can't blame the software
manufacturer for not supporting an underpowered, ill-equipped computer.

Jon

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Fine. Why don't you or Carl offer suggestions, then?

I thought Carl already did. I already emailed you over a month ago
with an offer of software. Apparantly neither of us warranted an answer.

I'd offer more advice if you:

1. Gave a complete description of the intended computer you plan to be
using this on - OS, mem, cpu, drives (and speeds), audio card, input
devices.
2. Gave a detailed description of
a. what you would like to be able to accomplish
b. the methods (with details, not generalities) by which you do
what you do right now.
3. Show an indication as to whether you would consider being flexible
and adventurous in your manner of working.

Cheers,
Jon