Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Re: Bach and tuning and Paul cont.

In a message dated 8/20/01 6:05:53 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> --- In tuning@y..., Afmmjr@a... wrote:
>
> >
> > Paul, do you know what you are talking about here?
>
> I've read about Casals' concept of "expressive intonation" in many
> different sources. The idea of heightening melodic tendencies by
> shrinking diatonic half steps, and enlarging chromatic ones, seems
> always to be connected with it. I bet I could even find a post by you
> that supports this.
>

Casals considered "expressive intonation" differently; he would intuit his
intonation. You are confusing general expressiveness and heightening the of
direction of pitch in a melodic situation.

> > Casals' expressive
> > intonation might have sharps higher or lower, depending.
>
> Well then you are agreeing that the intonation would depart from that
> of a keyboard. And that is the main point I was trying to make, for
> Neil.
>
The "depending" means that sometimes the sharp is flatter and sometimes it is
sharper. I am disagreeing with you, au contraire.

> > Listen to the
> > examples of his 2 minor key suites for examples by Casals contrary
> to your
> > assertion.
>
> Are there enharmonically equivalent pairs of pitches to be compared
> in these suites? If so, tell us what you've found -- I'll take your
> word for it.
> >
>
Yes, this was a radio broadcast open to hundreds of thousands. 2 different
minor keys played differently regarding the minor third itself. Casals
played it this way, and it mirrors Werckmeister's chromatic.

> And really, keyboard only for Bach, and then a switch for other

> pieces?
>
> Can you explain this sentence? I've read it ten times, and I still
> don't know what it means.
>
I mean that it makes little sense to me for Bach to switch tunings when
Werckmeister has so many distinct tunings built into it already. If Bach
used Werckmeister, he used it consistently. All his music seems to
demonstrate that it works to treat his solo works in the same way, and the
performances that are given with this attention are even more expressive than
the alternative straight just or meantone "rationalization". If the standard
meantone was sixth-comma, why do you presuppose that Bach would want 5/4
major thirds?

> > I am
> > fast coming to the conclusion that there is a "harmony" bias to
> this list.
> > Bach was keen on melodic relationships, and these don't change in
> solos, but
> > become even more important.
>
> If you're saying that the precise melodic relationships of
> Werckmeister III are of paramount importance, that how could Casals
> get away with playing "sharps higher or lower, depending" as you say
> above?

Because his "depending" confounds standard theory.

And why do you think Kirnberger was being exclusive to keyboard regarding
Bach's tuning?

Best, Johnny Reinhard

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., Afmmjr@a... wrote:

> > Well then you are agreeing that the intonation would depart from
that
> > of a keyboard. And that is the main point I was trying to make,
for
> > Neil.
> >
> The "depending" means that sometimes the sharp is flatter and
sometimes it is
> sharper.

Right -- and on a keyboard, the sharp is always identical to the
enharmonically equivalent flat, never flatter or sharper.

> I am disagreeing with you, au contraire.

How can that be? A keyboard doesn't make sharps differ from the
enharmonically equivalent flats, at least not the keyboards Bach used
(except perhaps clavichords, I suppose).

> > > Listen to the
> > > examples of his 2 minor key suites for examples by Casals
contrary
> > to your
> > > assertion.
> >
> > Are there enharmonically equivalent pairs of pitches to be
compared
> > in these suites? If so, tell us what you've found -- I'll take
your
> > word for it.
> > >
> >
> Yes, this was a radio broadcast open to hundreds of thousands. 2
different
> minor keys played differently regarding the minor third itself.
Casals
> played it this way, and it mirrors Werckmeister's chromatic.

That's not what I'm asking you!! I said _enharmonically equivalent
pairs of pitches_ -- for example, C# and Db.
>
> > > I am
> > > fast coming to the conclusion that there is a "harmony" bias to
> > this list.
> > > Bach was keen on melodic relationships, and these don't change
in
> > solos, but
> > > become even more important.
> >
> > If you're saying that the precise melodic relationships of
> > Werckmeister III are of paramount importance, that how could
Casals
> > get away with playing "sharps higher or lower, depending" as you
say
> > above?
>
> Because his "depending" confounds standard theory.

Can you elaborate any further? What is the logical possibility that
I'm missing here? How do we transcend the law of the excluded middle?

> And why do you think Kirnberger was being exclusive to keyboard
regarding
> Bach's tuning?

Because I haven't seen any evidence to the contrary. Please bring it
forward if you have it. So far, you seem to be contradicting
yourself, because you're saying that enharmonically equivalent
pitches should be played the same, but also that they shouldn't be.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., Afmmjr@a... wrote:

> If the standard
> meantone was sixth-comma, why do you presuppose that Bach would
want 5/4
> major thirds?

First of all, where did I presuppose that Bach would want 5/4 major
thirds? I simply meant that the record we have of Bach saying "tune
all major thirds wide" was in the context, as far as I know, of
tuning a keyboard. If it referred to all instruments (which I doubt),
then yes, it may have been an indication of 1/6-comma meantone -- but
why complicate matters by bringing that in?

Secondly, even if the standard tuning taught to string players was
sixth-comma meantone, as it became in the 18th century, that by no
means precludes an adaptive approach where notes would be tweaked by
a few cents, depending on context, to improve the harmonies here or
perhaps to narrow cadential semitones there. I would expect, though,
that melodic considerations would outweigh harmonic ones in all but
the slowest of passages, as I said in a recent post.

Johnny, please understand that I'm just trying to force you to
clarify your ideas. I'm sure you have wonderful intuitions and
abilities when it comes to performing Bach. It's just that I feel
you'll have a better chance of getting those across if you can
present them in a clear, contradiction-free way.

Perhaps what you are really trying to say is that an expressive
string player would _exaggerate_ certain characteristics and
irregularities that a certain key has in Werckmeister III, hence
leading to inequalities between enharmonically equivalent pitches?
Don't know . . . just trying to fish around for the picture you're
trying to paint with these contradictions.

Highest Regards,
Paul

🔗Afmmjr@aol.com

In a message dated 8/20/01 9:07:17 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> Johnny, please understand that I'm just trying to force you to
> clarify your ideas. I'm sure you have wonderful intuitions and
> abilities when it comes to performing Bach. It's just that I feel
> you'll have a better chance of getting those across if you can
> present them in a clear, contradiction-free way.
>
>

Paul, thank you for the attention. But force doesn't seem the best approach.
Basically, you invoked my opinion negatively to your own in a post to Neil.
I did my best to explain why I hold a different position from you.

As has happened before, you like to bring up my name when I disagree with
you. That's fine, I suppose. However, it does not make me interested to
post. I will try one more time.

Yes, Neil, I think the different keys would keep their character according to
widely used Werckmeister chromatic, rather than revert to any primordial
version of the scales. And no, Paul, I do not think tuning instructions are
for keyboards only with Bach, or most anyone else.

Tuning is always controlled by the instrument with the least flexibility in
tuning. In real time music, that is always the keyboard. So by extension,
any indication for keyboard would be for all the forces of music. Yes, this
condition has been different at different times in history (e.g
Bardi/Galleilei in Renaissance Italy). But my experiences researching Bach
indicate a comfortable uniformity with tuning, possible when there is one
central tuning (like today).

Best, Johnny Reinhard

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 8/20/01 9:07:17 PM Eastern Daylight Time,
> paul@s... writes:
>
>
> > Johnny, please understand that I'm just trying to force you to
> > clarify your ideas. I'm sure you have wonderful intuitions and
> > abilities when it comes to performing Bach. It's just that I feel
> > you'll have a better chance of getting those across if you can
> > present them in a clear, contradiction-free way.
> >
> >
>
> Paul, thank you for the attention. But force doesn't seem the best
approach.

Sorry about that.

> Basically, you invoked my opinion negatively to your own in a post
to Neil.

Sorry again. I just didn't want your opinion to go unignored.

> I did my best to explain why I hold a different position from you.
>
> As has happened before, you like to bring up my name when I
disagree with
> you. That's fine, I suppose. However, it does not make me
interested to
> post. I will try one more time.
>
> Yes, Neil, I think the different keys would keep their character
according to
> widely used Werckmeister chromatic, rather than revert to any
primordial
> version of the scales. And no, Paul, I do not think tuning
instructions are
> for keyboards only with Bach, or most anyone else.
>
> Tuning is always controlled by the instrument with the least
flexibility in
> tuning. In real time music, that is always the keyboard. So by
extension,
> any indication for keyboard would be for all the forces of music.
Yes, this
> condition has been different at different times in history (e.g
> Bardi/Galleilei in Renaissance Italy). But my experiences
researching Bach
> indicate a comfortable uniformity with tuning, possible when there
is one
> central tuning (like today).

So I'm still wondering, if you haven't run out of patience, where the
sharps differing from enharmonically equivalent flats comes in, if
the tuning is a 12-tone keyboard temperament?

🔗BobWendell@technet-inc.com

Tuning is always controlled by the instrument with the least
flexibility in
> tuning. In real time music, that is always the keyboard. So by
extension,
> any indication for keyboard would be for all the forces of music.
Yes, this
> condition has been different at different times in history (e.g
> Bardi/Galleilei in Renaissance Italy). But my experiences
researching Bach
> indicate a comfortable uniformity with tuning, possible when there
is one
> central tuning (like today).

Hi, all! I've been following this thread with rather keen interest.
The words above are definitely the words of a keyboardist with a
finite number of fixed pitches always on his palette (and perhaps
palate as well, chuckle). I challenge anyone to find me a string
player who can consistently duplicate on his instrument in an
unaccompanied solo context ANY temperament, let alone one as complex
and harmonic-location-specific as Werckmeister's.

Let's take string players with tin ears out of consideration and only
consider those with harmonically highly sensitive ears married to a
highly developed sense of melodic integrity and expression (with
"expression" not to be taken in the technical sense applied earlier
in this thread):

1) They will conform to the keyboard temperament only when the
harmonic structure currently being played on the keyboard dictates
it. This is a spontaneous adaptation that is intuitive, just as for a
singer with a highly developed ear.

2) The rest of the time, they will play whatever is the "best fit"
harmonically with the pattern of pitches currently being executed on
the keyboard. If the keyboardist is playing a clean C-G-C with no
third and a violinist is playing the minor seventh, the m7 will
intuively go to the 7th harmonic so the structure is 4:6:7:8. This is
UTTERLY independent of where the m7 is tuned on the keyboard, unless
it was recently sounded on the keyboard in a manner that would
produce a jarring melodic impression whether in a single melodic line
or one of several in a polyphonic texture.

3) They will continually and intuitively make "engineering tradeoffs"
between the latter kind of melodic or polyphonic contexts for a given
pitch and the "best fit" within its vertical harmonic nest.

I consider it simplistic to imagine that a solo violinist, including
Bach himself, would or even could play the Unaccompanied Sonatas and
Partitas to conform with Werckmeister's temperament simply because it
was Bach's preference for tuning his keyboards.

Respectfully yours,

Bob

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

See bottom of this message for reply.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> >
> > 2) The rest of the time, they will play whatever is the "best
fit"
> > harmonically with the pattern of pitches currently being executed
> on
> > the keyboard. If the keyboardist is playing a clean C-G-C with no
> > third and a violinist is playing the minor seventh, the m7 will
> > intuively go to the 7th harmonic so the structure is 4:6:7:8.
This
> is
> > UTTERLY independent of where the m7 is tuned on the keyboard,
> unless
> > it was recently sounded on the keyboard in a manner that would
> > produce a jarring melodic impression whether in a single melodic
> line
> > or one of several in a polyphonic texture.
>
> In performing Bach, you could _never_ get away with playing the 7th
> harmonic in this context. Even if it fits harmonically, which is
> arguable, the melodic intervals leading to and away from this tone
> would be prohibitively unidiomatic.

Hmmm....so final about that, Paul?! First, although this was
admittedly not so clear, I was simply making an illustration of
principle independent of the period and the specific interval in
question. I chose this example because the 7th is in the 30 cent
range down from any other whole step down from the octave. Even so, I
cannot see how one can say this in all instances across the board.

Bach is my all-time favorite composer, bar none. I have seen and
heard scale-dominated passages where you go right up to the minor
seventh and back down. This is not a terribly infrequent occurrence
in Bach or other composers of the era. (Please don't ask me to quote
any literature. I do not have anything specific in mind right now.)

To my ear, there is absolutely nothing rude, lude, shocking, or
"unidiomatic" about going that bare sneak up to the perfect JI
dominant seventh and back down. It works for me both melodically and
harmonically, resolving beautifully to the third down from the 7th
harmonic of a relative dominant in a melodically tight little lead-in
interval that is harmonically satisfying as well. (This assumes the
7th is not sounded on the keyboard simultaneously or in near
proximity time-wise, and if the 3rd is sounded, this ssumes it's
pretty pure.)

So.....???.........Don't get it. And how do we know it's
"unidiomiatic" (?), since we can research documentation on what
tuning systems were used for keyboards to some degree, but what
violinists actually did with their fingers intonation-wise is a bit
of a tougher one, I would say. I suspect they did what sounds good to
any well-trained, melodically and harmonically sensitive ear today as
long as that ear is not totally biased toward modernity through lack
of exposure to just intervals. The latter case doesn't fit my
definition of a sensitive, musical ear anyway.

Thanks for "listening" (chuckle)!

Bob

🔗Afmmjr@aol.com

In a message dated 8/21/01 4:44:18 PM Eastern Daylight Time,
BobWendell@technet-inc.com writes:

> The words above are definitely the words of a keyboardist with a
> finite number of fixed pitches always on his palette (and perhaps
> palate as well, chuckle).

(Chuckle), well those words were definitely NOT by a keyboardist. Surprise!

> player
who can consistently duplicate on his instrument in an
> unaccompanied solo context ANY temperament, let alone one as complex
> and harmonic-location-specific as Werckmeister's.
>
Wow, wrong again, Bob. Maybe it is because this is how the musicians in my
milieu work. I play in strict Werckmeister on my alto recorder, for example.
It is certainly as easy as playing in strict 12-tET. And please don't
challenge me, rather come to the September 29th performance in New York if
you find the time and money.

> Let's take string players with tin ears out of consideration and only
> consider those with harmonically highly sensitive ears married to a
> highly developed sense of melodic integrity and expression (with
> "expression" not to be taken in the technical sense applied earlier
> in this thread):
>
Actually, why work with tin-eared musicians of any type? Even my keyboard
players can hear.

> 1) They will conform to the keyboard temperament only when the
> harmonic structure currently being played on the keyboard dictates
> it. This is a spontaneous adaptation that is intuitive, just as for a
> singer with a highly developed ear.

You may be describing general current practice as you have experienced it,
but we are exploring different performance practices. First off, only when
you play in a tuning like Werckmeister's chromatic can you "believe" it
enough that it could never be considered inferior, or unachievable. And when
a continuo instrument is tuned into such a temperament, it behooves all the
members of the ensemble to take this reality into account. Most continuo
parts are improvised so there is no real telling which notes the keyboard
will include or exclude on any given chord.

> 2) The rest of the time, they will play whatever is the "best fit"
> harmonically with the pattern of pitches currently being executed on
> the keyboard. If the keyboardist is playing a clean C-G-C with no
> third and a violinist is playing the minor seventh, the m7 will
> intuitively go to the 7th harmonic so the structure is 4:6:7:8. This is
> UTTERLY independent of where the m7 is tuned on the keyboard, unless
> it was recently sounded on the keyboard in a manner that would
> produce a jarring melodic impression whether in a single melodic line
> or one of several in a polyphonic texture.
>

I agree with Paul, here. The Harmonic 7/4 seventh was indicated by Bach's
student Kirnberger by the letter "i" placed before the minor seventh. This
alone makes one think that there is a structural and functional difference
between the 16/9 and the 7/4.

> 3) They will continually and intuitively make "engineering tradeoffs"
> between the latter kind of melodic or polyphonic contexts for a given
> pitch and the "best fit" within its vertical harmonic nest.
>
The above is often true in common practice today. However, it is not true
for Bach in his backyard at the start of the 18th century. This is
specialized work, perhaps, but it does add new dimensions to Bach's music.
And that is why we pursue these matters.

> I consider it simplistic to imagine that a solo violinist, including
> Bach himself, would or even could play the Unaccompanied Sonatas and
> Partitas to conform with Werckmeister's temperament simply because it
> was Bach's preference for tuning his keyboards.
>

Then you misjudge me, and underestimate Bach.

> Respectfully yours,
>
> Bob
>
>
>
>
>
>

Best, Johnny Reinhard

🔗BobWendell@technet-inc.com

Hi, Johnny! Not wishing to insult or underestimate anyone, not you
and certainly not Bach! I have a very fine ear, however, and am
personally unacquainted with any musicians owning a more accurate
pair when it comes to intonation, excepting present company and
others in this tuning group if I can accept at face value all claims.

Certainly tempered shifts of five cents and even less can be a
significant error harmonically, depending on the interval. Certainly
five cents is audible for the P5 and very bad, of course, at the 8ve.
Neverthess, if we're talking about MELODIC intervals, and claiming
that when playing an unaccompanied solo on a MELODIC instrument, one
can discriminate MELODIC intervals with differences on the order of
FIVE cents and less (excepting those repeated consecutively between
the same two notes), as perfect comformance to a temperament like
Werckmeister inevitably implies, I have a VERY tough time swallowing
that!

On the other hand, I have no trouble accepting that a discriminating
ear, well-trained in recognizing just intervals harmonically and
melodically, can have developed a MELODIC sensitivity to differences
in whole steps on the order of 22 cents, beteen diatonic and
chromatic half steps on the order of 41 cents, a M3 14 cents flat to
one in 12-EDO, etc. I also recognize that similarly it is possible to
develop a sensitivity to the unique scalewise or MELODIC
characteristics and patterns of a temperament such as Werckmeister's
as they shift from key to key.

However, I do believe that the MUCH FINER distinctions that such an
ear intuitively makes HARMONICALLY tend toward JI if we assume
sufficient richness and good harmonicity in the timbres employed. In
the context of this understanding, I only meant to posit that such
musicians when playing melodic instruments intuitively tend both to
adapt melodically to the tuning of the accompanying instruments and
to the harmonic context on the basis of a JI best fit to whatever is
happening at the time.

Temperaments arose for reasons unrelated to instruments that have
infinite pitch flexibility. I consequently don't see why an
unaccompanied soloist should bother to adopt any temperament as a
template for intonational performance. Although I'm sure the melodic
patterns that habitual playing with tempered instruments always has
its influence, I doubt unaccompanied soloists consciously attempted
to do this historically and it seems to me a totally unnatural,
academic artifice to do so today.

Respectfully yours,

Bob

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> See bottom of this message for reply.
>
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., BobWendell@t... wrote:
> > >
> > > 2) The rest of the time, they will play whatever is the "best
> fit"
> > > harmonically with the pattern of pitches currently being
executed
> > on
> > > the keyboard. If the keyboardist is playing a clean C-G-C with
no
> > > third and a violinist is playing the minor seventh, the m7 will
> > > intuively go to the 7th harmonic so the structure is 4:6:7:8.
> This
> > is
> > > UTTERLY independent of where the m7 is tuned on the keyboard,
> > unless
> > > it was recently sounded on the keyboard in a manner that would
> > > produce a jarring melodic impression whether in a single
melodic
> > line
> > > or one of several in a polyphonic texture.
> >
> > In performing Bach, you could _never_ get away with playing the
7th
> > harmonic in this context. Even if it fits harmonically, which is
> > arguable, the melodic intervals leading to and away from this
tone
> > would be prohibitively unidiomatic.
>
> Hmmm....so final about that, Paul?! First, although this was
> admittedly not so clear, I was simply making an illustration of
> principle independent of the period and the specific interval in
> question. I chose this example because the 7th is in the 30 cent
> range down from any other whole step down from the octave. Even so,
I
> cannot see how one can say this in all instances across the board.
>
> Bach is my all-time favorite composer, bar none. I have seen and
> heard scale-dominated passages where you go right up to the minor
> seventh and back down. This is not a terribly infrequent occurrence
> in Bach or other composers of the era. (Please don't ask me to
quote
> any literature. I do not have anything specific in mind right now.)
>
> To my ear, there is absolutely nothing rude, lude, shocking, or
> "unidiomatic" about going that bare sneak up to the perfect JI
> dominant seventh and back down. It works for me both melodically
and
> harmonically, resolving beautifully to the third down from the 7th
> harmonic of a relative dominant in a melodically tight little lead-
in
> interval that is harmonically satisfying as well. (This assumes the
> 7th is not sounded on the keyboard simultaneously or in near
> proximity time-wise, and if the 3rd is sounded, this ssumes it's
> pretty pure.)
>
> So.....???.........Don't get it. And how do we know it's
> "unidiomiatic" (?), since we can research documentation on what
> tuning systems were used for keyboards to some degree, but what
> violinists actually did with their fingers intonation-wise is a bit
> of a tougher one, I would say. I suspect they did what sounds good
to
> any well-trained, melodically and harmonically sensitive ear today
as
> long as that ear is not totally biased toward modernity through
lack
> of exposure to just intervals. The latter case doesn't fit my
> definition of a sensitive, musical ear anyway.
>
> Thanks for "listening" (chuckle)!
>
> Bob

Well, Bob, ultimately it all comes down to each listener's
preference. There is a huge amount of discussion in the archives
about what various people feel is and isn't appropriate for Bach,
mostly revolving around the adaptively re-tuned MIDI Bach files that
John deLaubenfels created. You might want to listen to a bunch of
these -- they're over at www.adaptune.com.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Hi, Johnny! Not wishing to insult or underestimate anyone, not you
> and certainly not Bach! I have a very fine ear, however, and am
> personally unacquainted with any musicians owning a more accurate
> pair when it comes to intonation, excepting present company and
> others in this tuning group if I can accept at face value all
claims.
>
> Certainly tempered shifts of five cents and even less can be a
> significant error harmonically, depending on the interval.
Certainly
> five cents is audible for the P5 and very bad, of course, at the
8ve.

Very bad?? I would suggest that violinsts often play octaves
deliberately 5 cents out-of-tune, so that the two notes don't sound
like one note.

Bob, you agreed with me that most classical string ensembles don't
play major triads in anything like JI. So why would you assume that
more than a very few violinists would shoot for the 7th harmonic when
a bare root-fifth-octave was played on the keyboard?

> I consequently don't see why an
> unaccompanied soloist should bother to adopt any temperament as a
> template for intonational performance.

What about the adaptive JI we've discussed, with meantone as a
template?

> Although I'm sure the melodic
> patterns that habitual playing with tempered instruments always has
> its influence, I doubt unaccompanied soloists consciously attempted
> to do this historically and it seems to me a totally unnatural,
> academic artifice to do so today.

Considering that Bach wrote polyphonic music, where the melodies had
strong motivic relationships with one another, and directional
tendencies, based on intervals that normally came in only two sizes
per type (not three or more as in just intonation), or at least are
notated that way, wouldn't it appear "authentic", rather than "a
totally unnatural, academic artific" to you, to in some measure
respect these characteristics? Wouldn't you want to play the melodies
as Bach heard them in his head?

🔗BobWendell@technet-inc.com

See bottom for reply from Bob.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., Afmmjr@a... wrote:
>
> > I agree with Paul, here. The Harmonic 7/4 seventh was indicated
by
> Bach's
> > student Kirnberger by the letter "i" placed before the minor
> seventh. This
> > alone makes one think that there is a structural and functional
> difference
> > between the 16/9 and the 7/4.
>
> Let alone between 9/5 (which I think is more relevant in this
> context) and 7/4.

Hi! Are we all talking about the same thing? Of course there is a
functional difference between 7/4, 16/9, and 9/5. Never would I argue
with that! I'm talking ONLY of a 7/4 where it functions as the 7th in
a DOMINANT SEVENTH chord. I have already stated that even then, its
purity would and should be influenced by the constraints of the other
instruments with which one is playing.

If the temperament on the keyboard instrument excludes it ALWAYS, no
matter what the musical context, then you're ALL CORRECT even in my
humble little book. However, I personally would have no problem with
employing a 7/4 relationship in an implicit DOMINANT 7th chord
structure if there were nothing happening in the accompaniment that
would clash with it for the moment.

I realize this is not predictable when the keyboardist is
extemporaneously realizing figured bass, Johnny. However, it is
conceivable that even then, an imminent move to a dominant seventh
could be foreshadowed by a string player or other intonationally
flexible musician improvising ornamentation or playing a written 7th
leading down over such an otherwise unpredictable figured bass
realization.

To my ear, the tight leaning in of the 7th to a M3 together with its
harmonic purity when there is no unison or octave conflict is highly
satisfying and desirable, and I would not be surprised at all to find
this was done frequently in Bach's time. That his student had a
special notation for it only reinforces my convictions on this point.

🔗Afmmjr@aol.com

In a message dated 8/22/01 2:05:16 PM Eastern Daylight Time,
BobWendell@technet-inc.com writes:

> Certainly tempered shifts of five cents and even less can be a
> significant error harmonically, depending on the interval. Certainly
> five cents is audible for the P5 and very bad, of course, at the 8ve.
> Neverthess, if we're talking about MELODIC intervals, and claiming
> that when playing an unaccompanied solo on a MELODIC instrument, one
> can discriminate MELODIC intervals with differences on the order of
> FIVE cents and less (excepting those repeated consecutively between
> the same two notes), as perfect comformance to a temperament like
> Werckmeister inevitably implies, I have a VERY tough time swallowing
> that!

In contradistinction: if I sang a plaintive microtonal melody to you,
wouldn't you learn it by rote identically, if that was indeed your wish?
Ever hear an imitator imitate a celebrity's voice? Surely, with your ear you
could sing back a microtonal melody more exactly than at drop outs of 5 cents?

> On the other hand, I have no trouble accepting that a discriminating
> ear, well-trained in recognizing just intervals harmonically and
> melodically, can have developed a MELODIC sensitivity to differences
> in whole steps on the order of 22 cents, between diatonic and
> chromatic half steps on the order of 41 cents, a M3 14 cents flat to
> one in 12-EDO, etc. I also recognize that similarly it is possible to
> develop a sensitivity to the unique scalewise or MELODIC
> characteristics and patterns of a temperament such as Werckmeister's
> as they shift from key to key.

As in Pythagorean tuning, there really isn't so much a modulating of key to
key as there is a set of 12 memorized interval relationships; any one of
which could serve as the tonic of a key. This is the reason why Kirnberger
considered a modulating the movement of any chord to another chord. It was
still not about key changes in Bach's day. That is why the interval memory
is so direct, and easy, to muster even when playing solo.

> However, I do believe that the MUCH FINER distinctions that such an
> ear intuitively makes HARMONICALLY tend toward JI if we assume
> sufficient richness and good harmonicity in the timbres employed. In
> the context of this understanding, I only meant to posit that such
> musicians when playing melodic instruments intuitively tend both to
> adapt melodically to the tuning of the accompanying instruments and
> to the harmonic context on the basis of a JI best fit to whatever is
> happening at the time.
>
Here we part paths. I don't believe you can say a lust for just is always in
the cards. There are performance techniques that were different back then
which aid in this tuning usage, most obviously the continuo itself. Frankly,
a solo melody instrument is not aided in its richness because it is in a just
tuning. It depends on the writing. Bach added many different harmonies in
double, and triple stops. His 6th cello suite was for an instrument with
even a lower harmony added, the viola pomposa. All melody is harmony for
Bach, and this is why it is not difficult to play modally for a solo work,
keeping to a tuning. Certainly on a recorder, it's a breeze (pardon the pun).

> Temperaments arose for reasons unrelated to instruments that have
> infinite pitch flexibility. I consequently don't see why an
> unaccompanied soloist should bother to adopt any temperament as a
> template for intonational performance.

How rare is it to hear any pop vocalist singing in 12-tET or pure just? All
sorts of melodic connections are made for musical reasons. Baroque musicians
would had recourse to hear and internalize all the Werckmeister
relationships. And there were only 12. It is a 12 note Blues scale,
essentially. I've played in it quite a bit and feel quite comfortable with
it. The only solo work for winds by Bach is Bach in B Minor, which mirrors
equal temperament in Werckmeister's chromatic.

Although I'm sure the melodic
> patterns that habitual playing with tempered instruments always has
> its influence, I doubt unaccompanied soloists consciously attempted
> to do this historically and it seems to me a totally unnatural,
> academic artifice to do so today.

On my concerts players consciously play all of their intonation when doing
early music. It is essentially the pedigree to be performed on my concerts.

Years ago I had the wonderful opportunity to perform with Odetta on one of my
concerts. She sang without guitar (at my request) a number of hollars,
children's songs, and a powerful work called "Black Woman." She spent
serious woodshedding time working out the curly cues in the tuning so that
she would produce exactly the intonation she knew to be right. As a superb
folk singer, she must capture exactly the intonation of the folk. And this
takes time every day before her concerts, for hours it seems.

> Respectfully yours,
>
> Bob
>
>
>
>
>

Thank you for your well stated points. Best, Johnny Reinhard

🔗BobWendell@technet-inc.com

Bob had said:
Certainly
> > five cents is audible for the P5 and very bad, of course, at the
> 8ve.
>
Paul replied:
> Very bad?? I would suggest that violinists often play octaves
> deliberately 5 cents out-of-tune, so that the two notes don't sound
> like one note.

Bob now answers:
Well, if we're going to be suddenly happy about 5 cent errors at the
octave, I don't know why any of us should make so much fuss about JI.
alternative temperaments, or much of anything else with regard to
precise intonation. I personally find that musicians who deliberately
play sharp to stand out on solos bother the living daylights out of
me. I frankly can't stand that! Absolutely despise it! They stand out
alright! Just like a recently used outhouse.

Paul:
So why would you assume that
> more than a very few violinists would shoot for the 7th harmonic
when
> a bare root-fifth-octave was played on the keyboard?

I don't. As many of you have stated, standard practice is not
considered a norm here, and it has never been an ideal for me. Hence
my carefully worded predefinition of the kind of performer to which I
was referring.

Bob had said:
> > I consequently don't see why an
> > unaccompanied soloist should bother to adopt any temperament as a
> > template for intonational performance.
>
Paul replied:
> What about the adaptive JI we've discussed, with meantone as a
> template?

Meantone (1/4-comma variety) can be seen conceptually as a template
for adaptive JI. However, if it were literally used as a template, it
would just be meantone, wouldn't it, and not adaptive JI? My choir
doesn't even know what meantone is, but under properly trained,
rehearsed and other ideal circumstances, they sponataneously use
adaptive JI because their ears have been trained to seek just
harmonic intervallic relationships among their parts.

Paul had said:
Considering that Bach wrote polyphonic music, where the melodies had
> strong motivic relationships with one another, and directional
> tendencies, based on intervals that normally came in only two sizes
> per type (not three or more as in just intonation), or at least are
> notated that way, wouldn't it appear "authentic", rather than "a
> totally unnatural, academic artific" to you, to in some measure
> respect these characteristics? Wouldn't you want to play the
melodies
> as Bach heard them in his head?

Bob answers:
"In some measure" is key here. I have recognized that habitual
playing with tempered instruments has its influence. I just don't
believe it's realistic to imagine that string and other
intonationally flexible performers explicitly set about with
conscious deliberation to conform to some tempered template. This
strikes me as arising from some kind of current idealism that is not
essential for explaining the historical realities, whatever they
might have been.

Perhaps this harks back to an earlier mild lack of convergence in our
opinions, Paul, concerning the relative importance of melodic versus
harmonic precision in tuning intervals. I believe that the human ear
detects harmonic imprecision much more readily than sequential,
melodic imprecision. On the other hand, it is indeed necessary in
order to justly tune in musically faster-moving contexts, to have a
melodic sense of the shifting width of intervals.

I personally, when in good practice, notice that I make the comma
difference between first and second whole steps of a major scale, and
certainly between diatonic and chromatic half-steps, but these
melodically subtle microtonal differences would be large, hugely
significant, and intolerable errors if they represented deviations
from JI in harmonic tuning.

When playing with other instruments or double stopping, I naturally
seek pure JI intervals. However, when I play with a tempered
instrument, I just play whatever sounds well tuned, and the
adaptation is quite spontaneous and unconscious. The temperament
simply moves my ear as far from JI as is needed to sound in accord
with it.

Whenever, something is held long enough for the discrepancies to
cause pain to the ear, a violinist has ways to quickly fudge and
adapt, as you have so aptly pointed out, Paul. What even very good
musicians with fine ears notice is that it sounds very precisely in
tune. Rarely if ever do people find the slight melodic shifts needed
for this fudging very notiecable.

Why should it have been different in Bach's time? Temperaments have a
good reason for existing on fixed-pitch instruments, at least before
the digital age and still on most acoustic instruments. More flexible
instruments don't require tempering.

I have run across one reference in this group to an "equal-tempered
sax". As a wind player also, I find this amusing. Brass and other
wind intruments are quite intonationally flexible. They're not
confined to any specific temperament just because the factory
adjustments used 12-EDO as the calibration standard.

So why should we imagine that Bach or anyone else "heard these
melodies in their heads" in such a way as to preclude subtle,
microtonal shifts in their intervals sequentially played. Even in
Bach's polyphonic contexts to which you refer, often the thematic
material shifts so that such gross distinctions as whole and half
steps fall in different locations occasionally.

So who's to worry about whether the M2s are 9/8, 10/9, or the same
size when considered as a strictly MELODIC issue? I don't mean here
to contradict myself on the need make these melodic distinctions in
order to play harmonically in tune with tempered instruments. I just
dont' think anyone, including Bach, cared much about these subtle
melodic differences outside of compatability with harmonic
considerations.

🔗BobWendell@technet-inc.com

🔗James <jmkh@uswest.net>

At 12:02 AM 8/23/01 +0000,Bob wrote:

>Bob's answer:
>In Bach's time, microtonal melodies were not in vogue.

How solid is the evidence for this statement? It is something that I am very curious about, and I don't know where to find the answer. It certainly must have been true that microtonal folk music existed in that time and place, given that it appears to have existed almost everywhere....

> I believe they
>conceived of harmonic structure (intuitively, not theoretically) in
>basically the 12-tone manner in which it was notated and played. I am
>not referring to melodic schemes that contain shifts of 5 cents in
>pitch. I think that would seem to them the same way it does to me
>when I'm thinking in terms of Baroque harmony: a tuning slide and not
>a separate, discrete pitch.
>
>The multiple 31-tone keyboard schemes referred to in some threads
>here were not put in place as microtonal systems, but strictly out of
>a motivation to achieve mechanically accesible just harmonies. The
>"blues" and other folk melodic concepts therefore do not apply, I
>don't think, to analysis of these issues for this music. To attempt
>to apply it is to my mind, a superimposition of our times onto
>theirs.
>
>
>
>
>
>
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🔗graham@microtonal.co.uk

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:

> However, I personally would have no problem with
> employing a 7/4 relationship in an implicit DOMINANT 7th chord
> structure if there were nothing happening in the accompaniment that
> would clash with it for the moment.

In the context of Bach, that's your opinion. There are others. I
encourage you to look through the archives at discussions concerning
John deLaubenfels' adaptive retunings of Bach.
>
> To my ear, the tight leaning in of the 7th to a M3 together with
its
> harmonic purity when there is no unison or octave conflict is
highly
> satisfying and desirable,

True -- but does it have the "push" toward resolution that a truly
dissonant dominant seventh chord needs in the idiom?

May I recommend a book for you? _The Structure of Recognizable
Diatonic Tunings_ by Easley Blackwood.

> That his student had a
> special notation for it only reinforces my convictions on this >
point.

This notation was used to refer to a different note, not the one used
in the dominant seventh chord.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Bob had said:
> Certainly
> > > five cents is audible for the P5 and very bad, of course, at
the
> > 8ve.
> >
> Paul replied:
> > Very bad?? I would suggest that violinists often play octaves
> > deliberately 5 cents out-of-tune, so that the two notes don't
sound
> > like one note.
>
> Bob now answers:
> Well, if we're going to be suddenly happy about 5 cent errors at
the
> octave, I don't know why any of us should make so much fuss about
JI.
> alternative temperaments, or much of anything else with regard to
> precise intonation.

Why not? It's a long way from 100 cents to 5 cents. And in fact,
controlling such effects requires even _more_ precise intonation than
simply conveying a "just" sound.

> Bob had said:
> > > I consequently don't see why an
> > > unaccompanied soloist should bother to adopt any temperament as
a
> > > template for intonational performance.
> >
> Paul replied:
> > What about the adaptive JI we've discussed, with meantone as a
> > template?
>
> Meantone (1/4-comma variety) can be seen conceptually as a template
> for adaptive JI. However, if it were literally used as a template,
it
> would just be meantone, wouldn't it, and not adaptive JI?

Well you know what I mean by "template".

> My choir
> doesn't even know what meantone is, but under properly trained,
> rehearsed and other ideal circumstances, they sponataneously use
> adaptive JI because their ears have been trained to seek just
> harmonic intervallic relationships among their parts.

But didn't you agree that a lot of experience doing this solidified
meantone-like intervals as the "aiming" process in each melodic line?
That is, the singer won't have the opportunity to fine-tune his or
her pitch to form a just harmony with the other pitches sounding,
until enough time has gone by during which all the singers are
singing simultaneously, judgment is made, and adjustments work
themselves out. To minimize the errors in the first part of the
process, don't your singers, intuitively and because of experience,
sing meantone-like _melodic_ intervals, as a way of "aiming" for the
adaptively just target that they want to hit?
>
> I personally, when in good practice, notice that I make the comma
> difference between first and second whole steps of a major scale,

Depending on what the underlying harmony is, right?
>
> Whenever, something is held long enough for the discrepancies to
> cause pain to the ear, a violinist has ways to quickly fudge and
> adapt, as you have so aptly pointed out, Paul. What even very good
> musicians with fine ears notice is that it sounds very precisely in
> tune. Rarely if ever do people find the slight melodic shifts
needed
> for this fudging very notiecable.

But it just isn't the reality for most professional musicians. They
have their own systematic "fudges", which tend _not_ to conform with
any search for harmonic purity, but rather are elements of melodic
expression. (The most glaring exception is Barbershop singing.) Like
it or not, this is the situation our musical culture is in, and of
all the world's musical cultures, ours is certainly one of the most
_harmonically_ oriented.

> Why should it have been different in Bach's time?

Indeed.

> Temperaments have a
> good reason for existing on fixed-pitch instruments, at least
before
> the digital age and still on most acoustic instruments. More
flexible
> instruments don't require tempering.

Yet melodic logic stands up on its own, and isn't always compatible,
in an obvious way, with harmonic logic. Also, there are different
types of harmonic logic -- Pythagorean was the standard tuning in the
West from about 800-1420 (I'll let Margo address the finer points of
this generalization).
>
> So why should we imagine that Bach or anyone else "heard these
> melodies in their heads" in such a way as to preclude subtle,
> microtonal shifts in their intervals sequentially played.

This is where I agree with you and part company with Johnny. If we're
talking about shifts on the order of 5 cents.

> Even in
> Bach's polyphonic contexts to which you refer, often the thematic
> material shifts so that such gross distinctions as whole and half
> steps fall in different locations occasionally.

Well I think very powerful tonal effects are intended, and realized,
in such circumstances.

> So who's to worry about whether the M2s are 9/8, 10/9, or the same
> size when considered as a strictly MELODIC issue?

It's not a large concern, but I do feel that Bach's melodies suffer
if one has to use consecutive whole tones that differ by as much as
9:8 differs from 10:9. Mozart may be an even better example in this
regard. John deLaubenfels, please chime in with your
feelings/experiences.

🔗John A. deLaubenfels <jdl@adaptune.com>

[Bob Wendell wrote:]
>>However, I personally would have no problem with
>>employing a 7/4 relationship in an implicit DOMINANT 7th chord
>>structure if there were nothing happening in the accompaniment that
>>would clash with it for the moment.

[Paul E:]
>In the context of Bach, that's your opinion. There are others. I
>encourage you to look through the archives at discussions concerning
>John deLaubenfels' adaptive retunings of Bach.

Sorry to be so late in jumping in; I've been lurking but distracted by
work (the kind that pays actual dollars! ;-) ). Bob, when it comes to
dom 7ths, my taste runs to 7/4, and I've got lots of midi files (many
more than are currently on my website) which contrast 9/5 and 16/9 to
7/4. So I'm with you! However, from all I can gather on this list, 7/4
is "inauthentic", meaning that the preponderance of available evidence
suggests that Bach (and many others over a wide range of time) didn't
use it.

I've pretty much let go of worry when it comes to authenticity, though:
I just tune music the way I like it best, and try to be clear that what
I'm presenting is not what the original composer presented, for better
or worse. It is, of course, a very interesting question what the
original composer thought or felt or believed or practiced, and we have
many wonderful scholars on this list who give informed opinions on that
subject. My allegiance is to beauty; everything else must suffer if
necessary. Natch, I may turn out to be a total wacko whose notion of
beauty is completely distorted from the mainstream ;-> ! But there are
a significant portion of list members who also prefer 7/4 dom 7ths, from
what I can gather.

[Bob:]
>>To my ear, the tight leaning in of the 7th to a M3 together with its
>>harmonic purity when there is no unison or octave conflict is highly
>>satisfying and desirable,

[Paul:]
>True -- but does it have the "push" toward resolution that a truly
>dissonant dominant seventh chord needs in the idiom?

Paul, we've discussed this many times. The answer for you would seem
to be No, but for me it's definitely Yes. A 4:5:6:7 dom 7th to me
sounds both wonderfully concordant and infinitely longing, and the
resolution to tonic is the perfect answer to that longing. As we both
know, there are horizontal prices to be paid for 4:5:6:7 tunings, but
to my ear these are the _only_ genuine prices, and I pay them willingly!

[Johnny Reinhard wrote:]
>>Bob, you're speaking of the 7/4 as a "night cap" for the dominant,
>>sort of like the Piccardy third making a surprise major triad in a
>>final chord. I agree this could happen.

[Paul E:]
>But wouldn't it make the dominant seventh sound "final", rather than
>needing to resolve? If there were a Bach movement that _ended_ on a
>dominant seventh chord, then perhaps this would work . . .

Not to my ear! I can accept a tonic 7th in music that uses the 7th
degree heavily in I, IV, and V, but for Bach (and many others), the 7/4
dom 7th begs for resolution, IMO.

JdL

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

Bob answers:
On the melodic 5-cent offset issue, I give up. The octave and the
unison are the intervals that historically have not been compromised.
Yet we are advocating a mistuning of 5 cents, when even at the fifth
Vicento went to great lengths to eliminate the quarter-comma error
with multiple keyboards????

Yet Johnny Reinhard says he reacts negatively even to MELODIC errors
of 5 cents from the standard in use at the moment (Werckmeister in
this case). I feel squeezed from both extremes. I have already stated
that I find this position of Johnny's difficult to accept, unless
there is a reference tone that allows the perception to become
harmonic. All I can say is my ears find a 5-cent pitch
discrepancy at the octave or unison absolutely intolerable.

Bob also said:
Rarely if ever do people find the slight melodic shifts needed
> for this fudging very noticeable (adaptive JI or shifting from JI
to intervals that accord with a tempered accompaniment).

Paul replied:
> But didn't you agree that a lot of experience doing this solidified
> meantone-like intervals as the "aiming" process in each melodic
line?
> That is, the singer won't have the opportunity to fine-tune his or
> her pitch to form a just harmony with the other pitches sounding,
> until enough time has gone by during which all the singers are
> singing simultaneously, judgment is made, and adjustments work
> themselves out. To minimize the errors in the first part of the
> process, don't your singers, intuitively and because of experience,
> sing meantone-like _melodic_ intervals, as a way of "aiming" for
the
> adaptively just target that they want to hit?

Bob:
Yes! I think these are simply a kind of ongoing "engineering
tradeoffs" they make intuitively to reconcile pure harmonic intervals
with a stable sense of pitch (that doesn't drift).

Paul:
But it just isn't the reality for most professional musicians. They
have their own systematic "fudges", which tend _not_ to conform with
any search for harmonic purity, but rather are elements of melodic
expression.

Bob:
Since when has this kind of "standard practice" become a criterion
for the value or utility of anything we say here?

Paul:
(The most glaring exception is Barbershop singing.)

Bob:
Right on! I'm not crazy about the depth of the music, but it's fun to
do and I LOVE that aspect of it when I can find singers who can do it
that way out here in the middle of corn and hogs. (Rare. Not many in
my choir are into that.)

Paul:
Like it or not, this is the situation our musical culture is in, and
of all the world's musical cultures, ours is certainly one of the
most _harmonically_ oriented.>

Bob:
Sad irony, huh?

Bob also said:
> Temperaments have a
> good reason for existing on fixed-pitch instruments, at least
before
> the digital age and still on most acoustic instruments. More
flexible
> instruments don't require tempering.

Paul:
Yet melodic logic stands up on its own, and isn't always compatible,
in an obvious way, with harmonic logic. Also, there are different
types of harmonic logic -- Pythagorean was the standard tuning in the
West from about 800-1420 (I'll let Margo address the finer points of
this generalization).>

Bob:
Agreed! However, I believe the Gothic preference for perfect fifths
and fourths as consonances evolved naturally toward the newly
perceived consonance of thirds in the Renaissance because of the
prominence of a cappella vocal music in the church.

The Pythagorean 3-limit tuning was something THEORISTS hung onto for
a long time because they were dealing with fixed pitches and
vocalists were forced to conform. (There was also the symbolism of
the Trinity in 3-limit). When this constraint was removed for a
sufficiently significant time and intensity of practice, bang, the
thirds suddenly shone forth as consonant.

Bob also said:
> Bach's polyphonic contexts to which you refer, often the thematic
> material shifts so that such gross distinctions as whole and half
> steps fall in different locations occasionally.

Paul:
Well I think very powerful tonal effects are intended, and realized,
in such circumstances.

Bob:
Of course, but the melodic conformity to the general outline of the
melody was preserved anyway. It didn't matter so much that the
intervals were not precisley in imitation of the original theme. This
is precisely my point. How much more would he be willing to admit
microtonal differences within the same interval type if the harmony
constrains it that way?

Conversely, notice how often his (traditional) harmonic logic is
often locally non-existent for a short time in the service of
contrapuntal integrity. However, it always comes out in the wash as
harmonically sensible in the overall thrust of the phrase. He was
quite daring in his use of passing tones and even this kind of brief
polytonality in order to extend the contrapuntal possibilities.

Bob also said:
> So who's to worry about whether the M2s are 9/8, 10/9, or the same
> size when considered as a strictly MELODIC issue?

Paul:
It's not a large concern, but I do feel that Bach's melodies suffer
if one has to use consecutive whole tones that differ by as much as
9:8 differs from 10:9.

Bob:
I don't advocate JI in every circumstance as I've already clearly
stated and implied in multiple contexts. I think JI intervals are the
guiding first principle that good musicians intuitively use, but make
all kinds of "engineering tradeoffs" to avoid pitch drift and other
problems of pure JI, or if accompanied by keyboards or other fixed
pitch instruments, to accomodate the temperament used. However, I
personally don't find anything incongruent about hearing something
unaccompanied from Bach in which the two steps are "justly" different
(chuckle).

🔗BobWendell@technet-inc.com

Thanks, John! Wow! I feel better already. Felt attacked from both
sides (in a very gentlemanly manner, of course):

One who thinks five-cent errors are acceptable at the octave and
unison and another who thinks they're not even acceptable as errors
in melodic leaps with no reference tone that would allow the error to
be perceived as harmonic!

Sincerely,

Bob

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Bob Wendell wrote:]
> >>However, I personally would have no problem with
> >>employing a 7/4 relationship in an implicit DOMINANT 7th chord
> >>structure if there were nothing happening in the accompaniment
that
> >>would clash with it for the moment.
>
> [Paul E:]
> >In the context of Bach, that's your opinion. There are others. I
> >encourage you to look through the archives at discussions
concerning
> >John deLaubenfels' adaptive retunings of Bach.
>
> Sorry to be so late in jumping in; I've been lurking but distracted
by
> work (the kind that pays actual dollars! ;-) ). Bob, when it comes
to
> dom 7ths, my taste runs to 7/4, and I've got lots of midi files
(many
> more than are currently on my website) which contrast 9/5 and 16/9
to
> 7/4. So I'm with you! However, from all I can gather on this
list, 7/4
> is "inauthentic", meaning that the preponderance of available
evidence
> suggests that Bach (and many others over a wide range of time)
didn't
> use it.
>
> I've pretty much let go of worry when it comes to authenticity,
though:
> I just tune music the way I like it best, and try to be clear that
what
> I'm presenting is not what the original composer presented, for
better
> or worse. It is, of course, a very interesting question what the
> original composer thought or felt or believed or practiced, and we
have
> many wonderful scholars on this list who give informed opinions on
that
> subject. My allegiance is to beauty; everything else must suffer if
> necessary. Natch, I may turn out to be a total wacko whose notion
of
> beauty is completely distorted from the mainstream ;-> ! But there
are
> a significant portion of list members who also prefer 7/4 dom 7ths,
from
> what I can gather.
>
>
> [Bob:]
> >>To my ear, the tight leaning in of the 7th to a M3 together with
its
> >>harmonic purity when there is no unison or octave conflict is
highly
> >>satisfying and desirable,
>
> [Paul:]
> >True -- but does it have the "push" toward resolution that a truly
> >dissonant dominant seventh chord needs in the idiom?
>
> Paul, we've discussed this many times. The answer for you would
seem
> to be No, but for me it's definitely Yes. A 4:5:6:7 dom 7th to me
> sounds both wonderfully concordant and infinitely longing, and the
> resolution to tonic is the perfect answer to that longing. As we
both
> know, there are horizontal prices to be paid for 4:5:6:7 tunings,
but
> to my ear these are the _only_ genuine prices, and I pay them
willingly!
>
>
>
> [Johnny Reinhard wrote:]
> >>Bob, you're speaking of the 7/4 as a "night cap" for the
dominant,
> >>sort of like the Piccardy third making a surprise major triad in
a
> >>final chord. I agree this could happen.
>
> [Paul E:]
> >But wouldn't it make the dominant seventh sound "final", rather
than
> >needing to resolve? If there were a Bach movement that _ended_ on
a
> >dominant seventh chord, then perhaps this would work . . .
>
> Not to my ear! I can accept a tonic 7th in music that uses the 7th
> degree heavily in I, IV, and V, but for Bach (and many others), the
7/4
> dom 7th begs for resolution, IMO.
>
> JdL

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Bob answers:
> On the melodic 5-cent offset issue, I give up. The octave and the
> unison are the intervals that historically have not been
compromised.
> Yet we are advocating a mistuning of 5 cents, when even at the
fifth
> Vicento went to great lengths to eliminate the quarter-comma error
> with multiple keyboards????

I'm saying that as a special, expressive effect, an octave can be
played deliberately a little off. I'm not advocating this as any kind
of norm for tuning keyboards or anything. Just noticing that this is
done in real musical performance.
>
> Paul:
> But it just isn't the reality for most professional musicians. They
> have their own systematic "fudges", which tend _not_ to conform
with
> any search for harmonic purity, but rather are elements of melodic
> expression.
>
> Bob:
> Since when has this kind of "standard practice" become a criterion
> for the value or utility of anything we say here?

Perhaps because we shouldn't feel so presumptous about our ability to
say what is right and what is wrong regarding the work of history's
master composers that we can simply ignore what is going on in the
world outside this little list.
>
> Paul:
> Yet melodic logic stands up on its own, and isn't always
compatible,
> in an obvious way, with harmonic logic. Also, there are different
> types of harmonic logic -- Pythagorean was the standard tuning in
the
> West from about 800-1420 (I'll let Margo address the finer points
of
> this generalization).>
>
>
> Bob:
> Agreed! However, I believe the Gothic preference for perfect fifths
> and fourths as consonances evolved naturally toward the newly
> perceived consonance of thirds in the Renaissance because of the
> prominence of a cappella vocal music in the church.
>
> The Pythagorean 3-limit tuning was something THEORISTS hung onto
for
> a long time because they were dealing with fixed pitches and
> vocalists were forced to conform. (There was also the symbolism of
> the Trinity in 3-limit). When this constraint was removed for a
> sufficiently significant time and intensity of practice, bang, the
> thirds suddenly shone forth as consonant.

I think it's the other way around. I think the constraint was removed
in the _theory_, in the early 16th century, because already in
_practice_ for a century or two (depending on geographic locale)
thirds and sixths were being used as consonances.
>
> Bob also said:
> > Bach's polyphonic contexts to which you refer, often the thematic
> > material shifts so that such gross distinctions as whole and half
> > steps fall in different locations occasionally.
>
> Paul:
> Well I think very powerful tonal effects are intended, and
realized,
> in such circumstances.
>
> Bob:
> Of course, but the melodic conformity to the general outline of the
> melody was preserved anyway. It didn't matter so much that the
> intervals were not precisley in imitation of the original theme.

I think it mattered a lot -- it has a huge tonal implication.

> This
> is precisely my point. How much more would he be willing to admit
> microtonal differences within the same interval type if the harmony
> constrains it that way?

I see the line of reasoning but it doesn't ring true for me. It's
very easy to sound "melodically out-of-tune" as well as "harmonically
out-of-tune".

Listen to Blackwood's piece in 17-tET. It's in a fairly traditional,
tonal style. By all accounts, 5-limit harmony should be positively
horrible in this tuning. But due to the choice of timbres, voicings,
and most importantly the strength of the melody, the piece sounds
absolutely wonderful. The particular melodic intervals become a motif
in themselves which unifies the piece and gives it so
much "character".

🔗John A. deLaubenfels <jdl@adaptune.com>

[Bob wrote:]
>>So who's to worry about whether the M2s are 9/8, 10/9, or the same
>>size when considered as a strictly MELODIC issue?

[Paul E:]
>It's not a large concern, but I do feel that Bach's melodies suffer
>if one has to use consecutive whole tones that differ by as much as
>9:8 differs from 10:9. Mozart may be an even better example in this
>regard. John deLaubenfels, please chime in with your
>feelings/experiences.

On the question of melodic unevenness I am still highly undecided. In
my recent tuning experiments with melodic springs, I seem to find that
I prefer either positive spring constants (pulling melodic steps toward
evenness) or negative spring constants (pushing melodic steps away from
evenness) to no melodic springs at all (in which harmonic considerations
dominate). What to make of this?

I do agree that the difference between 9/8 and 10/9 can be melodically
significant, and sometimes unpleasant. I like Bob's term, "engineering",
for calculating, either intuitively or coldly (by computer), the best
mix of tradeoffs between the competing forces. But, on this score, is
there really any substantial disagreement between the three of us?

JdL

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Bob wrote:]
> >>So who's to worry about whether the M2s are 9/8, 10/9, or the
same
> >>size when considered as a strictly MELODIC issue?
>
> [Paul E:]
> >It's not a large concern, but I do feel that Bach's melodies
suffer
> >if one has to use consecutive whole tones that differ by as much
as
> >9:8 differs from 10:9. Mozart may be an even better example in
this
> >regard. John deLaubenfels, please chime in with your
> >feelings/experiences.
>
> On the question of melodic unevenness I am still highly undecided.
In
> my recent tuning experiments with melodic springs, I seem to find
that
> I prefer either positive spring constants (pulling melodic steps
toward
> evenness) or negative spring constants (pushing melodic steps away
from
> evenness) to no melodic springs at all (in which harmonic
considerations
> dominate). What to make of this?

This is interesting, but what are the actual differences between
whole step sizes you see in these sequences?
>
> I do agree that the difference between 9/8 and 10/9 can be
melodically
> significant, and sometimes unpleasant. I like Bob's
term, "engineering",
> for calculating, either intuitively or coldly (by computer), the
best
> mix of tradeoffs between the competing forces. But, on this score,
is
> there really any substantial disagreement between the three of us?

Bob seems to be saying that the grounding springs are relatively
unimportant, and that the "melodic springs" are completely
unimportant. The vertical springs matter the most to Bob. I'm happy
living without the melodic springs, but the grounding springs are
important for me -- perhaps more important than the vertical springs.

🔗John A. deLaubenfels <jdl@adaptune.com>

[I wrote:]
>>On the question of melodic unevenness I am still highly undecided. In
>>my recent tuning experiments with melodic springs, I seem to find that
>>I prefer either positive spring constants (pulling melodic steps
>>toward evenness) or negative spring constants (pushing melodic steps
>>away from evenness) to no melodic springs at all (in which harmonic
>>considerations dominate). What to make of this?

[Paul:]
>This is interesting, but what are the actual differences between
>whole step sizes you see in these sequences?

Well, that answer is as available to you as it is to me, in the contents
of the midi files that my program outputs in adaptive tuning. I _do_
have the program output an RMS melodic deviation, but the specific cases
of noticeable and unpleasant deviation from expectation have only a
loose relationship to this number. For the Rhapsody in Blue on my
website, I'm showing 8.1 cents RMS melodic deviation from ideal, which
could easily translate into consecutive steps 16.2 cents from each
other, near a syntonic comma. This is a sequence I find challenging in
horizontal unevenness.

[JdL:]
>>I do agree that the difference between 9/8 and 10/9 can be melodically
>>significant, and sometimes unpleasant. I like Bob's term,
>>"engineering", for calculating, either intuitively or coldly (by
>>computer), the best mix of tradeoffs between the competing forces.
>>But, on this score, is there really any substantial disagreement
>>between the three of us?

[Paul:]
>Bob seems to be saying that the grounding springs are relatively
>unimportant, and that the "melodic springs" are completely
>unimportant. The vertical springs matter the most to Bob. I'm happy
>living without the melodic springs, but the grounding springs are
>important for me -- perhaps more important than the vertical springs.

Really?? I must've missed more than I thought I did! Bob, are you
saying this? "Grounding springs" in my model tend to keep the center
of tuning deviation from shifting over time; they control tuning drift.
Are you saying that drift is relatively unimportant? If so, I would
agree with Paul on the other side; I find that weakening grounding
springs tends to leave me with an uneasy feeling after I hear a piece,
even though the vertical intervals may all be lovely. Things get a
little too squirrelly in some subtle way. I can provide examples of
any (reasonable) MIDI sequence if you'd like to do a comparison listen.

Strangely, Paul, you did not mention horizontal springs! For most of
my time on this list, you have been most critical of horizontal motion
in my tuning experiments; do I have that well under control now?

JdL

🔗Afmmjr@aol.com

In a message dated 8/23/01 4:48:31 PM Eastern Daylight Time,
BobWendell@technet-inc.com writes:

> Yet Johnny Reinhard says he reacts negatively even to MELODIC errors
> of 5 cents from the standard in use at the moment (Werckmeister in
> this case). I feel squeezed from both extremes. I have already stated
> that I find this position of Johnny's difficult to accept, unless
> there is a reference tone that allows the perception to become
> harmonic.

Please try to accept that fact. One can learn to hear internally with the
necessary accuracy to play perfect Just intervals. Within any single note
there are the harmonics of the Just intervals you will be wanting to achieve.
In other words, with a single musical tone there is the melodic DNA to match
exact harmonics in interval making.

> Bob:
> Yes! I think these are simply a kind of ongoing "engineering
> tradeoffs" they make intuitively to reconcile pure harmonic intervals
> with a stable sense of pitch (that doesn't drift).
>

This is true today, but not back then. Imagine that Werckmeister has all the
musical space between Just and Pythagorean sewn up. It's built into the
system, the unequalness of the melodic intervals. Messing with it is both
undesirable and dangerous.

Imagine that your world knew nothing of a full circle of 12 major and minor
keys. And that thanks to Werckmeister's FAMOUS treatise, everyone had a
starting point of only 12 notes that did not change in their relationships.
Truly not hard to do, and dangerous to fudge. There is so much variety that
there is little need to create new relationships with fudging.

> Bob:
> It didn't matter so much that the
> intervals were not precisley in imitation of the original theme. This
> is precisely my point. How much more would he be willing to admit
> microtonal differences within the same interval type if the harmony
> constrains it that way?
>
There is a misunderstanding here. There are no exact imitations in
Werckmeister. The fact that Bach's music works so well in equal temperament
is certainly a tribute to Bach, but the world of nuances left out is a
paucity. Werckmeister's temperament liberated the composer to all the
harmonies being usable, for the first time published.

>
> Bob also said:
> > So who's to worry about whether the M2s are 9/8, 10/9, or the same
> > size when considered as a strictly MELODIC issue?
>
> Paul:
> It's not a large concern, but I do feel that Bach's melodies suffer
> if one has to use consecutive whole tones that differ by as much as
> 9:8 differs from 10:9.
>

Bob, have you listened to successful performances of Bach in Werckmeister?
Theory alone cannot explain it.

Best, Johnny Reinhard

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> [Paul:]
> what are the actual differences between
> >whole step sizes you see in these sequences?
>
> Well, that answer is as available to you as it is to me, in the
contents
> of the midi files that my program outputs in adaptive tuning. I
_do_
> have the program output an RMS melodic deviation, but the specific
cases
> of noticeable and unpleasant deviation from expectation have only a
> loose relationship to this number. For the Rhapsody in Blue on my
> website, I'm showing 8.1 cents RMS melodic deviation from ideal,
which
> could easily translate into consecutive steps 16.2 cents from each
> other, near a syntonic comma. This is a sequence I find
challenging in
> horizontal unevenness.

How about Bach?

> [JdL:]
> >>I do agree that the difference between 9/8 and 10/9 can be
melodically
> >>significant, and sometimes unpleasant. I like Bob's term,
> >>"engineering", for calculating, either intuitively or coldly (by
> >>computer), the best mix of tradeoffs between the competing
forces.
> >>But, on this score, is there really any substantial disagreement
> >>between the three of us?
>
> [Paul:]
> >Bob seems to be saying that the grounding springs are relatively
> >unimportant, and that the "melodic springs" are completely
> >unimportant. The vertical springs matter the most to Bob. I'm
happy
> >living without the melodic springs, but the grounding springs are
> >important for me -- perhaps more important than the vertical
springs.
>
> Really?? I must've missed more than I thought I did! Bob, are you
> saying this?

Not directly, but in my view, indirectly.

> "Grounding springs" in my model tend to keep the center
> of tuning deviation from shifting over time; they control tuning
drift.
> Are you saying that drift is relatively unimportant?

Wait a minute -- grounding springs do more than control drift. You
only need a grounding spring to one note to control drift. What I'm
talking about is the grounding to the COFT. I'm saying, echoing
Johnny just a little, that a melodic framework dictated by the
harmonic needs of the piece (let's assume only 12 notated notes,
since your software doesn't currently accept more) should determine
the melodic norm for the piece, and stuck to somewhat closely. Bob
doesn't seem to be as concerned with sticking to a set melodic
framework.

> If so, I would
> agree with Paul on the other side; I find that weakening grounding
> springs tends to leave me with an uneasy feeling after I hear a
piece,
> even though the vertical intervals may all be lovely. Things get a
> little too squirrelly in some subtle way. I can provide examples of
> any (reasonable) MIDI sequence if you'd like to do a comparison
listen.

I think this would be most valuable.
>
> Strangely, Paul, you did not mention horizontal springs!

Oops -- I forgot about those! Do you allow two non-consecutive
occurences of a note to get a horizontal spring between them, if
they're close in time?

> For most of
> my time on this list, you have been most critical of horizontal
motion
> in my tuning experiments; do I have that well under control now?

There was never a problem once you adopted the COFT methodology. In
fact, I wonder what would happen if you now eliminated the horizontal
springs altogether.

🔗John A. deLaubenfels <jdl@adaptune.com>

[I wrote:]
>>For the Rhapsody in Blue on my website, I'm showing 8.1 cents RMS
>>melodic deviation from ideal, which could easily translate into
>>consecutive steps 16.2 cents from each other, near a syntonic comma.
>>This is a sequence I find challenging in horizontal unevenness.

[Paul:]
>How about Bach?

It would depend on the piece and the treatment (5 vs. 7 limit, etc.).
The Gershwin above is 7-limit, and of course has heavy use of 7th
chords (dominant and otherwise!), so it's particularly challenging.
I tend to see RMS melodic deviations of around 5 cents for 5-limit
treatments of 18th and 19th century music.

[Paul:]
>>>Bob seems to be saying that the grounding springs are relatively
>>>unimportant, and that the "melodic springs" are completely
>>>unimportant. The vertical springs matter the most to Bob. I'm happy
>>>living without the melodic springs, but the grounding springs are
>>>important for me -- perhaps more important than the vertical
>>>springs.

[JdL:]
>>Really?? I must've missed more than I thought I did! Bob, are you
>>saying this?

[Paul:]
>Not directly, but in my view, indirectly.

Bob?

[JdL:]
>>"Grounding springs" in my model tend to keep the center of tuning
>>deviation from shifting over time; they control tuning drift.
>>Are you saying that drift is relatively unimportant?

[Paul:]
>Wait a minute -- grounding springs do more than control drift. You
>only need a grounding spring to one note to control drift.

So we once speculated, but when I tried it on a real sequence, the
results were poor: the pitch that was grounded, when it played different
roles in chords, flung the other pitches away from uniform tuning; also,
extended passages in a modulated key where the grounded note is absent
get tuned all over the map with no drift control whatever.

[Paul:]
>What I'm
>talking about is the grounding to the COFT. I'm saying, echoing
>Johnny just a little, that a melodic framework dictated by the
>harmonic needs of the piece (let's assume only 12 notated notes,
>since your software doesn't currently accept more) should determine
>the melodic norm for the piece, and stuck to somewhat closely. Bob
>doesn't seem to be as concerned with sticking to a set melodic
>framework.

I see your point, but typically the grounding springs are weak enough
that they do little to influence the tuning of any given note; they
exert significant influence on a larger scale. The difference between
grounding to 12-tET and grounding to COFT is a subtle one.

[JdL:]
>>I find that weakening grounding springs tends to leave me with an
>>uneasy feeling after I hear a piece, even though the vertical
>>intervals may all be lovely. Things get a little too squirrelly in
>>some subtle way. I can provide examples of any (reasonable) MIDI
>>sequence if you'd like to do a comparison listen.

[Paul:]
>I think this would be most valuable.

Are you interested, Bob? What sequence(s)?

[JdL:]
>>Strangely, Paul, you did not mention horizontal springs!

[Paul:]
>Oops -- I forgot about those! Do you allow two non-consecutive
>occurences of a note to get a horizontal spring between them, if
>they're close in time?

Right now I only spring consecutive instances of the same pitch class.
Of course two springs in series do indirectly form a (weaker) spring
between the outlying notes as well.

[JdL:]
>>For most of my time on this list, you have been most critical of
>>horizontal motion in my tuning experiments; do I have that well under
>>control now?

[Paul:]
>There was never a problem once you adopted the COFT methodology. In
>fact, I wonder what would happen if you now eliminated the horizontal
>springs altogether.

I don't think you'd like it! If you pick a piece, I'll do a comparison.
How about the Gershwin? That otta sound wild!

JdL

🔗BobWendell@technet-inc.com

Grounding springs?

Bob

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> > [Bob wrote:]
> > >>So who's to worry about whether the M2s are 9/8, 10/9, or the
> same
> > >>size when considered as a strictly MELODIC issue?
> >
> > [Paul E:]
> > >It's not a large concern, but I do feel that Bach's melodies
> suffer
> > >if one has to use consecutive whole tones that differ by as much
> as
> > >9:8 differs from 10:9. Mozart may be an even better example in
> this
> > >regard. John deLaubenfels, please chime in with your
> > >feelings/experiences.
> >
> > On the question of melodic unevenness I am still highly
undecided.
> In
> > my recent tuning experiments with melodic springs, I seem to find
> that
> > I prefer either positive spring constants (pulling melodic steps
> toward
> > evenness) or negative spring constants (pushing melodic steps
away
> from
> > evenness) to no melodic springs at all (in which harmonic
> considerations
> > dominate). What to make of this?
>
> This is interesting, but what are the actual differences between
> whole step sizes you see in these sequences?
> >
> > I do agree that the difference between 9/8 and 10/9 can be
> melodically
> > significant, and sometimes unpleasant. I like Bob's
> term, "engineering",
> > for calculating, either intuitively or coldly (by computer), the
> best
> > mix of tradeoffs between the competing forces. But, on this
score,
> is
> > there really any substantial disagreement between the three of us?
>
> Bob seems to be saying that the grounding springs are relatively
> unimportant, and that the "melodic springs" are completely
> unimportant. The vertical springs matter the most to Bob. I'm happy
> living without the melodic springs, but the grounding springs are
> important for me -- perhaps more important than the vertical
springs.

🔗BobWendell@technet-inc.com

Bob had said:
It didn't matter so much that the intervals were not precisley in
imitation of the original theme. This is precisely my point. How much
more would he be willing to admit microtonal differences within the
same interval type if the harmony constrains it that way?

Johnny Reinhard commented:
There is a misunderstanding here. There are no exact imitations in
Werckmeister. The fact that Bach's music works so well in equal
temperament is certainly a tribute to Bach, but the world of nuances
left out is a paucity. Werckmeister's temperament liberated the
composer to all the harmonies being usable, for the first time
published

Bob answers:
My statement was answering Paul's objection that the difference of JI
intervals EVEN IN SOLO VIOLIN PERFORMANCE was unacceptably
unidiomatic from a melodic perspective. Your point underscores mine
as I see it. In a microtonally precise sense, there is no exact
melodic imitation in the first place in Werckmeister's temperament.

For me, another telling point:
Many advocates of 12-EDO opposing JI have pointed to the difference
in the whole steps of JI as a great evil of some kind. I posit that
it is nothing more in effect than A SMOOTH MOVE from the 9th to the
10th harmonic! It is perfectly natural and acceptable melodically as
long as it doesn't conflict with anything else harmonically.

This is in principle no different from the division of the perfect
fifth into a major and minor third (4:5:6). It is analogous precisely
as a division of the major third ((8:9:10)! Anyone proposing that we
split the perfect fifth into two equal intervals in the interest of
melodic integrity??

I think I hear Johnny Reinhard saying that Werckmeister ruled, no
matter what the instrument or performance context, in spite of the
essential nature and actual historical evolution of temperaments as
compromises made in the interest of reconciling the physical
ergonomics of keyboard playing and JI. I personally can't imagine
that the practical musicians of any era were so academically or
musically rigid! I return to my earlier statement of opinion that
this is an academic superimposition of some of our thinking onto
theirs.

🔗BobWendell@technet-inc.com

Bob:
Hi, all! I wasn't previously aware of the "springs" concept. This is
getting very interesting now! Is it correct to infer that this is a
concept arising out of software technology that allows us to specify
parameters controlling what we have been calling "fudging" or
"engineering tradeoffs" horizontally, vertically, and for longer-term
"drift resistance"?

> [Paul:]
> >>>Bob seems to be saying that the grounding springs are relatively
> >>>unimportant, and that the "melodic springs" are completely
> >>>unimportant. The vertical springs matter the most to Bob. I'm
happy
> >>>living without the melodic springs, but the grounding springs
are
> >>>important for me -- perhaps more important than the vertical
> >>>springs.
>
> [JdL:]
> >>Really?? I must've missed more than I thought I did! Bob, are
you
> >>saying this?
>
> [Paul:]
> >Not directly, but in my view, indirectly.
>
> Bob?

Bob replies:
Well, if my inference above is correct, I would say this assessment
is close. I replied to Paul (or was it Johnny) already in this same
thread that I think of 8:9:10 as a SMOOTH MELODIC MOVE up the
harmonic sequence. It is no more disconcerting to me than the 4:5:6
division of P5 into M3 and m3. I asked if anyone is proposing that we
split the p5 into two equal intervals in the interest of melodic
integrity!!!

I do NOT like pitch drift, however. I think there is a strong
tradition based on a psychoacoustic predisposition in human hearing
toward a stable sense of a pitch center around which we can construct
musical forms for a sense of return and completion.

So the grounding spring (if I'm correct in my understanding of it) is
indeed important to me, perhaps even equally so. This is where what
we have called "fudging" is necessary in the implementation of
"engineering tradeoffs" between vertical purity and drift. Since I
perceive the 8:9:10 sequence as melodically natural, a simple, smooth
climb up the harmonic sequence, I don't see the problems with melodic
integrity that others here seem to. So I would say that my current
understanding indicates my priorities as under:

1) vertical springs and grounding springs
3) horizontal springs

However, one caveat is that to some degree horizontal springs are
implicit automatically, I would imagine, in the tradeoffs between
equally important vertical and grounding springs. (???)

🔗BobWendell@technet-inc.com

🔗John A. deLaubenfels <jdl@adaptune.com>

[Bob wrote:]
>Hi, all! I wasn't previously aware of the "springs" concept. This is
>getting very interesting now! Is it correct to infer that this is a
>concept arising out of software technology that allows us to specify
>parameters controlling what we have been calling "fudging" or
>"engineering tradeoffs" horizontally, vertically, and for longer-term
>"drift resistance"?

I can lay claim to being the author of the "springs" tuning model; I
first reported it

/tuning/topicId_7890.html#7890

I do want to credit many on this list, Paul E more than any one other
person, for critiquing my earlier, pre-spring work, since if not for
that criticism I was pretty content with the earlier methods. Some
on the list, notably John Starrett, prefer the pre-spring treatments,
and there are some examples of it in MIDI format in the files section of
crazy_music, if you're interested.

[Bob:]
>I replied to Paul (or was it Johnny) already in this same
>thread that I think of 8:9:10 as a SMOOTH MELODIC MOVE up the
>harmonic sequence. It is no more disconcerting to me than the 4:5:6
>division of P5 into M3 and m3. I asked if anyone is proposing that we
>split the p5 into two equal intervals in the interest of melodic
>integrity!!!

The logic of this is compelling, but I'm not sure my ear always agrees!
It seems more accepting of variation of jumps of 7:8 and larger than of
7:8 and smaller (with 7:8 an approximate boundary). This might well be
something that would disappear with enough exposure to music with uneven
step sizes, I don't know.

[Bob:]
>I do NOT like pitch drift, however. I think there is a strong
>tradition based on a psychoacoustic predisposition in human hearing
>toward a stable sense of a pitch center around which we can construct
>musical forms for a sense of return and completion.

So you, Paul, and I agree on this point.

>So the grounding spring (if I'm correct in my understanding of it) is
>indeed important to me, perhaps even equally so. This is where what
>we have called "fudging" is necessary in the implementation of
>"engineering tradeoffs" between vertical purity and drift. Since I
>perceive the 8:9:10 sequence as melodically natural, a simple, smooth
>climb up the harmonic sequence, I don't see the problems with melodic
>integrity that others here seem to. So I would say that my current
>understanding indicates my priorities as under:

>1) vertical springs and grounding springs
>3) horizontal springs

>However, one caveat is that to some degree horizontal springs are
>implicit automatically, I would imagine, in the tradeoffs between
>equally important vertical and grounding springs. (???)

You are quite right, and Paul made this point as well. This morning I
tuned Rhapsody in Blue (piano reduction) in 7-limit with negligible
horizontal springs, and was astonished to find that it sounded pretty
good to my ear; the other spring types kept horizontal motion under
fairly reasonable control. I could do up a test sequence, however, that
would not be so nice, I think! For example, G-B-D-F -> G-C-F, with the
common notes tied and 7-limit tuning: the F is pulled low, then pushed
much higher, relative to G, and grounding springs will only slightly
moderate the movement. I'm sure I could find musically plausible
transitions which are much worse; I hit them when improvising using
real-time adaptive tuning (JI Relay, for the PC, available from my web
site).

Bob, you haven't yet said (or I missed it) whether you have General MIDI
capability. Many on this list _hate_ using MIDI for anything, and I can
understand the objections, but it's all I can work with for my tuning
experiments. I can, of course, make MP3's of my work, but getting them
uploaded via my phone line is problematic. MIDI files are nice 'n'
compact, in contrast, since they are instructions rather than actual
sound.

JdL

http://www.adaptune.com

🔗BobWendell@technet-inc.com

Thanks so much for the informative reply, John! Very creative
thinking in coming up with such a concept. I congratulate you and
Paul for his contributions as well.

I only have the ability to listen to midi files that the common
players allow for internet audio, like the Windows Media Player and
RealAudio, etc. I have only a funky Casio 12-ET keyboard with midi
OUTPUT only. All my tuning experience is with physical systems like
harpsichords and pianos, and of course I play the violin (sort of,
now) and the trumpet (similar situation). I mostly sing these days.

My resources are limited and my wife has little appreciation for such
musical predilictions as I express here, so I dream of access to
electronic capabilities that will allow me to experiment freely.
She's not like Haydn's wife, though (chuckle). She does appreciate
and take pride in what I'm doing with the choir.

Warmly,

Bob

P.S All my discussion here is based on my ear, personal practice, and
whatever understanding I have of intonation and intonation systems. I
have never been exposed to the experimental means many of you have
discussed with me.

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Bob wrote:]
> >Hi, all! I wasn't previously aware of the "springs" concept. This
is
> >getting very interesting now! Is it correct to infer that this is
a
> >concept arising out of software technology that allows us to
specify
> >parameters controlling what we have been calling "fudging" or
> >"engineering tradeoffs" horizontally, vertically, and for longer-
term
> >"drift resistance"?
>
> I can lay claim to being the author of the "springs" tuning model;
I
> first reported it
>
> /tuning/topicId_7890.html#7890
>
> I do want to credit many on this list, Paul E more than any one
other
> person, for critiquing my earlier, pre-spring work, since if not for
> that criticism I was pretty content with the earlier methods. Some
> on the list, notably John Starrett, prefer the pre-spring
treatments,
> and there are some examples of it in MIDI format in the files
section of
> crazy_music, if you're interested.
>
> [Bob:]
> >I replied to Paul (or was it Johnny) already in this same
> >thread that I think of 8:9:10 as a SMOOTH MELODIC MOVE up the
> >harmonic sequence. It is no more disconcerting to me than the
4:5:6
> >division of P5 into M3 and m3. I asked if anyone is proposing that
we
> >split the p5 into two equal intervals in the interest of melodic
> >integrity!!!
>
> The logic of this is compelling, but I'm not sure my ear always
agrees!
> It seems more accepting of variation of jumps of 7:8 and larger
than of
> 7:8 and smaller (with 7:8 an approximate boundary). This might
well be
> something that would disappear with enough exposure to music with
uneven
> step sizes, I don't know.
>
> [Bob:]
> >I do NOT like pitch drift, however. I think there is a strong
> >tradition based on a psychoacoustic predisposition in human
hearing
> >toward a stable sense of a pitch center around which we can
construct
> >musical forms for a sense of return and completion.
>
> So you, Paul, and I agree on this point.
>
> >So the grounding spring (if I'm correct in my understanding of it)
is
> >indeed important to me, perhaps even equally so. This is where
what
> >we have called "fudging" is necessary in the implementation of
> >"engineering tradeoffs" between vertical purity and drift. Since I
> >perceive the 8:9:10 sequence as melodically natural, a simple,
smooth
> >climb up the harmonic sequence, I don't see the problems with
melodic
> >integrity that others here seem to. So I would say that my current
> >understanding indicates my priorities as under:
>
> >1) vertical springs and grounding springs
> >3) horizontal springs
>
> >However, one caveat is that to some degree horizontal springs are
> >implicit automatically, I would imagine, in the tradeoffs between
> >equally important vertical and grounding springs. (???)
>
> You are quite right, and Paul made this point as well. This
morning I
> tuned Rhapsody in Blue (piano reduction) in 7-limit with negligible
> horizontal springs, and was astonished to find that it sounded
pretty
> good to my ear; the other spring types kept horizontal motion under
> fairly reasonable control. I could do up a test sequence, however,
that
> would not be so nice, I think! For example, G-B-D-F -> G-C-F, with
the
> common notes tied and 7-limit tuning: the F is pulled low, then
pushed
> much higher, relative to G, and grounding springs will only
slightly
> moderate the movement. I'm sure I could find musically plausible
> transitions which are much worse; I hit them when improvising using
> real-time adaptive tuning (JI Relay, for the PC, available from my
web
> site).
>
> Bob, you haven't yet said (or I missed it) whether you have General
MIDI
> capability. Many on this list _hate_ using MIDI for anything, and
I can
> understand the objections, but it's all I can work with for my
tuning
> experiments. I can, of course, make MP3's of my work, but getting
them
> uploaded via my phone line is problematic. MIDI files are nice 'n'
> compact, in contrast, since they are instructions rather than
actual
> sound.
>
> JdL
>
> http://www.adaptune.com

🔗jpehrson@rcn.com

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Paul:]
> >How about Bach?
>
> It would depend on the piece and the treatment (5 vs. 7 limit,
etc.).
> The Gershwin above is 7-limit, and of course has heavy use of 7th
> chords (dominant and otherwise!), so it's particularly challenging.
> I tend to see RMS melodic deviations of around 5 cents for 5-limit
> treatments of 18th and 19th century music.

Well I was asking specifically about the versions that _you_ liked,
that is, the ones with positive melodic springs, and the ones with
negative melodic springs.
>
> [Paul:]
> >What I'm
> >talking about is the grounding to the COFT. I'm saying, echoing
> >Johnny just a little, that a melodic framework dictated by the
> >harmonic needs of the piece (let's assume only 12 notated notes,
> >since your software doesn't currently accept more) should
determine
> >the melodic norm for the piece, and stuck to somewhat closely. Bob
> >doesn't seem to be as concerned with sticking to a set melodic
> >framework.
>
> I see your point, but typically the grounding springs are weak
enough
> that they do little to influence the tuning of any given note; they
> exert significant influence on a larger scale. The difference
between
> grounding to 12-tET and grounding to COFT is a subtle one.

Not as I recall -- when you first made the change, all the audible
problems disappeared (from the Back)!
>
> Right now I only spring consecutive instances of the same pitch
class.
> Of course two springs in series do indirectly form a (weaker)
spring
> between the outlying notes as well.

Can you give an example??
>
> [JdL:]
> >>For most of my time on this list, you have been most critical of
> >>horizontal motion in my tuning experiments; do I have that well
under
> >>control now?
>
> [Paul:]
> >There was never a problem once you adopted the COFT methodology.
In
> >fact, I wonder what would happen if you now eliminated the
horizontal
> >springs altogether.
>
> I don't think you'd like it! If you pick a piece, I'll do a
comparison.
> How about the Gershwin? That otta sound wild!

How about the Bach?

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Bob had said:
> It didn't matter so much that the intervals were not precisley in
> imitation of the original theme. This is precisely my point. How
much
> more would he be willing to admit microtonal differences within the
> same interval type if the harmony constrains it that way?
>
> Johnny Reinhard commented:
> There is a misunderstanding here. There are no exact imitations in
> Werckmeister. The fact that Bach's music works so well in equal
> temperament is certainly a tribute to Bach, but the world of
nuances
> left out is a paucity. Werckmeister's temperament liberated the
> composer to all the harmonies being usable, for the first time
> published
>
> Bob answers:
> My statement was answering Paul's objection that the difference of
JI
> intervals EVEN IN SOLO VIOLIN PERFORMANCE was unacceptably
> unidiomatic from a melodic perspective. Your point underscores mine
> as I see it. In a microtonally precise sense, there is no exact
> melodic imitation in the first place in Werckmeister's temperament.

The largest major second in Werckmeister is Pythagorean. The smallest
is less than 12 cents narrower. Even in the few keys where these come
in succession in the scale, the effect is much less jagged than a
full comma difference. In fact it doesn't sound jagged at all.
>
> For me, another telling point:
> Many advocates of 12-EDO opposing JI have pointed to the difference
> in the whole steps of JI as a great evil of some kind. I posit that
> it is nothing more in effect than A SMOOTH MOVE from the 9th to the
> 10th harmonic!

This is a great effect in Indian music -- but in Western music the
harmony varies. What if you have a iim7 chord underneath?
>
> This is in principle no different from the division of the perfect
> fifth into a major and minor third (4:5:6). It is analogous
precisely
> as a division of the major third ((8:9:10)! Anyone proposing that
we
> split the perfect fifth into two equal intervals in the interest of
> melodic integrity??

This can be a great effect _melodically_, found in many world musics,
and in Blackwood's 14-tET etude, for example.

🔗Paul Erlich <paul@stretch-music.com>

🔗paul@stretch-music.com

🔗jpehrson@rcn.com

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_27184.html#27347

> --- In tuning@y..., BobWendell@t... wrote:
>
> > > Bob had replied:
> > > Since when has this kind of "standard practice" become a
> criterion
> > > for the value or utility of anything we say here?
> >
> > Paul replied:
> > Perhaps because we shouldn't feel so presumptous about our
ability
> to
> > say what is right and what is wrong regarding the work of
history's
> > master composers that we can simply ignore what is going on in
the
> > world outside this little list.
> >
> > Bob answers:
> > Well, if we're going to take that tack, we've already excluded 90%
+
> > of the musical world outside of this tuning group by the mere
> nature
> > of the content here, so I don't get that. It seems implicitly
> > contradictory.
>
> Huh? Just because we discuss some very specialized subjects doesn't
> mean we should allow our musical philosophies to retreat into an
> obscure, irrelevant corner.

I very much agree with this statement. In fact, I'm toward going in
the *opposite* direction with practical stuff, like the 72-tET
discussions we have been having and tunings that *general* musicians
would be able to handle!

___________ ________ _______
Joseph Pehrson

🔗BobWendell@technet-inc.com

Paul, I have to ask one thing! Why do we keep shifting contexts for
the meaning of what I've said. Meaning is always context-dependent,
as I'm sure you must understand.

In the messages exchanged as seen immediately below, I reiterate to
Johnny that I was referring to your original objection to the
syntonic comma difference between the two whole-steps in JI as
unidiomatic even for a SOLO INSTRUMENT playing Bach (came up in the
context of the Unaccompanied Partitas and Sonatas). Here there is no
question of violating some harmonic structure in the continuo, so why
is that reinserted into this discussion?.

And when I ask:
Anyone proposing that we split the perfect fifth into two equal
intervals in the interest of melodic integrity??

You answer:
> This can be a great effect _melodically_, found in many world
musics,
> and in Blackwood's 14-tET etude, for example.

How far out of context are we going to go with this? If JI whole
steps are unidiomatic in Bach, how do we take the world musics and
Blackwood composition you just mentioned above!!?????

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Bob had said:
> > It didn't matter so much that the intervals were not precisley in
> > imitation of the original theme. This is precisely my point. How
> much
> > more would he be willing to admit microtonal differences within
the
> > same interval type if the harmony constrains it that way?
> >
> > Johnny Reinhard commented:
> > There is a misunderstanding here. There are no exact imitations
in
> > Werckmeister. The fact that Bach's music works so well in equal
> > temperament is certainly a tribute to Bach, but the world of
> nuances
> > left out is a paucity. Werckmeister's temperament liberated the
> > composer to all the harmonies being usable, for the first time
> > published
> >
> > Bob answers:
> > My statement was answering Paul's objection that the difference
of
> JI
> > intervals EVEN IN SOLO VIOLIN PERFORMANCE was unacceptably
> > unidiomatic from a melodic perspective. Your point underscores
mine
> > as I see it. In a microtonally precise sense, there is no exact
> > melodic imitation in the first place in Werckmeister's
temperament.
>
> The largest major second in Werckmeister is Pythagorean. The
smallest
> is less than 12 cents narrower. Even in the few keys where these
come
> in succession in the scale, the effect is much less jagged than a
> full comma difference. In fact it doesn't sound jagged at all.
> >
> > For me, another telling point:
> > Many advocates of 12-EDO opposing JI have pointed to the
difference
> > in the whole steps of JI as a great evil of some kind. I posit
that
> > it is nothing more in effect than A SMOOTH MOVE from the 9th to
the
> > 10th harmonic!
>
> This is a great effect in Indian music -- but in Western music the
> harmony varies. What if you have a iim7 chord underneath?
> >
> > This is in principle no different from the division of the
perfect
> > fifth into a major and minor third (4:5:6). It is analogous
> precisely
> > as a division of the major third ((8:9:10)! Anyone proposing that
> we
> > split the perfect fifth into two equal intervals in the interest
of
> > melodic integrity??
>
> This can be a great effect _melodically_, found in many world
musics,
> and in Blackwood's 14-tET etude, for example.

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_27184.html#27353

> --- In tuning@y..., jpehrson@r... wrote:
>
> >
> > If I'm understanding this at all correctly, in John's system we
> don't
> > *have* to eliminate this unison vector (creating a *meantone* I
> > believe, yes??) but we can, essentially, "ride along" the
vector...
> >
> > Am I getting this right at all??
>
> I'm not sure what you mean. Perhaps we can start by discussing
> Vicentino's second tuning of 1555, which is a much simpler means of
> achieving adaptive JI? You're familiar with this, yes? It's two
> chains of 1/4-comma meantone, tunes 1/4 comma apart. This allows
you
> to make all triads just, which all "pitch shifts" are only 1/4 of a
> comma. So in this case, are we "riding along" the vector (whatever
> you mean by that)?

Hi Paul...

Well, if I'm understanding John's system, it would mean that, in some
cases the D, let's say, is 10/9 and in other cases it's 9/8, yes??
and the program *gradually* changes the D from one position to
another... rather than in a meantone where it's smack in the middle
of the syntonic comma, yes??

So if one were riding *between* the two values for D rather than
halving the distance as in meantone, I would say that is "riding
along" the syntonic comma.

Does that make any sense?

_________ _________ ________
Joseph Pehrson

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Paul, I have to ask one thing! Why do we keep shifting contexts for
> the meaning of what I've said. Meaning is always context-dependent,
> as I'm sure you must understand.
>
> In the messages exchanged as seen immediately below, I reiterate to
> Johnny that I was referring to your original objection to the
> syntonic comma difference between the two whole-steps in JI as
> unidiomatic even for a SOLO INSTRUMENT playing Bach (came up in the
> context of the Unaccompanied Partitas and Sonatas). Here there is
no
> question of violating some harmonic structure in the continuo, so
why
> is that reinserted into this discussion?.

I don't know what you mean. THe following has absolutely nothing to
do with harmonic structure, or continuo:

You wrote,

> > > My statement was answering Paul's objection that the difference
> of
> > JI
> > > intervals EVEN IN SOLO VIOLIN PERFORMANCE was unacceptably
> > > unidiomatic from a melodic perspective. Your point underscores
> mine
> > > as I see it. In a microtonally precise sense, there is no exact
> > > melodic imitation in the first place in Werckmeister's
> temperament.

I wrote,
> >
> > The largest major second in Werckmeister is Pythagorean. The
> smallest
> > is less than 12 cents narrower. Even in the few keys where these
> come
> > in succession in the scale, the effect is much less jagged than a
> > full comma difference. In fact it doesn't sound jagged at all.

The point being, on a purely melodic level, Werckmeister doesn't
create the melodic jaggedness that I sometimes find in melodies which
alternate 9/8 and 10/9 whole steps.

> And when I ask:
> Anyone proposing that we split the perfect fifth into two equal
> intervals in the interest of melodic integrity??
>
> You answer:
> > This can be a great effect _melodically_, found in many world
> musics,
> > and in Blackwood's 14-tET etude, for example.
>
> How far out of context are we going to go with this? If JI whole
> steps are unidiomatic in Bach, how do we take the world musics and
> Blackwood composition you just mentioned above!!?????

The point is that different styles have different aesthetics
concerning melody. Melody isn't always concerned with mimicking a
harmonic series. The level to which it is depends on musical style.
In Indian music, even 8:9:10 is very appropriate, given the
sustaining drone and its overtones and the nature of the melodies. In
many non-harmonic world musics, dividing a perfect fifth into two
audibly equal melodic parts is important for the effect. I'm
suggesting that Western common-practice music falls somewhere in-
between.

🔗BobWendell@technet-inc.com

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_27184.html#27360

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Hi Paul...
> >
> > Well, if I'm understanding John's system, it would mean that, in
> some
> > cases the D, let's say, is 10/9 and in other cases it's 9/8, yes??
>
> It rarely would move by such extreme amounts.
>
> > and the program *gradually* changes the D from one position to
> > another... rather than in a meantone where it's smack in the
middle
> > of the syntonic comma, yes??
> >
> > So if one were riding *between* the two values for D rather than
> > halving the distance as in meantone, I would say that is "riding
> > along" the syntonic comma.
> >
> > Does that make any sense?
>
> Can you map out a musical passage that would demonstrate the kind
of
> movement you're talking about? Putting aside whether John's program
> would ever give it as output?
>
> What you may be missing is that in all _clever_ adaptive tuning
> schemes, the burden of the syntonic comma is never carried by just
> one note (say D) . . . it's _spread out_ over many different notes.

Hmmm... I see what you're saying.

So "adaptive tuning" could be seen as "multi dimensional??"

That means that all of the "unison vectors" are changing
simultaneously, yes??

________ ________ _________
Joseph Pehrson

🔗BobWendell@technet-inc.com

Again, I haven't intentionally implied that we retreat into any
irrelevant corners, but I can tell you that most musicians would
consider the topics we discuss in here as belonging to an irrelevant
corner. On the other hand, no one would like to change that
perception more than I. I'm all for making things as practical and
practicable as possible!

And if I were into elitism of some sort, the choir I founded and
conduct could never exist, since half the members when entering it
were marginal music readers, to be kind, and some still are. Many
came in with all kinds of severe intonation problems. I'm perpetually
dealing with those and have necessarily become rather expert at doing
so after all these years. So I of all people have put to the test the
implementation of precise intonation in a population that by no means
represents an elite.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_27184.html#27347
>
> > --- In tuning@y..., BobWendell@t... wrote:
> >
> > > > Bob had replied:
> > > > Since when has this kind of "standard practice" become a
> > criterion
> > > > for the value or utility of anything we say here?
> > >
> > > Paul replied:
> > > Perhaps because we shouldn't feel so presumptous about our
> ability
> > to
> > > say what is right and what is wrong regarding the work of
> history's
> > > master composers that we can simply ignore what is going on in
> the
> > > world outside this little list.
> > >
> > > Bob answers:
> > > Well, if we're going to take that tack, we've already excluded
90%
> +
> > > of the musical world outside of this tuning group by the mere
> > nature
> > > of the content here, so I don't get that. It seems implicitly
> > > contradictory.
> >
> > Huh? Just because we discuss some very specialized subjects
doesn't
> > mean we should allow our musical philosophies to retreat into an
> > obscure, irrelevant corner.
>
> I very much agree with this statement. In fact, I'm toward going
in
> the *opposite* direction with practical stuff, like the 72-tET
> discussions we have been having and tunings that *general*
musicians
> would be able to handle!
>
> ___________ ________ _______
> Joseph Pehrson

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> See bottom:
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., BobWendell@t... wrote:
> >
> > > So the grounding spring (if I'm correct in my understanding of
it)
> >
> > I don't think you are. The grounding springs make all notes
> gravitate
> > toward a fixed-pitch 12-tone tuning, the COFT (Calculated Optimal
> > Fixed Temperament) for the piece in question.
>
> I think I am. John clearly confirmed that implicitly in his answer.
> Nothing I inferred conflicts in any way with the more technically
> specific explanation you just gave above. Do you skip large chunks
in
> messages before you respond? (See my preceding post in this thread.)

I'm sorry. I read everything. I simply thought you were
misunderstanding because you seemed to be saying, in response to
Johnny, that you didn't feel there was much of a desire to keep
pitches "pinned down" to anything like a fixed-pitch tuning, when
playing Bach on free-pitched instruments. Thus, it didn't sound like
grounding springs would be very important to you. Please tell me why
I was wrong -- I didn't follow your previous explanation, so I
assumed you were misunderstanding this aspect of John's model (I've
certainly misunderstood many aspects of it on many occasions, even
after such a long period of exposure to it).

There are at least four types of springs in John's model, at least
once the COFT has been calculated:

grounding springs
vertical springs
horizontal springs
melodic springs

Am I missing any?

Anyway, Bob, you're clearly an extremely intelligent person, and I
sincerely apologize if you feel I insulted you in any way.
Communication is always tough on this medium. Let's keep trying!

🔗jpehrson@rcn.com

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

Don't worry about communications, Paul. I'm an extremely flexible and
understanding fellow, and although I may get a bit frustrated at
times, I don't let it affect relationships, either short or long-
term. You don't seem to either, and I'm grateful for that.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > See bottom:
> >
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > > --- In tuning@y..., BobWendell@t... wrote:
> > >
> > > > So the grounding spring (if I'm correct in my understanding
of
> it)
> > >
> > > I don't think you are. The grounding springs make all notes
> > gravitate
> > > toward a fixed-pitch 12-tone tuning, the COFT (Calculated
Optimal
> > > Fixed Temperament) for the piece in question.
> >
> > I think I am. John clearly confirmed that implicitly in his
answer.
> > Nothing I inferred conflicts in any way with the more technically
> > specific explanation you just gave above. Do you skip large
chunks
> in
> > messages before you respond? (See my preceding post in this
thread.)
>
> I'm sorry. I read everything. I simply thought you were
> misunderstanding because you seemed to be saying, in response to
> Johnny, that you didn't feel there was much of a desire to keep
> pitches "pinned down" to anything like a fixed-pitch tuning, when
> playing Bach on free-pitched instruments. Thus, it didn't sound
like
> grounding springs would be very important to you. Please tell me
why
> I was wrong -- I didn't follow your previous explanation, so I
> assumed you were misunderstanding this aspect of John's model (I've
> certainly misunderstood many aspects of it on many occasions, even
> after such a long period of exposure to it).
>
> There are at least four types of springs in John's model, at least
> once the COFT has been calculated:
>
> grounding springs
> vertical springs
> horizontal springs
> melodic springs
>
> Am I missing any?
>
> Anyway, Bob, you're clearly an extremely intelligent person, and I
> sincerely apologize if you feel I insulted you in any way.
> Communication is always tough on this medium. Let's keep trying!

🔗John A. deLaubenfels <jdl@adaptune.com>

[Bob wrote:]
>Thanks so much for the informative reply, John! Very creative
>thinking in coming up with such a concept. I congratulate you and
>Paul for his contributions as well.

Thanks much, Bob! I know without any doubt that what I'm doing now
will be very primitive by the time I'm dead or not long after, but I
_do_ think the spring model is a flexible and useful vehicle for
resolving the tradeoffs of adaptive tuning. Somewhat to the bafflement
of my wife, I have elected not to try to build protective fences around
the idea, and encourage everyone to use it in ways I have not foreseen.
Mind you, if it turns out I can get clever enough at this game to make
some money from it, I won't complain! ;->

>I only have the ability to listen to midi files that the common
>players allow for internet audio, like the Windows Media Player and
>RealAudio, etc. I have only a funky Casio 12-ET keyboard with midi
>OUTPUT only. All my tuning experience is with physical systems like
>harpsichords and pianos, and of course I play the violin (sort of,
>now) and the trumpet (similar situation). I mostly sing these days.

So you have a PC with a soundcard capable of playing MIDI files? That
probably means General MIDI compatibility, if your PC was manufactured
in the last five to seven years. How's the piano voice?

>My resources are limited and my wife has little appreciation for such
>musical predilictions as I express here, so I dream of access to
>electronic capabilities that will allow me to experiment freely.
>She's not like Haydn's wife, though (chuckle). She does appreciate
>and take pride in what I'm doing with the choir.

Funny you should mention Haydn; I just read a bio of him this week, w/
a reference to his not-very-nice wife! My own wife, a professional
musician and music teacher, tolerates my work and occasionally
compliments it; other times she asks "How much longer is this?" ;->
Our resources are also limited, and I haven't yet acquired a really good
module for playing the files I tune. But my Roland VSC-88 soft-synth
is not bad, and only about $60 at a discount.

>P.S All my discussion here is based on my ear, personal practice, and
>whatever understanding I have of intonation and intonation systems. I
>have never been exposed to the experimental means many of you have
>discussed with me.

Your background and what you've said about yourself leave me no doubt
that your ear is superior to mine in pitch resolution. I have the
luxury of letting my program tune a file, then let the sound wash over
me (so much easier than singing the correct pitch!). Has anybody asked
what recordings of your group's work may be available?

JdL

🔗jpehrson@rcn.com

🔗BobWendell@technet-inc.com

> Bob had said:>
Agreed! However, I believe the Gothic preference for perfect fifths
> and fourths as consonances evolved naturally toward the newly
> perceived consonance of thirds in the Renaissance because of the
> prominence of a cappella vocal music in the church. >
> The Pythagorean 3-limit tuning was something THEORISTS hung onto
for
> a long time because they were dealing with fixed pitches and
> vocalists were forced to conform. (There was also the symbolism of
> the Trinity in 3-limit). When this constraint was removed for a
> sufficiently significant time and intensity of practice, bang, the
> thirds suddenly shone forth as consonant.

Paul replied:
I think it's the other way around. I think the constraint was removed
in the _theory_, in the early 16th century, because already in
_practice_ for a century or two (depending on geographic locale)
thirds and sixths were being used as consonances.

Bob Answers:
How does this contradict what I've said? I only see that it puts a
broad timing on the phenomenon to which I refer...something I hadn't
bothered to specify. You too imply here that the theory was
responding to practice, which is the essence of my point. And the
practice evolved in a cappella music that allowed human ears to find
their intuitive way harmonically, unshackled by theoretical
constraints.

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

Bob had said:
(In the context of melodic solo performance)
Here there is no question of violating some harmonic structure in the
continuo, so why is that reinserted into this discussion?.
>
Paul replied:
> I don't know what you mean. The following has absolutely nothing to
> do with harmonic structure, or continuo: (etc.)

Bob Answers:
This is what I mean -

Paul said:
This is a great effect in Indian music -- but in Western music the
harmony varies. What if you have a iim7 chord underneath?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Paul, I have to ask one thing! Why do we keep shifting contexts
for
> > the meaning of what I've said. Meaning is always context-
dependent,
> > as I'm sure you must understand.
> >
> > In the messages exchanged as seen immediately below, I reiterate
to
> > Johnny that I was referring to your original objection to the
> > syntonic comma difference between the two whole-steps in JI as
> > unidiomatic even for a SOLO INSTRUMENT playing Bach (came up in
the
> > context of the Unaccompanied Partitas and Sonatas). Here there is
> no
> > question of violating some harmonic structure in the continuo, so
> why
> > is that reinserted into this discussion?.
>
> I don't know what you mean. THe following has absolutely nothing to
> do with harmonic structure, or continuo:
>
> You wrote,
>
> > > > My statement was answering Paul's objection that the
difference
> > of
> > > JI
> > > > intervals EVEN IN SOLO VIOLIN PERFORMANCE was unacceptably
> > > > unidiomatic from a melodic perspective. Your point
underscores
> > mine
> > > > as I see it. In a microtonally precise sense, there is no
exact
> > > > melodic imitation in the first place in Werckmeister's
> > temperament.
>
> I wrote,
> > >
> > > The largest major second in Werckmeister is Pythagorean. The
> > smallest
> > > is less than 12 cents narrower. Even in the few keys where
these
> > come
> > > in succession in the scale, the effect is much less jagged than
a
> > > full comma difference. In fact it doesn't sound jagged at all.
>
> The point being, on a purely melodic level, Werckmeister doesn't
> create the melodic jaggedness that I sometimes find in melodies
which
> alternate 9/8 and 10/9 whole steps.
>
> > And when I ask:
> > Anyone proposing that we split the perfect fifth into two equal
> > intervals in the interest of melodic integrity??
> >
> > You answer:
> > > This can be a great effect _melodically_, found in many world
> > musics,
> > > and in Blackwood's 14-tET etude, for example.
> >
> > How far out of context are we going to go with this? If JI whole
> > steps are unidiomatic in Bach, how do we take the world musics
and
> > Blackwood composition you just mentioned above!!?????
>
> The point is that different styles have different aesthetics
> concerning melody. Melody isn't always concerned with mimicking a
> harmonic series. The level to which it is depends on musical style.
> In Indian music, even 8:9:10 is very appropriate, given the
> sustaining drone and its overtones and the nature of the melodies.
In
> many non-harmonic world musics, dividing a perfect fifth into two
> audibly equal melodic parts is important for the effect. I'm
> suggesting that Western common-practice music falls somewhere in-
> between.

🔗jpehrson@rcn.com

🔗BobWendell@technet-inc.com

Thanks for your encouraging reply, John! Please visit our site at
http:www.cangelic.org

It has streaming audio from our first CD. We've released a second
that is at an even higher level of performance, but I haven't had the
time to get it up on our site yet. If you would like both, I could
ship them personally and avoid the middle-man fee we have to pay our
credit card/fulfillment service.

Gratefully,

Bob

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Bob wrote:]
> >Thanks so much for the informative reply, John! Very creative
> >thinking in coming up with such a concept. I congratulate you and
> >Paul for his contributions as well.
>
> Thanks much, Bob! I know without any doubt that what I'm doing now
> will be very primitive by the time I'm dead or not long after, but I
> _do_ think the spring model is a flexible and useful vehicle for
> resolving the tradeoffs of adaptive tuning. Somewhat to the
bafflement
> of my wife, I have elected not to try to build protective fences
around
> the idea, and encourage everyone to use it in ways I have not
foreseen.
> Mind you, if it turns out I can get clever enough at this game to
make
> some money from it, I won't complain! ;->
>
> >I only have the ability to listen to midi files that the common
> >players allow for internet audio, like the Windows Media Player
and
> >RealAudio, etc. I have only a funky Casio 12-ET keyboard with midi
> >OUTPUT only. All my tuning experience is with physical systems
like
> >harpsichords and pianos, and of course I play the violin (sort of,
> >now) and the trumpet (similar situation). I mostly sing these
days.
>
> So you have a PC with a soundcard capable of playing MIDI files?
That
> probably means General MIDI compatibility, if your PC was
manufactured
> in the last five to seven years. How's the piano voice?
>
> >My resources are limited and my wife has little appreciation for
such
> >musical predilictions as I express here, so I dream of access to
> >electronic capabilities that will allow me to experiment freely.
> >She's not like Haydn's wife, though (chuckle). She does appreciate
> >and take pride in what I'm doing with the choir.
>
> Funny you should mention Haydn; I just read a bio of him this week,
w/
> a reference to his not-very-nice wife! My own wife, a professional
> musician and music teacher, tolerates my work and occasionally
> compliments it; other times she asks "How much longer is this?" ;->
> Our resources are also limited, and I haven't yet acquired a really
good
> module for playing the files I tune. But my Roland VSC-88 soft-
synth
> is not bad, and only about $60 at a discount.
>
> >P.S All my discussion here is based on my ear, personal practice,
and
> >whatever understanding I have of intonation and intonation
systems. I
> >have never been exposed to the experimental means many of you have
> >discussed with me.
>
> Your background and what you've said about yourself leave me no
doubt
> that your ear is superior to mine in pitch resolution. I have the
> luxury of letting my program tune a file, then let the sound wash
over
> me (so much easier than singing the correct pitch!). Has anybody
asked
> what recordings of your group's work may be available?
>
> JdL

🔗Paul Erlich <paul@stretch-music.com>

🔗John Starrett <jstarret@carbon.cudenver.edu>

🔗Afmmjr@aol.com

In a message dated 8/24/01 11:38:26 AM Eastern Daylight Time,
BobWendell@technet-inc.com writes:

> I think I hear Johnny Reinhard saying that Werckmeister ruled, no
> matter what the instrument or performance context, in spite of the
> essential nature and actual historical evolution of temperaments as
> compromises made in the interest of reconciling the physical
> ergonomics of keyboard playing and JI. I personally can't imagine
> that the practical musicians of any era were so academically or
> musically rigid! I return to my earlier statement of opinion that
> this is an academic superimposition of some of our thinking onto
>

Bob, I do understand somewhat where you are coming from. But to break away
from my earlier tradition-fed perspectives, I had to do radical things. I
have been to Germany several times now to discover what the musical culture
at the time of Bach was composed of. Since the wall came down, I have been
able to visit what had been only fabled towns of yore.

Actually, keeping the notes of Werckmeister together is a musical talent, an
it really is like remembering a 12-note blues scale. I had the opportunity
to teach a modern orchestra to play baroque operas in meantone. Only the
horn players had any real difficulty.

Now, while Werckmeister becomes a grid for the mind to measure before
playing, I'm sure there is expressivity above and below the targeted note.
The level of playing was often quite low in Bach's experience, many of which
were students.

Still, there was nothing else! There were no other chromatic tunings. If
one was a chromatic composer -and player- then to deviate from the grid would
be to embellish or cherish, but within the tonal context set up by the
temperament. It is not appropriate, IMO, to compare modern approaches to a
historical approach.

Now, I completely understand that you have not share my experiences, nor
heard what I've heard. This will be my challenge to better report on my
discoveries. I will promise not to fudge my findings. Please listen to Bach
in Werckmeister for a first hand revelation.

Respectfully, Johnny Reinhard

🔗John A. deLaubenfels <jdl@adaptune.com>

[Paul E wrote:]
>>>How about Bach?

[I wrote:]
>>It would depend on the piece and the treatment (5 vs. 7 limit, etc.).
>>The Gershwin above is 7-limit, and of course has heavy use of 7th
>>chords (dominant and otherwise!), so it's particularly challenging.
>>I tend to see RMS melodic deviations of around 5 cents for 5-limit
>>treatments of 18th and 19th century music.

[Paul:]
>Well I was asking specifically about the versions that _you_ liked,
>that is, the ones with positive melodic springs, and the ones with
>negative melodic springs.

I haven't tried melodic springs on the Bach (we're talking about the
Bach/Busoni piece we've tuned so often, I presume?).

[JdL:]
>>I see your point, but typically the grounding springs are weak enough
>>that they do little to influence the tuning of any given note; they
>>exert significant influence on a larger scale. The difference between
>>grounding to 12-tET and grounding to COFT is a subtle one.

[Paul:]
>Not as I recall -- when you first made the change, all the audible
>problems disappeared (from the Back)!

Hmmm... my recollection is that it took awhile after the spring/COFT
model to finally get a version of the Bach that you liked (on that day,
I opened a bottle of champagne! ;-> ). One of the later things was
handling a half-diminished 7th chord (E, G, Bb, D) with a utonal 5-limit
file, to avoid a pythagorean major third at the top (!). Of course, now
we have a tuning-file-free option as well, and for 5-limit, I tend to
use that nowadays (as we've discussed, that high 7th degree in a dom 7th
took me some time to accept).

[JdL:]
>>Right now I only spring consecutive instances of the same pitch class.
>>Of course two springs in series do indirectly form a (weaker) spring
>>between the outlying notes as well.

[Paul:]
>Can you give an example??

If we look at three consecutive instances of the E pitch class, E-E-E, I
put a spring where each "-" is. For the outer two to move relative to
each other, there is an effective spring formed by the two actual
springs, with k2 = 1 / (1/k0 + 1/k1). Yes? Of course, it's not _quite_
the same thing as including a specific spring between the outer two.
The model itself would of course accommodate such additional springs
without difficulty, though with slightly slowed convergence during the
relaxation phase.

[JdL:]
>>>>For most of my time on this list, you have been most critical of
>>>>horizontal motion in my tuning experiments; do I have that well
>>>>under control now?

[Paul:]
>>>There was never a problem once you adopted the COFT methodology. In
>>>fact, I wonder what would happen if you now eliminated the horizontal
>>>springs altogether.

[JdL:]
>>I don't think you'd like it! If you pick a piece, I'll do a
>>comparison. How about the Gershwin? That otta sound wild!

[Paul:]
>How about the Bach?

I've already had to eat my words when I did the Gershwin - I was very
surprised that your prediction came very largely true. I'd be glad to
do a tuning or two on the Bach: please let me know what you'd like:

. 5-limit, I presume; with or without tuning files?

. Any melodic springs?

. Probably semi-soft vertical springs, as usual for piano? Or more
rigid?

. And negligible horizontal springs?

===============================================================

[Paul wrote:]
>There are at least four types of springs in John's model, at least
>once the COFT has been calculated:

>grounding springs
>vertical springs
>horizontal springs
>melodic springs

>Am I missing any?

That's the list as of today. The melodic springs are a new addition, as
you know, and I've not used them all that much so far.

===============================================================

[Joseph Pehrson wrote:]
>>Hmmm... I see what you're saying.

>>So "adaptive tuning" could be seen as "multi dimensional??"

[Paul:]
>Absolutely. John has to construct a spring model in thousands of
>dimensions (right, John)!

Right. Each "node" in the model (a single pitch class over a brief
period of time during which there is no change to the set of notes
sounding) is an independent degree of freedom, which can also be called
a dimension. The "spring matrix" is a 2-D construct, NxN (if N is the
number of nodes). I never form the complete NxN (it would be HUGE),
though; I use a linked list to attach each node to all the other nodes
it's sprung to. Am I saying this clearly?

===============================================================

[Bob wrote:]
>Thanks for your encouraging reply, John! Please visit our site at
>http://www.cangelic.org

Somehow I missed that before. Lovely cover!! Can't wait to hear the
music! (I don't stream for s*** with my horrible connection).

>It has streaming audio from our first CD. We've released a second
>that is at an even higher level of performance, but I haven't had the
>time to get it up on our site yet. If you would like both, I could
>ship them personally and avoid the middle-man fee we have to pay our
>credit card/fulfillment service.

Wow, that sounds great! I'll write you off-list for details.

JdL

🔗jpehrson@rcn.com

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_27184.html#27395

> [Joseph Pehrson wrote:]
> >>Hmmm... I see what you're saying.
>
> >>So "adaptive tuning" could be seen as "multi dimensional??"
>
> [Paul:]
> >Absolutely. John has to construct a spring model in thousands of
> >dimensions (right, John)!
>
> Right. Each "node" in the model (a single pitch class over a brief
> period of time during which there is no change to the set of notes
> sounding) is an independent degree of freedom, which can also be
called
> a dimension. The "spring matrix" is a 2-D construct, NxN (if N is
the
> number of nodes). I never form the complete NxN (it would be HUGE),
> though; I use a linked list to attach each node to all the other
nodes
> it's sprung to. Am I saying this clearly?
>

Well... kind of. I think that at some point in the future, when your
method is down and will no longer "adapt" (bad pun) it might be
great if you were to develop an "adaptive tuning for dummies..."
article.

You know, John, "yo be the man..." on this. I don't think *anybody*
has gone as far in the direction of adaptive tuning as *you* have!

Has there been anybody?? I don't believe so...

_________ ________ _________
Joseph Pehrson

🔗Afmmjr@aol.com

In a message dated 8/25/01 10:37:57 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

> --- In tuning@y..., Afmmjr@a... wrote:
>
> /tuning/topicId_27184.html#27388
>
> I had the opportunity to teach a modern orchestra to play baroque
> operas in meantone. Only the horn players had any real difficulty.
> >
>
> Hi Johnny...
>
> Just out of curiosity... how *does* one teach instrumentalists to
> practically play in 1/4 comma meantone??
>
> Thanks!
>
> ________ _______ _____
> Joseph Pehrson
>

Each instrument receives different attention. Actually, I had meant to write
that I taught an orchestra Werckmeister III as both consultant and
bassoonist. Check the archives for a review by Joe Monzo. Joe?

First the harpsichordist was tuned. Difficult to phrase with confidence at
first in the new tuning? A lot of reaction time in listening hard to the new
sounds, really quite subtle, and yet of increasing interest.

The flutist was Andrew Bolotowsky and the oboist Ron Kozak, virtuoso
microtonalists. They knew how to use a tuning machine and to match cents
figures with specific fingerings and/or particular embouchure matched with
appropriate velocity.

Fingerings are devised using the open tone holes and unusual key combinations
that allow for just about any pitches.

The strings that have performed with the AFMM most are the most comfortable,
which shouldn't seem like a surprise. Once again, it's like learning a
12-note blues scale playing in Werckmeister. Quarter comma meantone is
easier as there are less differences (except in varieties of meantones). I
have often used an alto recorder that has been scotch taped into a particular
tuning as the model for a tuning (for quarter comma and sixth comma
ensembles).

Brass must first be based on the correct fundamental. Horns will have to do
partial shadings of the bell, which are damn hard to remember exactly. Greg
Evans is a master, and a member of the AFMM Board of Directors. Trumpets
need an extra quartertone piston, unless they are John Charles Thomas. Tuba
player Dave Grego plays a quartertone tuba, which allows for so many new
combinations, that any pitch can be gotten.

Hearing in the head accurate to a cent is a valuable tool to playing these
tunings acceptably well. Sure the instrument may not give off the exact
pitch intended. But the pitch must be intended more accurately in the mind
than sometimes elicited, and not the other way around.

Singers seem to be political about the whole thing. They seem to convince
themselves more of what ought to be and shy away from theory, especially if
it is contrary to experience. Throughout history singers were considered
apart from instrumentalists, not real musicians, but singers. I do not want
to encourage this notion, but singers really just want to lock in, to feel
comfortable singing, with as little thinking as possible. But they do it so
well.

Best, Johnny Reinhard

🔗jpehrson@rcn.com

🔗monz <joemonz@yahoo.com>

> From: <Afmmjr@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, August 25, 2001 8:09 PM
> Subject: Re: [tuning] another question for Johnny
>
>
> Each instrument receives different attention. Actually, I had meant to
write
> that I taught an orchestra Werckmeister III as both consultant and
> bassoonist. Check the archives for a review by Joe Monzo. Joe?

I did post this review to the tuning list, but a nicer version
of it was published online by David Beardsley in his _Juxtaposition_
ezine.

There's a link to it on my "List of Works" page, but I just got an
error message when I clicked on it. (Dave: does _Juxtaposition_ have
a new URL that we need to know about?)

A cached copy of it is available from Google at:

http://www.google.com/search?q=cache:77a3uBouE4E:www.virtulink.com/immp/jux/
soho.htm+%2B%22mozart%22+%2B%22nine-year%22&hl=en

(Copy the broken link and paste into a text editor, remove the line break,
and copy and paste the unbroken link into your browser.)

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗David Beardsley <davidbeardsley@biink.com>

🔗Paul Erlich <paul@stretch-music.com>

Historically, isn't it true that the vast majority, if not all,
theorists who devised temperaments, did so with a harmonic rationale,
not a melodic one -- based on the evidence of their writings?

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Paul E wrote:]
> >>>How about Bach?
>
> [I wrote:]
> >>It would depend on the piece and the treatment (5 vs. 7 limit,
etc.).
> >>The Gershwin above is 7-limit, and of course has heavy use of 7th
> >>chords (dominant and otherwise!), so it's particularly
challenging.
> >>I tend to see RMS melodic deviations of around 5 cents for 5-limit
> >>treatments of 18th and 19th century music.
>
> [Paul:]
> >Well I was asking specifically about the versions that _you_
liked,
> >that is, the ones with positive melodic springs, and the ones with
> >negative melodic springs.
>
> I haven't tried melodic springs on the Bach (we're talking about
the
> Bach/Busoni piece we've tuned so often, I presume?).

So which piece _did_ try positive and negative melodic springs on,
where you decided you liked _either_ better than having no melodic
springs at all?
>
> [JdL:]
> >>I see your point, but typically the grounding springs are weak
enough
> >>that they do little to influence the tuning of any given note;
they
> >>exert significant influence on a larger scale. The difference
between
> >>grounding to 12-tET and grounding to COFT is a subtle one.
>
> [Paul:]
> >Not as I recall -- when you first made the change, all the audible
> >problems disappeared (from the Back)!
>
> Hmmm... my recollection is that it took awhile after the
spring/COFT
> model to finally get a version of the Bach that you liked (on that
day,
> I opened a bottle of champagne! ;-> ).

I thought the largest step of progress was made when you replaced 12-
tET with COFT as the "ground".
> I've already had to eat my words when I did the Gershwin - I was
very
> surprised that your prediction came very largely true. I'd be glad
to
> do a tuning or two on the Bach: please let me know what you'd like:
>
> . 5-limit, I presume; with or without tuning files?

without.
>
> . Any melodic springs?

no.
>
> . Probably semi-soft vertical springs, as usual for piano? Or
more
> rigid?

however you did the previous tuning-file-free, melodic-spring-free
version.
>
> . And negligible horizontal springs?

Exactly.

> Right. Each "node" in the model (a single pitch class over a brief
> period of time during which there is no change to the set of notes
> sounding) is an independent degree of freedom, which can also be
called
> a dimension. The "spring matrix" is a 2-D construct, NxN (if N is
the
> number of nodes). I never form the complete NxN (it would be HUGE),
> though; I use a linked list to attach each node to all the other
nodes
> it's sprung to. Am I saying this clearly?

I think it's what's called a "sparse matrix" in Matlab.

🔗Afmmjr@aol.com

In a message dated 8/26/01 5:21:50 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> Historically, isn't it true that the vast majority, if not all,
> theorists who devised temperaments, did so with a harmonic rationale,
> not a melodic one -- based on the evidence of their writings?
>

Isn't the melodic primary? Isn't the suitability of a melody necessary
before harmonizing? Isn't a temperament a setting for both?

Sure, there is always a harmonic element. That relates to the ancient Greek
sense of melody being incipiently harmonic. And there is the harmonic shape
of a melody taught in theory classes.

Different kinds of musicians utilize different aspects of music. Speaking as
a melodist (though the bassoon often harmonizes, I play it as a soloist),
Werckmeister is indeed great for the melodies...and it works harmonically as
well, though perhaps not as much as later theorists would insist upon. It
fully utilizes all the spaces between the Pythagorean and the Just. If
anything, it favors the Pythagorean--the melodic side of the spectrum.

When the music went more harmonic, then we had the classical period. Even
Bach's youngest son, thought of his father as old fashioned when he began to
usher in the new vertical sense of the classical era (reputedly calling his
father "the old wig). The classical era begins with the death of J.S. Bach,
and the master knew it was coming a full 10 years before his death.

Though more and more theorists came out with more harmonically related
temperaments, Werckmeister's Chromatic is especially rewarding for its
melodic components.

Best, Johnny Reinhard

🔗John A. deLaubenfels <jdl@adaptune.com>

[I wrote:]
>>Am I saying this clearly?

[Joseph Pehrson:]
>Well... kind of. I think that at some point in the future, when your
>method is down and will no longer "adapt" (bad pun) it might be
>great if you were to develop an "adaptive tuning for dummies..."
>article.

I think I need help, because my attempts so far seem to confuse even our
resident intellects such as Paul E. Yet, I see everything I do as so
very simple. It's the classic imperative of never letting the
programmer write his own documentation; his perspective is too twisted.

>You know, John, "yo be the man..." on this. I don't think *anybody*
>has gone as far in the direction of adaptive tuning as *you* have!

>Has there been anybody?? I don't believe so...

Thanks, Joe; as far as I know from this list, no one else is doing
"leisure" retuning, with knowledge of the future (i.e. the entire
sequence) in making decisions for the present. Real-time adaptive
tuning is more fun for improvisation, but the decisions made in
overlapping chords result in bad tuning decisions, for which I can
foresee no adequate solution (somebody, please prove me wrong!).
Anyway, my work is extremely primitive in the scheme of things, but it's
very fun to be (seemingly) on the "edge" just for the moment!

JdL

🔗jpehrson@rcn.com

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_27184.html#27438

> [I wrote:]
> >>Am I saying this clearly?
>
> [Joseph Pehrson:]
> >Well... kind of. I think that at some point in the future, when
your
> >method is down and will no longer "adapt" (bad pun) it might be
> >great if you were to develop an "adaptive tuning for dummies..."
> >article.
>
> I think I need help, because my attempts so far seem to confuse
even our resident intellects such as Paul E. Yet, I see everything I
do as so very simple. It's the classic imperative of never letting
the programmer write his own documentation; his perspective is too
twisted.
>
> >You know, John, "yo be the man..." on this. I don't think
*anybody* has gone as far in the direction of adaptive tuning as
*you* have!
>
> >Has there been anybody?? I don't believe so...
>
> Thanks, Joe; as far as I know from this list, no one else is doing
> "leisure" retuning, with knowledge of the future (i.e. the entire
> sequence) in making decisions for the present. Real-time adaptive
> tuning is more fun for improvisation, but the decisions made in
> overlapping chords result in bad tuning decisions, for which I can
> foresee no adequate solution (somebody, please prove me wrong!).
> Anyway, my work is extremely primitive in the scheme of things, but
it's very fun to be (seemingly) on the "edge" just for the moment!
>
> JdL

Well... maybe I'm just in a complementary mood... but I meant, John,
not only on *this* list but ANYPLACE...

I don't believe *anybody* else is doing this kind of "leisure" just
adaptive tuning *anyplace...*

Could *somebody* please correct me about this *anybody* and
*anyplace* if they know differently??

Your point about the documentation, John, is *partially* well taken.
What I suggest is that somewhere down the road, where all of this is
refined adequately, you lay it out step by step in an article...
maybe for "Perspectives" or something.

Drafts of your ideas could be put up on the list for commentary.

It should be readable both to the tuning "wiz bangs" and to a
general, hopefully educated, music enthusiast...

That's a tall order, I know... but if it starts "gradually" the more
advanced stuff can be toward the end...

You know... the same experience as never quite getting through the
end of a math text! :)

________ _________ __________
Joseph Pehrson

🔗John A. deLaubenfels <jdl@adaptune.com>

[I wrote:]
>>I haven't tried melodic springs on the Bach (we're talking about the
>>Bach/Busoni piece we've tuned so often, I presume?).

[Paul E:]
>So which piece _did_ try positive and negative melodic springs on,
>where you decided you liked _either_ better than having no melodic
>springs at all?

The ones on my web site! Chopin & Gershwin. To my ear, the effect was
particularly strong in the Chopin (5-limit).

[JdL:]
>>Hmmm... my recollection is that it took awhile after the spring/COFT
>>model to finally get a version of the Bach that you liked (on that
>>day, I opened a bottle of champagne! ;-> ).

[Paul:]
>I thought the largest step of progress was made when you replaced
>12-tET with COFT as the "ground".

Ok.

I'll do up a Bach/Busoni with: no tuning files, no melodic springs, no
horizontal springs, and the same rather soft vertical springs I've
used before with this piece. May take a day or so.

[JdL:]
>>Right. Each "node" in the model (a single pitch class over a brief
>>period of time during which there is no change to the set of notes
>>sounding) is an independent degree of freedom, which can also be
>>called a dimension. The "spring matrix" is a 2-D construct, NxN (if
>>N is the number of nodes). I never form the complete NxN (it would be
>>HUGE), though; I use a linked list to attach each node to all the
>>other nodes it's sprung to. Am I saying this clearly?

[Paul:]
>I think it's what's called a "sparse matrix" in Matlab.

Kyool.

JdL

🔗BobWendell@technet-inc.com

Thank you very much for your inspiring comments,Joseph. We just met
last night and watched the video from our second concert at
International Choral Festival 2001 in Sopron, Hungary, 44 miles from
Vienna.

The acoustics in that cathedral were fantastic, perfect for our
music, since it evolved in that kind of environment. It was
powerfully inspiring for the choir and we went over the top. My brain
can't seem to retain from one viewing to the next just how well that
went.

My interest in intonation actually comes from my violin background. I
quickly noticed when I first started lessons that the first finger E
on the D string could either be in tune with the G or the A string,
but not both. This was my first exposure to the syntonic comma. My
physics and math background has simply provided the basis for
generating ideas about what to do in terms of choral training with
the understanding of intonation that ensued.

I'm glad you liked the Renaissance stuff. That's what we seem to do
best. The choir really gets into that music more than any other, and
most of them never sang that music before coming to our choir. I
think it is the purest stuff in terms of the adaptive JI approach we
have to intonation, so it's a natural fit for them. It's my favorite
period, too, which I'm sure has a bearing on things. There is good
reason why it is often referred to as the golden age of vocal music.

Thanks again, Joseph!

Sincerely,

Bob

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> /tuning/topicId_27184.html#27378
>
> Congratulations, Bob, on your interesting website and accomplished
> choir:
>
> http://www.cangelic.org/
>
> It's nice you got the audio excerpts from your CD to stream
> so "easily." Some people around here are having trouble with
that.
> I believe it requires a two-computer set up with a
> dedicated "server..."
>
> Anyway, I particularly liked the Victoria and Palestrina selections
> which was no surprise, since that is the period in which I am most
> interested.
>
> It was also engrossing to see your discussion of tuning and
> intonation... even just intonation... as it related to your concept
> of the choir. Much of this interest seems to stem from your
> background in math and physics...
>
> Congrats again!
>
> ________ ________ ______
> Joseph Pehrson

🔗BobWendell@technet-inc.com

Hi, Paul! That's precisely the point I've been trying to make all
this time. Thank you! I'm not advocating the abandonment of melodic
considerations, but considering that all our western scales have
been constructed on the basis of harmonic relationships, western
melodic relationships, in my view, should never veer too far away
from harmonic relationships.

The shift in melodic relationships with key in Werckmeisters'
temperament do not occur in the absence of shifts in harmonic
relationships. It is indeed the latter than generate the former. So I
think sometimes we lose sight of first principles if we're not
careful.

I believe that rational harmonic relationships are the first
principle in harmonic music, and that all "fudging" ( meaning
purposeful departures from pure rational harmonies), whether dynamic
as in adaptive JI, fixed as in keyboard temperaments, or motivated by
melodic considerations, should always remain anchored to this first
principle of pitch organization.

Cheers,

Bob

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., Afmmjr@a... wrote:
> > In a message dated 8/24/01 11:38:26 AM Eastern Daylight Time,
> > BobWendell@t... writes:
> >
> >
> > > I think I hear Johnny Reinhard saying that Werckmeister ruled,
no
> > > matter what the instrument or performance context, in spite of
> the
> > > essential nature and actual historical evolution of
temperaments
> as
> > > compromises made in the interest of reconciling the physical
> > > ergonomics of keyboard playing and JI. I personally can't
imagine
> > > that the practical musicians of any era were so academically or
> > > musically rigid! I return to my earlier statement of opinion
that
> > > this is an academic superimposition of some of our thinking
onto
> > >
> >
> > Bob, I do understand somewhat where you are coming from. But to
> break away
> > from my earlier tradition-fed perspectives, I had to do radical
> things. I
> > have been to Germany several times now to discover what the
musical
> culture
> > at the time of Bach was composed of. Since the wall came down, I
> have been
> > able to visit what had been only fabled towns of yore.
> >
> > Actually, keeping the notes of Werckmeister together is a musical
> talent, an
> > it really is like remembering a 12-note blues scale.
>
> Historically, isn't it true that the vast majority, if not all,
> theorists who devised temperaments, did so with a harmonic
rationale,
> not a melodic one -- based on the evidence of their writings?

🔗BobWendell@technet-inc.com

Thank you so much, Johnny, for all your input in this thread. You are
right, of course. With regard to "Please listen to Bach
in Werckmeister for a first hand revelation", I would like to know
what I can do to comply with this request.

Sincerely,

Bob

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 8/24/01 11:38:26 AM Eastern Daylight Time,
> BobWendell@t... writes:
>
>
> > I think I hear Johnny Reinhard saying that Werckmeister ruled, no
> > matter what the instrument or performance context, in spite of
the
> > essential nature and actual historical evolution of temperaments
as
> > compromises made in the interest of reconciling the physical
> > ergonomics of keyboard playing and JI. I personally can't imagine
> > that the practical musicians of any era were so academically or
> > musically rigid! I return to my earlier statement of opinion that
> > this is an academic superimposition of some of our thinking onto
> >
>
> Bob, I do understand somewhat where you are coming from. But to
break away
> from my earlier tradition-fed perspectives, I had to do radical
things. I
> have been to Germany several times now to discover what the musical
culture
> at the time of Bach was composed of. Since the wall came down, I
have been
> able to visit what had been only fabled towns of yore.
>
> Actually, keeping the notes of Werckmeister together is a musical
talent, an
> it really is like remembering a 12-note blues scale. I had the
opportunity
> to teach a modern orchestra to play baroque operas in meantone.
Only the
> horn players had any real difficulty.
>
> Now, while Werckmeister becomes a grid for the mind to measure
before
> playing, I'm sure there is expressivity above and below the
targeted note.
> The level of playing was often quite low in Bach's experience, many
of which
> were students.
>
> Still, there was nothing else! There were no other chromatic
tunings. If
> one was a chromatic composer -and player- then to deviate from the
grid would
> be to embellish or cherish, but within the tonal context set up by
the
> temperament. It is not appropriate, IMO, to compare modern
approaches to a
> historical approach.
>
> Now, I completely understand that you have not share my
experiences, nor
> heard what I've heard. This will be my challenge to better report
on my
> discoveries. I will promise not to fudge my findings. Please
listen to Bach
> in Werckmeister for a first hand revelation.
>
> Respectfully, Johnny Reinhard

🔗BobWendell@technet-inc.com

Hi, Johnny. See my post #27456. It was not a direct reply to this,
which I hadn't read yet, but it goes right to the heart of the issues
you bring up here. - Bob

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 8/26/01 5:21:50 PM Eastern Daylight Time,
> paul@s... writes:
>
>
> > Historically, isn't it true that the vast majority, if not all,
> > theorists who devised temperaments, did so with a harmonic
rationale,
> > not a melodic one -- based on the evidence of their writings?
> >
>
> Isn't the melodic primary? Isn't the suitability of a melody
necessary
> before harmonizing? Isn't a temperament a setting for both?
>
> Sure, there is always a harmonic element. That relates to the
ancient Greek
> sense of melody being incipiently harmonic. And there is the
harmonic shape
> of a melody taught in theory classes.
>
> Different kinds of musicians utilize different aspects of music.
Speaking as
> a melodist (though the bassoon often harmonizes, I play it as a
soloist),
> Werckmeister is indeed great for the melodies...and it works
harmonically as
> well, though perhaps not as much as later theorists would insist
upon. It
> fully utilizes all the spaces between the Pythagorean and the
Just. If
> anything, it favors the Pythagorean--the melodic side of the
spectrum.
>
> When the music went more harmonic, then we had the classical
period. Even
> Bach's youngest son, thought of his father as old fashioned when he
began to
> usher in the new vertical sense of the classical era (reputedly
calling his
> father "the old wig). The classical era begins with the death of
J.S. Bach,
> and the master knew it was coming a full 10 years before his death.
>
> Though more and more theorists came out with more harmonically
related
> temperaments, Werckmeister's Chromatic is especially rewarding for
its
> melodic components.
>
> Best, Johnny Reinhard

🔗Paul Erlich <paul@stretch-music.com>

Yes.

> Isn't the suitability of a melody necessary
> before harmonizing?

Yes.

> Isn't a temperament a setting for both?

I'm suggesting that perhaps, within the range of variation of 12-tone
well-temperaments, there was no important melodic difference between
them, so the operative consideration were the harmonic ones.

>Speaking as
> a melodist (though the bassoon often harmonizes, I play it as a
soloist),
> Werckmeister is indeed great for the melodies...and it works
harmonically as
> well, though perhaps not as much as later theorists would insist
upon. It
> fully utilizes all the spaces between the Pythagorean and the
Just. If
> anything, it favors the Pythagorean--the melodic side of the
spectrum.

Is there any 12-tone well-temperament that does _not_ favor
Pythagorean?

🔗jpehrson@rcn.com

🔗Afmmjr@aol.com

After seeming to agree with my points, Paul opined:

> I'm suggesting that perhaps, within the range of variation of 12-tone
> well-temperaments, there was no important melodic difference between
> them, so the operative consideration were the harmonic ones.

And I am disagreeing. You see, I find more variation in Werckmeister's
chromatic than in any other well-temperament. It is the ur-wohltermeratur.
It RETAINS important melodic difference between keys. It is the steady
gradation of key morphing that distinguishes it.

> Is there any 12-tone well-temperament that does _not_ favor
> Pythagorean?
>
No, which says a lot for the importance of melody over harmony, at least
where Werckmeister is concerned. Of course, the placement of all those
melodies is harmony, and chord harmony is really quite basic. It was so
BASIC that keyboard players were expected to make up the chords out of their
heads extemporaneously...even Bach! The chords made it possible to play in
all the keys. But if you knew the chord possibilities for major and minor,
then 1 key was like another to Bach. Later generations heard the differences
between the keys and their affectations, but it hadn't happened by Bach. You
see Bach didn't modulate between keys, he explored all the relationships in a
tonal way he could. A modulation was from one chord to another chord. But
the melodies were more different than the harmonies (which rarely settled).

This is all about perspective.

Johnny